Discussion QA 9to17

Sales and operations planning: Planning supply and demand in a supply chain

CHAPTER NINE:

4. Discuss how you would set up a collaboration mechanism for the enterprises in a supply chain.

1. What are some obstacles to creating a flexible workforce? What are the benefits? A flexible worktorce possesses the ability to learn new tasks or switch tasks without significantly disrupting production, to expand (or contract) capacity via over or idle time, hiring and firing of seasonal workers, or subcontracting, and to work different schedules. A number of factors influence a producer's ability to realize a flexible workforce: restrictive labor agreements and work rules, a tight labor market, the education level, culture, or organizational culture ofthe work force, the complexity ofthe tasks, the proprietary nature of the production process, and restrictions imposed by other members of the supply chain. A flexible workforce opens the supply chain up to a wider range of alternatives when trying to match supply with demand. If subcontracting or temporary workers can be deployed, then a firm can function at a steady base rate and use the subs to buffer periods of high demand. 2. Discuss why subcontractors can often offer products and services to a company more cheaply than if the company produced them themselves? The subcontractor can offer services more cheaply for a number of reasons. In many cases, the subcontractor is a specialist in the area and is more flexible, hence cheaper. If a subcontractor is performing similar work for a number of clients, they can take advantage of the zero-sum nature of business competition. By aggregating orders from a number of clients, the subcontractor is able to satisfy peaks in demand from some of their clients because other standard clients will be experiencing valleys in demand. If subcontracting occurs because a [lfm is at capacity, the subcontractor (that is not overcapacity) can handle the production more cheaply simply because is expensive to operate a system at excess capacity. 3. In what industries would you tend to see dual facility types (some facilities focusing on only one type of product and others able to produce a wide variety)? In what industries would this be relatively rare? Why? Any industry where a lucrative product requires both unique labor skills and production facilities is a prime candidate for a dual facility operation. The healthcare industry is one example of a dual facility type; many large hospital chains have focused operations for trauma, heart, ob/gyn, and other specialties. Other industries with dual facility types include the legal profession, hospitality, construction, and many others. Industries where dual facility types are rare include tobacco products, alcoholic beverages, sawmills, and chemicals. The dividing point among these industries is the continuous flow nature of the non-dual producers. Ifprocessing requirements dictate that the product stream must visit the same steps of a process in the same sequence, then the higher volume and low process flexibility combination results in dedicated production facilities that simply can't have a broad product range.

Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall

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Collaboration mechanisms in a supply chain should begin with the initial partnering process as the supply chain is being established. All parties in the chain must be aligned and dedicated to the success ofthe entire chain. Trust and open communication are of primary importance; there should be a myriad of formal and informal communication channels open among all parties. If constancy of purpose is ever in question, each [lfm might devote some resources towards equitable "chain incentives" such that behaviors that benefit the entire supply chain are recognized and rewarded. The incentives, communication, and trust should be established at all levels of every chain member. Company leadership should provide for highly visible evidence ofthese activities on their level and among cross-business supply chain teams. 5. What are some product lines that use common parts across many products? What are the advantages of doing this? There are many producers, both manufacturing and service, that use common parts across many products. Some ofthese product lines include the food industry, construction, furniture, soap, plastics, perfumes, computer and office equipment, automotive, motorcycles, bicycles, airframe, and most back-office operations in the service industries. The use of common parts (and services) lowers costs and enables producers to meet variability in demand. Part commonality absorbs variability in dis aggregated demand from period to period since the aggregated demand is inherently less variable. The common parts may be produced or acquired at a more constant rate and stocked at a lower inventory level while maintaining a higher customer service level. 6. Discuss how a company can get marketing and operations to work together with the common goal of coordinating su pply and demand to maximize profitability. l\1arketing and operations often [md themselves at cross purposes; as the authors note, marketing often has incentives based on revenue, whereas operations has incentives based on cost. The cachet of new products, service gnarantees, co-promotions, and other marketing vehicles is quite often lost on members of the organization that must fulfill promises made by their ti"iends in marketing. As with all collaborations, open communication is a must on a nearconstant basis. Regnlar planning meetings must include full cross-functional participation and critical information must be shared as sales and operations occur. Having common performance measures is another way to get these two groups to work together for the common good of the company. Holding both groups responsible for Customer service, accuracy, on time delivery and quality and rewarding them jointly for achieving these goals will greatly increase their willingness to work together.


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7. How can a firm use pricing to change demand patterns?

2. What is the impact oflack of coordination on the performance of a supply chain?

A change in price, one of marketing's Four P's, will change demand assuming that there is some elasticity in demand. A firm can shift demand from a popular product or time to a less-popular product or what is traditionally an off-peak demand period by lowering prices. A firm can collect data on the impact of price changes on demand and use the correlation as an input into supply chain aggregate planning. In the absence of such coordination, it is virtually guaranteed that supply chain partners will face demand levels they had not anticipated and will be unable to satisfy. The increase in demand results from a combination of a) market growth, b) stealing share, and c) forward buying. The first two increase demand for the product and the third robs sales from the future.

The impact of lack of coordination is degradation of responsiveness and poor cost performance for all supply chain members. As the bullwhip effect rears its ugly head, supply chain partners fmd themselves with excessive inventory followed by stockouts and backorders. The fluctuations in inventory result in increased holding costs and lost sales, which in turn spike transportation and material handling costs. Ultimately, the struggle with cost and responsiveness hurts the relationships among supply chain partners as they seek to explain their lack of performance. 3. In what way can improper incentives lead to a lack of coordination in a supply chain? What countermeasures can be used to offset this effect?

8. Why would a firm want to offer pricing promotions in its peak-demand periods? If we assume that a pricing promotion serves to increase demand, then there are a couple of reasons a firm may offer pricing promotions during peak demand periods. Even at peak demand, the firm may have excess capacity and could meet this demand. The nature of the product and supply chain may be such that a promotion today results in an order that both the supply chain and customer recognize will be filled in the future, perhaps during an anticipated low demand period. If a flfm produces a product that is at the end of its life cycle, there may be incentive to exhaust accumulated materials and labor skills that are dedicated to its production. Finally, a flfm may be practicing a form of predatory pricing if it senses that a competitor, teetering on the brink of extinction, is starved for sales.

Incentive obstacles occur in situations when different participants in the supply chain are motivated by self interest. Incentives that focus only on the local impact of an action result in decisions being made that achieve a local optimum but can avoid a global (supply chain) optimum. All supply chain partners must agree on global performance measures and structure rewards such that members are appropriately motivated. Sales force incentives also are responsible for counterproductive supply chain behavior. Commissions that are based on a single short time frame can be gamed by the sales force to maximize commission but these actions inadvertently increase demand variability and exert pressure on the supply chain. Commissions should be structured to provide incentives to consistently sell large volumes of product over a broad time ±rame to the sell-through point.

9. Why would a firm want to offer pricing promotions during its low-demand periods? Pricing promotions during low-demand periods should serve to increase demand and sales. The increase in demand results from a combination of the fo llowing three factors: l\1arket growth - sales may be realized from customers that were not considering this product at the higher price. Stealing share - sales may be realized ±rom customers that were considering a competitors product. Forward buying - sales may be stolen from the future by customers that feel that price may rise in the future.

CHAPTER TEN:

Coordination in a supply chain

1. What is the bullwhip effect and how does it relate to lack of coordination in a supply chain? The bullwhip effect refers to the fluctuation in orders along the length of the supply chain as orders move from retailers to wholesalers to manufacturers to suppliers. The bullwhip effect relates directly to the lack of coordination (demand information flows) within the supply chain. Each supply chain member has a different idea of what demand is, and the demand estimates are grossly distorted and exaggerated as the supply chain partner is distanced from the customer.


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4. What problems result if each stage of a supply chain views its demand as the orders placed by the downstream stage? How should firms within a supply chain communicate to facilitate coordination? If each stage of a supply chain views its demand as the orders placed by their downstream counterpart, the bullwhip effect is realized by the supply chain. Each member develops a forecast that is based on something other than the true customer demand and hilarity ensues. Supply chain members should share point-of-sale (PaS) data so that all members are aware of the true customer demand for product. The beauty of data sharing requirements is that only aggregate pas data must be shared to mitigate the bullwhip effect; there is no need to share detailed pas data. 5. What factors lead to a batching of orders within a supply chain? How does this affect coordination? What actions can minimize large batches and improve coordination? Order batching is caused by a number of different factors. One mechanism is the price structure of TL and LTL shipment quantities; there is incentive to wait a while to make sure that a TL shipment is achieved. A customer's natural tendency to wait for a milestone, either real or perceived, can also cause batching. Customers may wait until Friday, Monday, the last or flfst day of the month, etc., just because that's when they always have or because that event reminds them to order. Order batching also occurs because customers are aware of an impending price


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reduction and want to take advantage of it. Batching adversely affects supply chain coordination because the supply chain will be starved for flow, then overwhelmed with demand. A supply chain can reconfigure their transportation and distribution system to allow for shipments to multiple customers on a single truck to achieve TL quantities. The chain can also assign (or encourage) days for placing orders and move from lot-size based to volume based quantity discounts (or abandon discounts and promotions altogether). 6. How do trade promotions and price fluctuations affect coordination in a supply chain? What pricing and promotion policies can facilitate coordination? Trade promotions and price fluctuations make supply chain coordination more difficult. Customers seek to purchase goods for less and engage in forward buying which creates spikes in demand that may exceed capacity. All parties would benefit ifthe supply chain used every day low pricing (EDLP) to mitigate forward buying and allow procurement, production, and logistics to function at a steadier pace. If price incentives must be offered, the chain is better served by implementing a volume-based quantity discount plan instead of a lot size based quantity discount, i.e., providing incentives to purchase large quantities over a long period of time, perhaps a year. 7. How is the building of strategic partnerships and trust valuable within a supply chain? Cooperation and trust within the supply chain help improve performance for the following reasons:

When stages trust each other, they are more likely to take the other party's objectives into consideration when making decisions, thereby facilitating win-win situations. Action-oriented managerial levers to achieve coordination become easier to implement and the supply chain becomes more agile. An increase in supply chain productivity results, either by elimination of duplicated effort or by allocating effort to the appropriate stage. Detailed sales and production information is shared; this allows the supply chain to coordinate production and distribution decisions. 8. What are the different CPFR scenarios and how do they benefit supply chain partners? Collaborative planning, forecasting, and replenishment (CPFR) is defmed as a business practice that combines the intelligence of multiple partners in the planning and fultillment of customer demand. In order to be successful, the two parties must have synchronized their data and established standards for exchanging the information. The four scenarios that sellers and buyers can collaborate along include: Retail event collaboration - the identification of specific SKUs that will be involved in sales promotions and sharing of information regarding the timing, duration, pricing, advertising, and display tactics to be deployed. The benefit of retail event collaborations is a reduction in stockouts, excess inventory and unplanned logistics costs. DC replenishment collaboration - the forecasting of DC withdrawals or demand from the DC to the manufacturer is converted to a stream of orders that are locked in over a


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specified time horizon. A successful DC replenishment collaboration reduces production costs at the manufacturer and inventory and stockouts at the retailer. Store replenishment collaboration - the forecasting of store-level orders that are committed over a specific time horizon. Such a collaboration results in greater visibility of sales for the manufacturer, improved replenishment accuracy and product availability, and reduced inventories. Collaborative assortment planning - the forecasting (collaborative interpretation) of industry trends, macroeconomic factors, and customer tastes for seasonal goods. This forecast is converted into a planned purchase order at the style/color/size level that is used to produce sample products for a fashion event before fmal merchandising decisions are made. The manufacturer benefits from this co llaboration by having more lead time to purchase raw materials and plan capacity.

CHAPTER ELEVEN:

Managing economies of scale in the supply chain: Cycle inventory

1. Consider a supermarket deciding on the size of its replenishment order from Proctor & Gamble. What costs should it take into account when making this decision? The main cost categories for the supermarket's inventory policy are material costs, ordering costs, and holding costs. Material cost is the money paid to Proctor and Gamble for the goods themselves. Ordering costs, also called procurement costs, are incurred by requesting the goods from the supplier and are fixed in the sense that they do not vary with the size of the order. Examples of such fixed costs are the labor required to place the order, handle the resultant paperwork and the transportation fee to ship the order. The holding cost is the cost to carry one unit in inventory for a specified period of time, usually one year. This cost is variable and includes the cost of capital and all of the costs associated with physically storing inventory shrinkage, spoilage or obsolescence, insurance, the cost of capital, the cost of the warehouse space, etc.

2. Discuss how various costs for the supermarket change as it decreases the lot size ordered from Proctor & Gamble. As the lot size ordered from the supplier decreases, the holding cost (variable with respect to lot size) decreases. As the lot size decreases, the ordering cost remains the same, but the annual ordering cost will rise since the total number of orders each year must increase. As the lot size decreases, the cost of the materials will drop on a per-order basis but will stay the same on an annual basis since total annual demand hasn't changed. The exception to this occurs if the supplier has a price hreak for an order size above a certain threshold; in this case the cost of the goods might increase if the reduced order size is not sufficient to trigger a substantial per unit discount.

3. As demand at the supermarket chain grows, how would you expect the cycle inventory measured in days of inventory to change? Explain.


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As the demand at the supermarket chain grows, we would expect the cycle inventory as measured in days of inventory to also increase, although the increase in cycle inventory is only 40% of the increase in demand. This is because the relationship between the optimal lot size Q'

and the annual demand D is Q' =

~2DS . Since D is under the radical, its doubling to 2D does he

not translate to a jump from a Q' to a 2Q' order; it translates to a jump from a Q' to a 1.4Q' order. 4. The manager at the supermarket in Question 1 wants to decrease the lot size without increasing the costs he incurs. What actions can he take to achieve his objective? One action would be to simply decrease the lot size and let the robust nature of the EOQ model work its magic. The total cost curve on either side of the optimal order quantity, the Q', is relatively flat, so movements in either direction have little impact on total annual procurement and carrying costs. If greater cuts in lot size are desired, the manager can aggregate multiple products in a single order. Recall that the EOQ model is based on a one-product-at-a-time assumption; if multiple products are aggregated, then the fIxed procurement cost is spread over all of the items and dramatic lot size reductions are possible. If the same products are being ordered by another supermarket in the same chain (or at least by stores that are willing to cooperate) the combined orders can be delivered by a single truck making multiple stops, thereby reducing transportation expense. Other techniques that should be deployed when aggregating across product lines include advanced shipping notices and RFID tags that will make inventory tracking and warehouse management simpler. 5. Discuss why supply chain profits may be hurt by a retailer making lot sizing decisions with the sole objective of minimizing its own costs. What advantage would result if the entire supply chain could coordinate this decision? A supply chain is coordinated if the decisions the retailer and supplier make maximize total supply chain profIts. In reality, each stage of a supply chain is likely to make lot-sizing decisions with an objective of minimizing its own overall costs. The result of this independent decision making can be a lack of coordination in a supply chain because actions that maximize retailer profits may not maximize supply chain profits. This decision has an effect on overall supply chain costs including inventory holding costs, production costs, transportation costs, ordering costs, and warehousing costs. 6. When are quantity discounts justified in a supply chain? Quantity discounts are justified in a supply chain as long as they are the fruits of a coordinated supply chain and maximize total supply chain profIts. For commodity products for which price is set by the market, manufacturers with large fIxed costs per lot can use lot size-based quantity discounts to maximize total supply chain profIts.

Lot size discounts are based on the quantity purchased per lot, not the rate of purchase. Lot sizebased discounts tend to raise cycle inventory in the supply chain by encouraging retailers to increase the size of each lot. Lot size-based discounts make sense only when the manufacturer incurs a very high fIxed cost per order. For commodity products for which price is set by the market, manufacturers with large fixed costs per lot can use lot size-based quantity discounts to maximize total supply chain profits. Volume discounts are based on the rate of purchase or volume purchased per specified time period. Volume-based discounts are compatible with small lots that reduce the cycle inventory. If the manufacturer does not incur a very high fIxed cost per order, it is better for the supply chain to have volume-based discounts. For products for which a firm has market power, volume-based discounts can be used to achieve coordination in the supply chain and maximize supply chain profIts. 8. Why do manufacturers such as Kraft and Sara Lee offer trade promotions? What impact do trade promotions have on the supply chain? How should trade promotions be structured to maximize their impact while minimizing the additional cost they impose on the supply chain? l\1anufacturers use trade promotions to offer a discounted price and a time period over which the discount is effective. The goal of manufacturers such as Kraft and Sara Lee is to influence retailers to act in a way that helps the manufacturer achieve its objectives. These objectives may include increased sales, a shifting of inventory from manufacturer to retailer, and defense against the competition. Trade promotions may cause a retailer to pass through some or all of the promotion to customers to spur sales, which increases sales for the entire supply chain. What happens more frequently in practice is that retailers may choose to pass through very little of the promotion to customers, purchase in greater quantities, and hold this cheaper inventory in greater quantities. This action increases both cycle inventory and flow times within the supply chain. Trade promotions should be structured such that a retailer's optimal response benefits the entire supply chain, i.e., retailers limit their forward buying and pass along more of the discount to end customers. If the manufacturer has accumulated excessive inventory, then a trade promotion may provide sufficient incentive to the buyer to forward buy, thus drawing inventories down to an appropriate level. The manufacturer may be able to smooth demand by shiftmg It to a penod of anticipated low demand with a trade promotion. Research has shown that trade promotions by the manufacturer are efiective for products with high deal elasticity that ensures high pass-through (passing the discount on to the consumer) and high holding costs that ensure low forward buying, paper goods being the poster child for this combination. Trade promotions are also more effective with strong brands relative to weak hrands and may make sense as a competitive response. 9. Why is it appropriate to include only the incremental cost when estimating the holding and order cost for a firm?

7. What is the difference between lot size-based and volume-based quantity discounts? Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall

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The cycle inventory models discussed in the chapter are robust; thus incremental (variable) costs per lot size are more important than costs that are fIxed with respect to lot size. The labor component of procurement or setup costs may be salaried; therefore changes in lot size do not impact this component.

CHAPTER TWELVE:

Managing uncertainty in the supply chain: Safety inventory

1. What is the role of safety inventory in the supply chain? Safety inventory is inventory carried to satisfy demand that exceeds the amount forecasted for a given period. As such, it tends to have a negative impact on supply chain cost but a positive impact on supply chain responsiveness. Safety inventory is carried because product demand and lead time are uncertain and a product shortage may result if actual demand during lead time exceeds the forecast amount. 2. Explain how a reduction in lead time can help a supply chain reduce safety inventory without hurting product availability. A reduction in lead time reduces supply chain safety inventory according to equations 11.2 through 11.4. The reorder point is driven by the demand during lead time, the standard deviation of demand during lead time, and the customer service level, the latter two combining to form the safety stock. If lead time falls, the standard deviation of demand during lead time also falls, resulting in less safety stock. Taking an intuitive (and extreme) approach, if lead time approached zero there would be no need for safety (or any) stock since customer orders could be fIlled instantaneously. 3. What are the pros and cons of the various measures of product availability? The common measures of product availability discussed in this chapter are product fIll rate, order fIll rate, and cycle service level (CSL). Product fill rate is the fraction of product demand that is satisfIed from product in inventory and should be measured over specified amounts of demand rather than time. Fill rate provides an accurate picture of the number of customers that receive their single-product orders. Order fill rate is the fraction of orders that are fIlled from available inventory and should be measured over a specifIed number of orders rather than time. In the multiproduct case, poor performance on one item can doom the order fIll rate to an extremely low score while the other products would have achieved very high fIll rates. Cycle service level is the fraction of replenishment cycles that end with all the customer demand being met. Cycle service levels tend to be lower than the other two metrics; a fIrm could maintain a cycle service level of 0% but have a 99% product fIll rate. 4. Describe the two types of ordering policies and the im pact that each of them has on safety inventory.


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The two types of ordering policies discussed in the text are continuous review and periodic review. Continuous review requires that inventory levels be monitored constantly with an order for a lot size ofQ placed when the inventory level drops as low as the reorder point. Since the level of inventory is known continuously, the level of safety inventory can be low; an order will be placed the minute the reorder point is reached. Periodic review requires less vigilance; tlie inventory level is measured at regular time intervals and an order is placed to raise tlie inventory level to a specified thresliold. Under tliis system the level of inventory is known once a period and merely estimated until the next count. More safety inventory must be carried under a periodic review system to guard against a surge in demand. 5. What is the impact of supply uncertainty on safety inventory? The required safety inventory increases with an increase in the standard deviation of periodic demand. The standard deviation of periodic demand is a function of the variance in the lead time and the variance in the demand. Anything that causes supply to be more deterministic will minimize the need for safety inventory. 6. Why can a Horne Depot with a few large stores provide a higher level of product availability with lower inventories than a hardware store chain such as Tru-Value, with many small stores? Horne Depot benefIts from substitution and from aggregation. Many of the products Horne Depot carries are not aggressively branded in the eyes of the do-it-yourselfer. This class of customers wants to perform a simple horne repair or improvement and is less concerned about a specific manufacturer than about getting all the supplies in one trip (although I should note that in my experience there is no such thing as a single trip to Horne Depot for any project). Horne Depot also benefIts from aggregation; the large box store draws customers from a wider area and what one part of the customer base doesn't need this month, the other part does. The highs and lows tend to cancel, thus stabilizing demand within each season. 7. Why is Amazon able to provide a large variety of books and music with less safety inventory than a bookstore chain selling through retail stores? Amazon is able to provide a large variety of books and music with less safety inventory through the power of aggregation. By holding best-selling items in geographically dispersed warehouses, Amazon can hold less inventory and still meet customer demand. Equations 11.12 through 11.16 illustrate the savings possible through aggregation versus a multiple location retail design. Intuitively, many small retail stores would each have their own safety inventory for their customer base and most of this safety inventory would languish on the shelves. If one site experienced a surge in demand, a stockout would result. A large centralized supply would need less safety inventory as the demand variances might cancel each other, e.g., high demand from one region is offset by low demand from another. Only if many regions had unanticipated high demand would the central supply be exhausted.


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8. In the 1980s, paint was sold by color and size in paint retail stores. Today paint is mixed at the paint store according to the color desired. Discuss what, if any, impact this change has on safety inventories in the supply chain.

12. What capabilities can local suppliers in high-cost countries develop if they are to effectively compete against overseas suppliers in low-cost countries? Discuss how each capability impacts the level of inventory in the supply chain.

The practice of adding pigmentation in the retail store is a classic example of postponement; paint stores can mix any color into a solid white base and produce exactly what the customer wants. This change has greatly reduced the amount of safety inventory required as the paint store must now stock far fewer product lines. The reduction in safety inventory has simultaneously reduced safety inventory storage costs and increased responsiveness.

Local suppliers can begin to understand better the demand within the country and the drivers of that demand. By reducing the demand uncertainty the suppliers can better plan levels of safety inventory. Also by understanding replenishment lead times, lead time variability, and desired product availability, they can design a supply chain that can be more efficient with inventory levels and transportation costs that should offset the difference in production costs between themselves and competitors in low-cost countries.

9. A new technology allows books to be printed in ten minutes. Barnes & Noble has decided to purchase these machines for each store. They must decide which books to carry in stock and which books to print on demand using this technology. Do you recommend it for bestsellers or for other books? Why? If Barnes & Noble must carry stock after purchasing this machine, they should carry items with a steady demand, bestsellers and the like. The fringe books that are rarely purchased would best be left to the 10 minute process which is effectively instantaneous production. The books with low demand would be too expensive to stock for sporadic demand; they would need only one of each, but the breadth of the product line would be overwhelming and prohibitively expensive to carry from month to month. 10. Consider a firm like Zara that has developed production capabilities with very short replenishment lead times. Do you think this capability is more valuable for its online operations or its store operations? Why? It is more valuable for its store operations. Because Zara has developed a strategy that uses local flexible production, the trigger for replenishment is closer to the retail store than to it's online facilities. Thus this strategy benefits the store operations to a greater extent than the online operations.

11. As a firm gets better at postponement (can postpone at lower cost), should it increaselleave unchanged/decrease the variety that it offers? Why? The typical response of most [lfms is to increase the variety that its offers, making the assumption that the more variety leads to greater demand. This is not always the case. As a firm increases variety, the number of component parts that need to be purchased and maintained increases thereby increasing the overall inventory holding costs. The better response is to maintain variety at the current levels, constantly monitoring the demand for each end item and adjusting the mix of products to reflect the overall demand. This means that as they add variety, they also may be taking away some items. Over the long haul this will lead to increased variety, but it is a managed and strategic move to increase variety instead of a direct response to postponement.


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CHAPTER THIRTEEN: Determining the optimal level of product

availability 1. Consider two products with the same cost but different margins. Which product should have a higher level of product availability? Why? The product with the higher margin should be stocked at a higher level of availability than the product with the lower margin. The product with the higher margin will have a higher Cu, which is the cost of understacking. The cost of understacking is the sale price less the cost and may be thought of by the supplier as profit foregone. A higher cost of understacking results in a higher critical fractile, so the optimal cycle service level will be higher, which will yield a higher availability. 2. Consider two products with the same margin carried by a retail store. Any leftover units of one product are worthless. Leftover units of the other product can be sold to outlet stores. Which product should have a higher level of availability? Why? The product with the higher salvage value should be stocked at a higher level of availability than those with the lower salvage value. The product with the higher salvage value will have a lower Co, which is the cost of overstocking. The cost of overstocking is the sale price less the salvage value. A lower cost of overstocking results in a higher critical fractile, so the optimal cycle service level will be higher, which will yield a higher availability. 3. A firm improves its forecast accuracy using better marketing intelligence. What impact will this have on supply chain inventories and profitability? Why? Improved forecast accuracy should result in a closer match between supply and demand, resulting in improved profitability. An improved match will result in lower levels of unplanned carryover inventory and shortages at the end of planning periods. The improved match will lower the expected costs of having too much or too little inventory. 4. How can postponement of product differentiation be used to improve supply chain profitability?


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Postponement refers to the delay of product differentiation until closer to the sale of the product. Postponement allows producers to leverage two features common to forecasts: forecasts with shorter time horizons tend to be more accurate than those with longer time horizons; and aggregate forecasts tend to be more accurate than forecasts for individual items/models. More accurate forecasts allow for a better match of supply and demand, thereby lowering mismatch costs and increasing profitability as discussed in the previous question. 5. What are some scenarios in which postponing product differentiation across all products may not be profitable? How can tailored postponement help in such situations? Postponement is valuable in a supply chain when a firm sells a large variety of products with highly unpredictable demand of about the same size that is not positively correlated. Postponement is not as valuable if a large traction of the demand comes trom a few products. In such a setting, tailored postponement is most effective whereby base loads are not postponed but the variation is postponed. 6. Zara has used local production in Europe to have short replenishment lead times. How does this capability of quick response help the company improve profits in a highly volatile trendy apparel marketplace? In a trendy apparel market there exists a high probability for inventory obsolescence due to the nature of the industry. Therefore, by postponing the fmal configuration of the goods, Zara provides flexibility to its inventory to minimize this trend and better meet the ever changing demand. 7. When can tailored sourcing be used to improve supply chain profits? What are some challenges with implementing tailored sourcing? In tailored sourcing, firms use a combination of two supply sources, one focusing on cost but unable to handle uncertainty, and the other focusing on flexibility to handle uncertainty but at a higher cost. For tailored sourcing to be efiective, having supply sources such that one serves as the backup to the other is not sufficient. The two sources must focus on different capabilities. The low-cost source must focus on being efficient and should be required to supply only the predictable portion of the demand. The flexible source should focus on being responsive and be required to supply the uncertain portion of the demand. As a result, tailored sourcing allows a firm to increase its profits and better match supply and demand. 8. Mattei has historically allowed toy retailers to place two orders for the holiday shopping season. Mattei is considering allowing retailers to place only one order. What impact will this have on retailer orders? What impact will this have on supply chain profits? Mattei needs to abandon this approach to supply chain management. Under the two-order system, retailers could place an order, assess market demand, and place a second order that takes advantage of the short time horizon and improved kuow ledge about market demand. The single-order system will require a less-educated guess about demand that will occur further in the future. The single-order system has a much higher risk of a gross mismatch between supply


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and demand, resulting in excessive stock-out situations (lost sales) and fire sales at the end of the season. Supply chain profits will decline if the ordering system is changed to a single-order system. 9. Discuss how an expensive supplier with short lead times who is used as a backup for a low cost supplier with long lead times can result in higher profits than using only the low-cost supplier. The two suppliers can be deployed so that the customer has the opportunity to place two (or more) orders during each demand cycle. The low-cost supplier with long lead times should receive the flfst order trom the customer. As demand is realized, the customer can refme their demand forecast. Ifthe forecast is overly optimistic, the excess inventory can be disposed for its salvage value. The salvage value should be the same regardless of supplier, but thanks to the lower purchase price, the cost of overstocking is much lower. The second order can be placed at a later time and can be used to match demand as closely as the production situation permits. It may be possible to use the second order to fill only flfm customer demand that was not met by the order trom the slow, low-cost supplier. Even if this is not the case, the second order gives the customer the ability to match supply and demand while taking advantage of each supplier's strength.

CHAPTER FOURTEEN:

Transportation

1. What modes of transportation are best suited for large, low-value shipments? Why? Rail and water transportation modes are best suited for large, low-value shipments. The price structure of the business make rail and water the modes of choice if low-value, large, heavy, or high-density items need to be transported. Air, package carriers, and trucks would not have the infrastructure required to accommodate large items; roads and bridges would be damaged and the storage capacity of the carriers is insufficient. 2. Why is it im port ant to account for congestion when pricing the use of transportation infrastructure? Infrastructure often requires goverrnnent ownership and is not something that can be increased in capacity in the short term. If congestion is not factored in to the price structure for infrastructure, then demand for the resources will exceed capacity and major delays will occur. Pricing may be used to force users to internalize the marginal impact of their choices, thus alleviating some of the demand during peak periods. 3. Wal-Mart designs its networks so that a DC supports several large retail stores. Explain how the company can use such a network to reduce transportation costs while replenishing inventories more frequently. A distribution center that supports several large retail stores can reduce supply chain costs in four ways: 1) Inbound shipments to the DC achieve economies of scale because each supplier


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sends a large shipment; 2) The outbound transportation costs for a DC can be low because it serves retail locations nearby; and very large inbound shipments that match retail demand can be cross-docked at the DC, which saves both 3) storage and 4) material-handling costs. A DC also can replenish retail inventories more frequently; the DC breaks bulk from manufacturers on one side of the warehouse and sends it to retail locations on the outbound side. Since retail demands are aggregated at the DC leve~ the amount of inventory actually stored at the DC is very low and as Little's Law indicates, the time between replenishments is low also. 4. Compare the transportation costs for an e-business such as Amazon.com and a retailer such as Home Depot when selling home-improvement materials. The primary difference between these retailers is that Home Depot does not incur any outbound transportation cost for residential customers while Amazon faces such charges. Home Depot has substantial inbound transportation charges but is able to offload the outbound transportation cost to the vast rnajority of their customers. Amazon must use high cost package carriers for much of its product line although they are able to avoid inbound transportation costs for items that are drop shipped. For items that are held in one oftheir warehouses, Amazon must pay both inbound and outbound. 5. What transportation challenges does Peapod face? Compare transportation costs at online grocers and supermarket chains. Peapod faces the burden of expensive outbound transportation costs and must account for congestion in the delivery area. Unlike traditional grocers who don't deliver their products, Peapod must deliver items in their fleet of climate-controlled trucks. These trucks must be scheduled with pricing incentives offered for peak and off-peak delivery times. Customers are keenly aware of the transportation component of their purchases and Peapod can use pricing incentives to spur their customers towards higher order amounts. Both Peapod and traditional grocers must pay the inbound transportation costs oftheir wares; there would appear to be no great advantage gained by either approach unless one vendor has such substantial market share as to gain price concessions that they other can't negotiate. 6. Do you expect aggregation of inventory at one location to be more effective when a company such as Dell sells computers or when a company such as Amazon.com sells books? Explain by considering transportation and inventory costs. Inventory aggregation is a good idea when inventory and facility costs form a large fraction of a supply chain's total costs. Inventory aggregation is useful for products with a large value to weight ratio and for products with high demand uncertainty. Both factors allow aggregation to work to Dell's advantage, while Amazon reaps less of a reward. Dell benefits trom aggregation because personal computers have an extremely high value to weight ratio; the demand for new items is uncertain, and Moore's Law makes holding excessive inventory an extremely unattractive proposition. Amazon benefits from aggregation when inventory costs are examined, but is hurt by increased transportation costs. Most items that Amazon sells have low value to weight ratios and Amazon


9-15

must ship them via package carrier, which is expensive. Amazon saves money on storage costs since they choose to stock more popular titles and allow other entities to hold items with more variable demand. 7. Discuss key drivers that may be used to tailor transportation. How does tailoring help? Tailored transportation is the term for use of different transportation networks and modes based on customer and product characteristics. Tailoring transportation allows fIrms to achieve cost and responsiveness targets that are appropriate for the supply chain. The key drivers are density and distance, customer size, and product demand and value. These drivers can be viewed as guide for ownership of Transportation options based on customer density and distance are summarized in the table and p d · ti h e supply I cha·rn. trad eo ffisort resent cost an responSIveness Short distance Medium distance Lon!! distance Private fleet with Cross-dock with Cross-dock with High density milk runs milk runs milk runs Third-party milk LTL carrier LTL or package Medium density runs carner Third-party milk LTL or package Package carrier Low density runs or LTL carrier carrIer Customer size and location dictate whether a supplier should use a TL or L TL carrier or milk runs. Very large customers can be supplied using a TL carrier, whereas smaller customers can use LTL carriers or milk runs. The authors discuss a customer-partitioning procedure for combining smaller customers' shipments with larger customers in order to achieve responsiveness and cost targets. Product demand and value determine whether aggregation strategies will benefit the supply chain The best combinations are shown in the tabk Product High Value Low Value Type

High demand

Disaggregate cycle inventory but aggregate safety inventory. Use an inexpensive mode of transportation for replenishing cycle inventory and a fast mode when replenishing safety inventory.

Low demand

Aggregate only safety Aggregate all inventories. If needed, inventory. Use inexpensive use fast mode of transportation for mode of transportation for filling customer orders. replenishing cycle inventory.

Disaggregate all inventories and use inexpensive mode of transportation for replenishment.


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CHAPTER FIFTEEN:

Sourcing

1. What are some ways that a firm such as Wal-Mart benefits from good sourcing decisions? The bottom line is that good sourcing decisions improve profits for the firm and total supply chain surplus. The authors' list of benefits derived from effective sourcing decisions includes: Better economies of scale can be achieved if orders within a iirm are aggregated. More efficient procurement transactions can significantly reduce the overall cost of purchasing. Design collaboration can result in products that are easier to manufacture and distribute, resulting in lower overall costs. Good procurement processes can facilitate coordination with the supplier and improve forecasting and planning (lowering inventories and improving the match of supply and demand). Appropriate supplier contracts can allow for the sharing of risk, resulting in higher profits for both the supplier and the buyer. Firms can achieve a lower purchase price by increasing competition through the use of auctions.

2. What factors lead Wal-Mart to own its trucks although many retailers outsource all their transportation? Wal-Mart is able to run its own fleet of trucks because it can ship TL throughout its supply chain. Wal-Mart's shipment sizes are large and the company achieves aggregation across the many retail stores it owns. IfWal-Mart elected to go with a carrier, they might be able to match Wal-Mart's costs, but Wal-Mart would cede control to the carrier. 3. How can a supplier with a lower price end up costing the buyer more than a supplier with a higher price? Lower price can be achieved by sacriiicing product quality, product reliability, and process contro~ which ultimately will cost the outsourcer more than the total variable cost saved. The cost of coordination is often underestimated; the outsourcer offloads relatively low-skilled labor but increases the burden on mid and upper management in controlling the production. A firm may also lose customer/supplier contact that causes them to miss opportunities that may have been recognized with a more direct relationship. 4. Explain why, for the same inventory level, a revenue-sharing contract results in lower sales effort from the retailer than if the retailer has paid for the product and is responsible for all remaining inventory.

manufacturer and retailer agree to share a fraction of the retailer's revenue after agreeing on a low wholesale price. The low wholesale price triggers a larger order from the retailer, and this can increase supply chain surplus if all product is sold. Wliat happens in practice is that the retailer has a smaller upside under the revenue sharing arrangement and loses the incentive to push merchandise. 5. For a manufacturer that sells to many retailers, why does a quantity flexibility contract result in less information distortion than a buy-back contract? A buy-back contract allows a retailer to return unsold inventory to the supplier; the contract will stipulate the maximum amount returnable and the reimbursement amount the retailer will receive. A buy-back contract provides an incentive for the retailer to place a larger order and make product more available and can increase total supply chain surplus. A downside of buyback contracts is information distortion, i.e., the supply chain is aware of the retailers' orders and not the actual customer demand until the sales period has ended. This problem is exacerbated by a situation involving multiple retailers each of which holds inventory. A quantity flexibility contract permits the retailer to change the quantity ordered after observing demand; the contracts are similar to buy-back contracts except no returns are required. With a quantity flexibility contract, retailers specify only the range within which they will purchase, well before actual demand arises. The supplier can aggregate inventory across all retailers and build a lower level of surplus inventory. Since retailers order closer to the point of sale when demand is more visible and less uncertain; the uncertainty is aggregated by a supplier that enjoys lower information distortion. 6. Most firms offer their sales force monetary incentives based on exceeding a specified target. What are some pros and cons of this approach? How would you modify these contracts to rectify some of the problems? Two incentive oriented contracts discussed in the chapter are the two-part tariff and the threshold contract. The two-part taritt" increases sales agent efiort by allowing the retailer to acquire product at cost and letting the dealer's margin be the supply chain margin. Threshold contracts establish greater rewards for the retailer as total sales reach successively higher hrackets. These incentives can increase supply chain profits but can also be gamed to maximize retailer/agent bonuses without benefiting the manufacturer. Sales can be postponed from one sales period to the next by slow-playing customers, post-dating paperwork, and minimizing efiorts. The sales that would have occurred in period 1 are delayed to period 2, during which sales efiorts are maximized; ior the same level of sales, the agent has an increased commission, but the manufacturer realizes a lower profit. This gamesmanship also causes information distortion at the producer. These problems can be avoided by modifying the contracts with a rolling horizon. Rather than creating a high bonus period over a fixed period of time, reduced bonuses can be offered continuously over a shorter time period. The rolling periods have many "last weeks" built in and lead to a more constant level of efiort from the retail sites.

The retailer puts forth a lower sales effort because they are paid less on a per unit basis to sell items under a revenue sharing contract than under a buyback or a classic retail contract. The


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7. An auto manufacturer sources both office supplies and subsystems such as seats. What, if any, difference in sourcing strategy would you recommend for the two types of products? For an auto manufacturer, seats are considered direct materials (components used to make finished goods) while ofiice supplies are indirect materials (goods used to support the operation of a firm). The procurement process for direct materials should be designed to ensure that components are available in the right place, in the right quantity, and at the right time. Sources should be carefully selected to ensure that quality and responsiveness are acceptable and that a long-term relationship is possible. The primary goal of the procurement process should be to make production plans and current levels of component inventory at the manufacturer visible to the supplier and should have alerts built into it if mismatches between supply and demand are detected. The procurement process for indirect materials should be on reducing the transaction cost of each order. These items are not critical and can be purchased in bulk with an eye towards aggregation and cost savings. Stockout costs are low in comparison with direct materials so sourcing decisions are not as critical. 8. Why do you think assembly in the consumer electronics industry is performed by third parties, whereas assembly in the auto industry is almost never outsourced? In the consumer electronics industry, the third parties aggregate the demand across multiple flfms when performing assemblies thereby gaining production economies of scale that no single firm in this industry can. The auto industry on the other hand, maintains volume levels for its models that each individual manufacturer can reap the benefits oftheir own assembly. 9. How can design collaboration with suppliers help a PC manufacturer improve performance? Design collaboration with suppliers can help a firm reduce cost, improve quality, and decrease time to market. These performance metrics are increasingly influenced by suppliers since between 50 and 70 percent of the spending at a manufacturer is through procurement. Costs can be reduced by designing the product for postponement and mass customization. If the product's design permits the use of standardized parts or modules, the manufacturer can save on inventory ho Iding costs and training for assembly and repair labor. Costs are also reduced by increasing attention to design for manufacturability. Quality is increased by applying robust design techniques, certifying suppliers, and conducting failure modes and effects analysis. Suppliers that are specialists in a required component can bring to bear the design skills that will improve fmished goods quality. Time to market can be decreased by bringing suppliers into the design team from the early stages of product design. An engineering drawing reference database can eliminate the necessity for designing new parts which reduces overall design time.


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10. For products such as home appliances, toys, garments, and consumer electronics, what factors would influence selecting an onshore, near-shore, or offshore supplier? The decision to outsource is based on the growth in supply chain surplus provided by the third party and the increase in risk incurred by using a third party. This growth in surplus needs to be looked at understanding the following: Capacity aggregation Inventory aggregation Transportation aggregation by transportation intermediaries Transportation aggregation by storage intermediaries Warehousing aggregation Procurement aggregation Information aggregation Receivables aggregation Relationship aggregation and Lower costs and higher quality.

CHAPTER SIXTEEN: Pricing and revenue management in a supply

chain 1. In what ways can a retailer such as Nordstrom take advantage of revenue management opportunities? Nordstrom can take advantage of revenue management by using dynamic pricing through their Nordstrom Rack stores. Dynamic pricing is the tactic of varying price over time and is suitable for fashion and seasonal items. The Nordstrom Rack web site indicates that there are currently 49 locations in 18 states and that the Nordstrom Rack stores are the off-price division of Nordstrom (positioned for the cost-conscious shopper). Merchandise that does not sell at the Nordstrom stores is discounted 50-75% and moved to the Rack stores where it is sold in a less attractive setting with a less generous return policy. Nordstrom Rack is positioned such that it does not compete with Nordstrom stores, but allows the parent company to reap the greatest return from all products stocked at Nordstrom. 2. What revenue management opportunities are available to a manufacturer? How can it take advantage of these opportunities? A manufacturer's most profitable use of revenue management comes through the tactic of overbooking, which is the overselling of an available asset that faces last-minute cancellations of customer orders. The manufacturer's valuable asset is production capacity, which is fmite and loses value after a certain date; in this case, capacity is worthless at the end of the production period or past the date that the supply chain can fill customer orders. The tradeoff is the cost of unused capacity with the cost of customer orders that can't be filled and therefore must be subcontracted. The manufacturer can compute the marginal cost of wasted capacity and the


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marginal cost of a capacity shortage, form the critical ratio, and apply this to their knowledge of the customer order distribution, thereby increasing asset utilization. 3. What revenue management opportunities are available to a trucking firm? How can it take advantage of these opportunities? A trucking iirm can use revenue management by oifering a two-tiered pricing system; charging smaller customers a higher price than larger customers that consume the majority of the fleet. The rationale is that the larger customers offer the trucking flfm steady demand and the ease of dealing with only one or very few customers. These bulk purchases are made at a discount while smaller customers must make spot purchases at higher prices to fill up remaining capacity. 4. What revenue management opportunities are available to the owner of a warehouse and how can it take advantage of them? A warehouse owner can lease capacity in bulk at a discount to a large company and fill up the remaining warehouse capacity at full price to smaller customers. The large customer offers more stable demand and more fully utilizes the warehouse owner's space, albeit at a discount. The smaller customer may never materialize, so holding space for them is a risky proposition and merits a premium price. 5. Explain the use of outlet stores such as Saks Fifth Avenue in the context of revenue management. How does the presence of outlet stores help Saks? How does it help its more valuable customer, who is willing to pay full price? One way that the presence of outlet stores helps Saks is by recouping their purchase price for items that do not sell in flagship stores. Items can be sold in the outlet stores at a lower margin or even at a loss. Saks also benefits by freeing up more sales floor capacity in their main stores, allowing them to stock with the current season's high margin merchandise. The full-price customers of Saks beneiit because the inventory level of in-season items at Saks is higher, thereiore they are more likely to iind what they want. Saks knows they can dump any unsold merchandise at the end of the season in their outlet store; therefore Saks initial order will be higher than if they did not use revenue management. 6. Demand for hairdresser is much higher over the weekend, when people are not at work. What revenue management techniques can be used by such a business? A hairdresser can use pricing and revenue management for seasonal demand; peaks on the weekend and valleys on weekdays. The hairdresser can provide off-peak discounting in order to shift demand from weekend to weekdays. The hairdresser should create a price structure such that the discount given during the off-peak period is more than offset by the decrease in cost because of a smaller peak and the increase in revenue during the ofi~peak period. This tactic increases proiits ior the hairdresser, decreases the price paid by a fraction of the customers, and also brings in potentially new customers during the off-peak discount period and is, in a word, fabulous.


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7. How can a golf course use revenue management to improve financial performance? A golf course can use pricing and revenue management for seasonal demand much in the way the hairdresser in the previous scenario can. By lowering the price for less popular tee times, a golf course manager can increase revenue by increasing the total number of players and perhaps capturing new players. A golf course manager can also engage in overbooking ior tee times, overselling the course in the event that a ioursome or individual players will cancel at the last minute. Overbooking will use up more of the golf course's capacity which might decrease the level of customer service but will improve the course's fmancial performance.

CHAPTER SEVENTEEN: Information technology in a supply chain 1. What processes within each macro process are best suited to being enabled by IT? What processes are least suited? The macro processes in a supply chain are customer relationship management (CJTh,1), internal supply chain management (ISCM), and supplier relationship management (SRM). Taken collectively, these macro processes span the entire supply chain. CRM processes focus on the downstream interactions between the enterprise and its customers. The key processes under CRM are marketing, selling, and order management, and of these three, the creative sub-processes ofthe marketing and selling processes are least suited to IT enablement. The best suited processes for IT enablement are pricing and profitability calculations, sales force automation, and order configuration and tracking. Within order management, virtually all processes reap the benefits of information technology. ISCM processes focus on internal operations within the enterprise and include strategic planning, demand planning, supply planning, fulfilhnent, and iield service. The use of IT to facilitate ISCM sub-processes is presented in glowing terms in separate chapters in this text. Huge gains in efficiency and responsiveness have been achieved via the application ofIT to all aspects ofISCM. SRM processes focus on upstream interaction between the enterprise and its suppliers and includes the sub-processes of design collaboration, sourcing, negotiating, buying, and supply collaboration. The authors indicate in chapter 14 that sourcing-related IT has had the most ups and downs of any supply chain software sector, with the primary problems being loss of flexibility and the requirement of collaboration. Electronic marketplaces once flourished but have since withered. This is not to say that IT does not playa role in SRM processes; in fact, all areas are supported by IT software. 2. What are some advantages of the software as a service (SaaS) model? Why has it been successful in the CRM space? The Software as a Service (SaaS) model implies the use of various applications in rent. Its socalled Cloud Computing. The essence of the model is that the customer does not buy the software, but pays for the service which it provides. The customer does not install software on the servers, but uses capacities of the developer, needing only to pay for the service, cloud server maintenance and consultation services. As a result the with SaaS customer gets access to the


9-22

necessary application on a cloud server of the developer which allows saving money and quickly introducing the software to the business. It is needless to say that as a result everyone wins: customers don't need to spend money on system administration, and suppliers, thanks to software installation on their cloud hosting, quickly provide the clients with the necessary servIce.

Currently SaaS is considered to be an alternative to the standard scheme of software installation on the customer's equipment (standard delivery model). These two models do have a lot of differences. In the case with SaaS the client pays not for possession of the program, but for its rent. The client makes a small periodic user's payment and is relieved of necessity to invest the essential sums purchasing the software. You don't have to buy the software, and the hardware platform for installing it. Don't forget that after the groupware system is implemented in a company, it needs constant further maintenance. If all these responsibilities are passed on to SaaS Providers (cloud computing providers), the customer will only need to use the functions of the cloud app making regular payments for access to the collaboration system and accompanying services. Secondly: in SaaS model the customer receives not the software, but only that functions which it provides (as a web service). And this is implementation of business functions that a customer needs. Thirdly: in SaaS introduction procedure is reduced to a minimum and is very simple the customer simply needs to receive a login/password for the cloud application and to enter it. SaaS collaboration systems do not require long adjustment, or especially difficult adaptation to requirements of the customer and expensive consulting services. As a result time of project performance reduces as well as all the expenses. Fourthly, the SaaS model provides universal access to the necessary application from any place where there is Internet. The majority of cloud computing companies (SaaS providers) undertake to grant ahnost constant access to the service. Fifthly, the SaaS-model allows small and medium business companies (Sl\1B companies) to use applications which were inaccessible earlier because of high costs. Instead of purchasing the program the customer for a small payment rents business functions which it is capable of Does one really need more? Besides that SaaS model provides automatic updating of software without any additional expenses for the customer and the possibility to change the volume ofthe functional at any time. If there is no necessity for certain functions of the collaboration system, it is always possible to cancel them and to pay only for the ones that are essential for work. SaaS CRM solutions are a catalyst for how organizations change their use of front office software systems and put users in control of customer facing business systems for the first time. SaaS enablement of software utilization without extended implementation time frames, software modification without IT bottleneck, world class infrastructure without capital expenditures and 24 by 7 uptime without around the clock staffmg are a few of the compelling advantages of SaaS. Other key benefits include the following: Low cost of entry and lower total cost of ownership (TCO) - elimination of capital expenditures and dramatic reduction in IT salaries Vested vendor interests - if the application utilization is not successfu~ the vendor loses the customer revenue opportunity Much lower risk - faster implementations and outsourced expertise dramatically lower risk


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3. A more powerful and secure IT infrastructure - few organizations can match the infrastructure and security investments made by SaaS vendors 4. Why is the supply chain management software dominated by the ERP players like SAP and Oracle? Both SAP and Oracle have done a good job in convincing top management ofthe benefits from ERP solutions. They have dominated the market by showing overall cost improvements in operations from the installation and use of their software. The have also managed to scale their solutions for all size companies allowing for not only the biggest fIrms to benefIt, but also small to medium size fIrms. 5. Identify a few examples of when the availability of real time information has been used to improve supply chain performance. The Wal-Mart & P&G experiences demonstrate how information sharing can be utilized for mutual advantage. Through sound information technologies Wal-Mart shares point of sale information trom its many retail outlet directly with P&G and other major suppliers. Lucent technologies was able to achieve a dramatic cut in costs and reduced product delivery times. This inevitable led to significant improvements in customer satisfaction and increased market share. 6. Discuss why the high tech industry has been the leader in adopting supply chain IT systems. The high tech industry has been the leader in adopting supply chain IT systems because of the mindset of the decision-makers in this sector. The high tech workforce tends to be early adopters of new technologies; they understand there is a risk associated with adoption but are willing to assume the risk and proceed. High tech corporate cultures lend themselves to such ventures; there is little resistance to change because survival in this sector depends on it.

CHAPTER EIGHTEEN:

Sustainability and the supply chain

1. What are some benefits to improved sustain ability of a supply chain? Reducing risk and improving fmancial performance of the supply chain Attracting customers who value sustainability Making the world more sustainable. 2. What are some challenges that limit the effort put in by supply chains to improve sustainability? When it requires efforts that do not provide obvious return on investment for a company Insufficient return on investment Customer's unwillingness to pay a premium for green products


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Difficulty evaluating sustainability across a product life cycle One of the biggest challenges to building sustainable supply chains is that in the short to medium term, an improved focus on sustainability provides benefits that are shared but costs that may be local to a firm. 3. Describe the "tragedy of the commons" in the context of supply chain sustain ability. What are some "mutually coercive" mechanisms that could be implemented to encourage supply chain sustainability?

3. Other indirect emissions - corning from production of purchased materials, outsourced activities, contractor-owned vehicles, waste disposa~ and employee business travel. 5. Study the CSR reports for a couple of firms. Identify actions across a few supply chain drivers that have improved sustain ability. Which areas has the company found challenging to improve? You will find the Campbell's 2010 CSR Executive Summary report as part of this Instructor's l\1anual in the Chapter 18 discussion folder. Here is a brieffrom that report:

Every company and supply chain faces the challenge of the tragedy of the commons as it operates in agio bal environment. They must compete against others that may be extracting benefits from the envirornnental or resource commons without spending to maintain these commons. They must compete in a market where customers often value low cost and are not willing to pay the price of a more sustainable solution, either in the form of a higher price or reduced consumption. Two potentially "mutually coercive" mechanisms that could be implemented are "cap-andtrade" and an emission tax. With "cap-and-trade" there would be constrained aggregate emissions, which would create a limited number of tradeable emission allowances that emission sources must secure and surrender in proportion to their emissions. With an emission tax, each entity generating greenhouse gases is charged a tax proportional to the size of the emissions. 4. What are some problems with firms reporting their sustainability performance based on metrics that do not consider their extended supply chain? A major challenge relates to the scope over which a supply chain measures in regards to the following four categories: Energy consumption Water consumption Greenhouse gas emissions Waste generation. If a company reports only energy consumption within its own operations, and then decides to outsource some production to an offshore supplier, its own energy consumption will show a decline even though the energy consumption of the entire supply chain may have increased. If it decides to bring some production in-house and onshore, the energy consumption within its operations will show an increase even if the energy consumption for the entire supply chain has decreased. Thus companies must defme the scope across which all metrics are measured. The Greenhouse Gas Protocol defmes three scope levels which companies should report metrics: 1. Direct emissions - refers to emissions from sources that are owned or controlled

by the reporting entity 2. Indirect emissions - from grid-sourced electricity and other utility services including heat, stearn, and cooling


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Chapter 7: Demand Forecasting in a Supply Chain

Exercise Solutions: In addition you will find the Hershey Company 2009 CSR Executive Summary and their Scorecard results for 2010 as previewed below:

CORPORATE SOCIAL RESPONSIBILITY SCORECARD 2010

Problem 7-1: We utilize a static model with leve~ trend, and seasonality components to evaluate the forecasts for year 6. Initially, we deseasonalize the demand and utilize regression in estimating the trend and level components. We then estimate the seasonal factors for each period and evaluate forecasts. EXCEL Worksheet 7-1 provides the solution to this problem.

The Hershey Company 2010 Corporate Social Responsibility Scorecard outlines our progress In advancing the pnontles we established in our 2009 Corporate SOCIal Responsibility Report We understand that operating a sustainable, competitive bUSIness reqUires a commitment to improvmg our economIC, environmental, and social performance.

The model utilized for forecasting is: F,+I = [L + (t + I)T]S'+i

This scorecard shows how we performed against the goals published in our 2009 CSR Report as well as against newer targets established to further advance our priorities.

The deseasonalized regression model is:

Within thiSscorecard, we use the following to mdlCate our progress:

::

:~:~~:~~h:~~:~~a::t ;~!c!~~~t within or

••

On track. We expect to achieve the target Within

•

the time frame spe
D,

5997.261 + 70.245 t

The seasonal indices for each of the twelve months are:

Under development We are working to further

define this target Needs improvement. We have made some progress but either lack sufficient data or have not progressed as we had expected toward achievmg this target.

We look forward to COf'lunumg to report on our periOfTTlance, and we welcome your feedba
The He rshcy Compa ny

6. Even if a product is designed to be recyclable, discuss some challenges in designing a closed-loop su pply chain that can recycle sustain ably. Does a company gain or lose economically by selling remanufactured products along with new ones How can a [lfm ensure sufficient access to used products if it plans to remanufacture Who should be responsible for collecting used products (the retailer, the manufacturer, or a third party) What incentives need to be in place for the economic interests of the entire supply chain to be aligned Do any decisions change ifthe product has a short or long life cycle What incentives need to be in place for suppliers to design and produce durable products?


=

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Month JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

S.I 0.427 0.475 0.463 0.398 0.621 0.834 0.853 1.151 1.733 1.778 2.124 1095

For example, the forecast for January of Year 6 is obtained by the following calculation: F61 = [5997.261 + (61)

* 70.245] * 0.4266 =

4386

The quality of the forecasting method is quite good given that the forecast errors are not too high.

Problem 7-2:


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200

Moving Average

Actual Demand

Forecasted Demand 160

130 125 120 115 110 105 100 95 90 85 80

140

Sales

120 100 80 60

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16

40

Periods

20 0 P1

EXPONENTIAL SMOOTHING Actual Demand

Unit Demand

Un it Deman d

180

Forecasted Demand

130 125 120 115 110 105 100 95 90 85 80 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16

Periods

P2

P3

P4

P5

P6

P7

P8

P9

Period

P10

P11

P12

P13

P14

P15

P16

Period Sales level

o

EXPONENTIAL SMOOTHING

4 5 6 7 8

125 12D 115 ;; 110 E 1D5 ~ 1DD

'2

5

95

1000 1113 1271 1445 1558 1648 1724 1850

9

1864

10 11 12

2076 2187 II

Forecast

1659 1461 1357 1331 1365 1423 1491 1561 1647 1712 1821 1925 2005

1659 1461 1357 1331 1365 1423 1491 1561 1647 1712 1821 1925

A,

bias

MSE

MAO

659 348

659 348

659 1007 1093 979 786 561 328 39 -178 -542 -887 -1153

434281 277797 187652 143984 122618 110614 102597 100243 94317 98107 100042 97596

659 504

" "

·114 -193 -225 ·233 ·289 -217 ·364 -346 -266

114 193 225 233 289 217 364 346 266

Percent Error MAPE

66 31 7 8 12 14 14 16 12 18 16 12

36' 302 280 271 265 268 263 273

279 278

66

49 35 28 25 23 22 21

20 20 19 19

TS 1.00 2.00 3.00 3.24 2.81 2,07 1.24 0.14 -0.68 -1 .99 -3,18 -4.14

200S 200S

13

9D 85

E,

14

W~~ro-.-'-r.-.-~r-r-ro-.-,~

Estimate of sl andarddeviationol forecaslerror: 1£B

1 2 3 4 5 6 7 8 9 1D 11 12 13 14 1516 Pe riods

Holl's m ooet Period Sales level

o

EXPONENTIAL SMOOTHING 7

8 9 10 11 12

13D~--------------------------~~

125 12D

'5! 115

13

li 110

14

E 1D5

~ 5

'1000 1113 1271 1445 1558 1648 1724 1850 1864 2076 2187 1

Trend

948 " 109 " 1054 108.7 1160 108.5 1269 108.5 1381 108.8 1493 109.2 1604 109.4 1714 109.4 1825 109.6 1931 109.2 2042 109.4 2152 109.5 2258 109.1

1DO

Forecast

E,

A,

bias

MSE

MAO

1057 1163 1269 1377 1490 1602 1714 1824 1935 2040 2152 2262 2367 2476

57

57

57

57

50 -2 -6' -68 -46 -10 -26 71 -36 -15 71

50 2 68 68 46 10 26 71 36 15 71

107 105 37 -31

3249 2868 1913 2577 2997 2847 2455 2234 2541 2414 2216 2449

-77 -87

-, ,3 -43 -78 -94

-23

9D 85

6

6 5 3

• •

53 36 44

0 5

49 48 43 41 44 43 41 43

Estimate of standard d evia ~ on offorecast error:

95

Percent Error "'APE

••4

3 I I

3 3 3 3 3 3

• 2 I

3

TS 1,00 2.00 2.88 0.84 -0.64 ·1.59 -2.03 -2.77 ..(J.97 -1 .81 -2.30 -0.53

2ill..

Problem 7-7: Worksheet 7-7 reexamines the A&D Electronics data with the Holt's model being run with the original alpha at .05 and beta at .1 and a revised Holt's with an alpha and beta both of 5

w h~~~~~~---r-~"----'~---r-~

1 2 3 4 5 6 7 8 9 1D 11 12 13 14 15 16 Pe riods

Period

From the data and the graphs, it is evident that the alpha of.9 is a better tracker of the forecast. Problem 7-6: 10 11

Worksheet 7-6 looks at the forecast for A&D Electronics and compares the results of simple exponential smoothing model with the Holt's model. In looking at the results of these two models, it is evident the Holt's model is a better forecasting model.

12

Sale$ L evel

940 1 054 ' 160 1269 ' 381 1493 1604 1 7 14 1825 1931 204 2 2152 2258

Trend

109 1087 '08 5 108.5 1088 '092 109.4 1094 '096 109.2 '095 109. 1

Foreca$t

1' 63 1269 1 377 1490 1602 1 714 1824 1935 2040 2152 2262 2367 2476

E,

A,

bh' $

MSE

MAD

57 50 -2 -68 -68 -4. -10 -26 71 -36 -15 71

57 50 2 68 68 4. 10 26 71 36 15 71

57 ,"7 105 37

3249 2868 1913 2577 2997 2 847 2 4 55 2234 254 1 2 414 2216 2449

57 53 36

-" -77 -87 _113 -43 -78 _9' ·23

44

'9 .8 43 41

44 ' 3 41

.3

Perc;ent Error MAPE

6

6 5 3

3

3

~0 . 53

. .. 4

0 5

3 1 1 4 2 1 3

TS

1 .00 200 2 .88 06' -064 -1 .59 -20 3 _277 -0.97 _181 _230

4

3 3 3 3

e of standard deviation of forecas t efTor ~

Holl's mode! Wit h alpha equal to .05 and beta equal to . , has lower forecast error


9-31


9-32

Period Sales Level

1000 1113 1271 1445 1558

'648

9 '0

"' 2

1724 1850 '884 2076 2167 1

Trend

109 94.8 92.2 107.4 13 1.6 139.1 130.5 11 2.6 107.0 81 .0 100.7 108.1 90.8

948 1029 11 18 1241 1397 ' 543 ' 665 1760 1861 1916 2037 2152 2226

'3 14

Forecast

E,

A,

bias

MSE

MAD

57 '0 -6 ' -97

57 '0 6' 97 30 34 72 22 '0' 79 30 69

57 67 7 ·90 -120 ·86 -' 5 8

3249 1677 2346 4111 3467 3084 3376 3017 3889 4123 3829 3909

57

Percent Error MAPE

Overtime constraints:

TS

~

1057 1123 1210 1348 1528 1682 '796 1872 '968 1997 2137 2260 2316 2407

-30 34 72 22

'0' -79 -30

69

'12 33 3 73

34

43 56 5' 48 52 '8 54 57 54 55

,

6

5 7 2 2

6 3 4 5 4 4

•,

•3

6

4 4 3 3

•, 3

1.00 2.00 0.1 5 -1.61 -2.36 -1 .79 ·0.28 0.16 2.07 0.59 006 1.31

0, - 20W,

<;

0, t

~

1, ... ,12

Production constraints: P - ~ - 960W, < 0 1 12 , 1000 1000 - , t ~ , ...

Workforce constraints: W,

~

1250, t

~

0, ... ,12

Estimate of standard deviation of forecast error: ~

(a) Worksheet 8.1 provides the solution to this problem and the corresponding aggregate plan. The total cost of the plan is $360,400,000.

Chapter 8: Aggregate Planning in a Supply Chain

Exercise Solutions:

(b) If the number of overtime hours per employee were increased from 20 to 40 it would result in decreasing the total cost to $356,450,000. So, it is advantageous to do it.

We defme a comprehensive set of decision variables that are utilized in problems 8-1 to 8-3 depending on the problem context.

(c) If the number of employees is decreased to 1200 and the overtime hours per employee are held at 20 and 40 then the total costs of the plan are $363,324,000 and $357,422,000, respectively. If the number of employees is increased to 1300 and the overtime hours per employee are held at 20 and 40 then the total costs of the plan are $358,790,000 and $356,270,000, respectively. So, the value of additional overtime increases as workforce size decreases.

Decision Variables: H, ~ # of workers hired in month t (t ~ 1, .. ,12) L, ~ # of workers laid-off in month t (t ~ 1, .. ,12) W, ~ # of workers employed in month t (t ~ 1, .. ,12) 0, ~ # of hours of overtime in month t (t ~ 1, .. ,12) I,~ # of units (OOOs) held in inventory at the end of month t (t ~ 1, .. ,12) C,~ # of units (OOOs) subcontracted in month t (t ~ 1, .. ,12) P,~ # of units (OOOs) produced in month t (t ~ 1, .. ,12)

(d) We add a new constraint: P,

<;

1291.667, t

~

1, ... 12 . The cost will be $363,049,982.

Problem 8-2:

We now include the subcontract option in the model: 12

Parameters: D, ~ # of units (OOOs) demanded in time period t (t ~ 1, ... 12)

12

12

12

12

Minimize 3200L:W, + 30L:0, + 3000L:I, + 20000L:P, + 26000L: c, 1=1

t =l

1=1

1=1

1=1

Subject to:

Problem 8-1 : 12

12

12

Inventory constraints: 1'_1 + P, + C, -I, ~ D"

12

Minimize 3200L:W, + 30L: 0 , + 3000L:i , + 20000L:I--; t=l

1=1

1=1

1=1

t

~

1, .. ,12

10 ~I'2 ~50

Subject to:


Inventory constraints: 1'_1 + P, -I, ~ DO' t ~ 1, .. ,12

0, - 20W,

<;

0, t

~

1, ... ,12

10 ~I'2 ~50

Production constraints: Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall

9-33


9-34

0 , - 20(W, + T,) "' 0, t = 1, ... ,12 p _ ~ _ 960W, < 0 I 12 , 1000 1000 - , t = , ...

Production constraints:

Workforce constraints:

p _~_ 960(W, +T, ) <0 ' 1000 1000 '

I 12 t = ,...

W, = 1250, t = 0, ... ,12 Full-Time Workforce constraints: Worksheet 8-2 provides the solution to this problem.

W, = 1250, t = 0, ... ,12 (a) Without the subcontract option the total cost is $360,400,000 (from problem 8-1) and the total number of units produced is 14,900,000. Thus, the cost per unit is $24.19.

Temporary Workforce constraints:

(b) Third party production must be used in periods 5, 6, 7, and 10 for a total of 1,050,000 units. If the subcontract cost per unit decreases to $25 per unit then a total of 1,650,000 units must be acquired trom this option.

T, - 7',-1 - H , + L, = 0, 1~

t = 1, ... ,12

=0

T,",50

(c) If the subcontract cost increases to $28 per unit then a total of 700,000 units must be acquired from this option. (d) The total number of units produced, including subcontract production, is 14,900. So, using subcontract the total cost incurred is $357,450,000, which leads to an average cost of $23.99 per unit. Without the subcontract option, the cost per unit is $24.18 (from a). Therefore, it is still beneficial for Skycell to use subcontracting option even if the per unit cost is higher. Without using subcontracting, Skycell would need to use overtime to produce extra units to fulfill demand. The cost of using overtime is 1.5 times regular labor cost. In addition, in the absence of subcontracting, ho Iding costs will also increase due to extra units being carried into future time periods.

(a) IT otal cost = $

358,210,000

Ht

Tt

Lt

Period

# Hired 0 1

2

# Laid off

# Temp 0

0 0 0

3

Problem 8-3:

4

We defme and include a new decision variable for this model called T" which represents the number of temporary workers employed in time period t. Since hiring and layoff of temporary workers is allowed, we include hiring and layoff costs in the model. Also, note that there is no subcontract option available for this case. The LP model for this case is shown below:

6 7 8

5

12

12

12

12

12

11

Minimize 800L:H, + 1200L:L, + 3200L: (W, + T, )+ 30L:O, + 3000L:I, + 20000L:P, t=l

t =l

t=l

1=1

1=1

12

1=1

0 50

9

10 12

(0)

50 0

50 50

Pt

1,250 1,250 1,250 1,250 1,250 1,250 1,250 1,250 1,250 1,250 1,250 1,250

950 1184 1200 1404 1404 1404 1404 900 1100 1200 1346 1404

(b)

Subject to:

IT atal cost = $

Inventory constraints: 1'_1 + P, -I, = D" t = 1, .. ,12

356,658,667

Ht

10 =112 =50

Tt

Lt

Period

# Hired



0 50 50 50 50

50 0

Wt

# Workforce Production 0 1,250 0

0

9-35

# Laid off 0

# Temp 0

Wt

Pt

# Workforce Production 0 1,250 0


9-36

1

0

2

(0)

3

96

96

1,250 1,250 1,250 1,250 1250 1,250 1,250 1,250 1,250 1,250 1,250

4

100

1,250

0 100

4

100 100 100 100

5

6 7 8

0

9 10 11 12

(0) (0)

0 100

950 1100 1200 1326 1458 1458 1458 900 1100 1200 1292 1458

Temporary Workforce constraints: (not needed)

IT otal cost = $

356,926,500

Ht Period

Lt

# Hired 0

0

1

2 3

156 154

5

9 10 11 12

(d) Since there is no difference between regular employees and temporary employees in terms of productivity and cost of hiring and layoffs, this problem is equivalent to using at most 1300 employees and allowing hiring and layoffs. So, the formulation can be revised as follows. 12

12

12

12

12

t =l

t =l

1=1

1=1

363 208 44 110 0

50

0 0 50 50 50 50 50 0 0 0 50 50

Pt

# Permanent # workforce 1,250 990 1,146 1,250 1,250 1,250 1,250 1,250 938 1,146 1,190 1,250 1,250

1,300 990 1,146 1,300 1,300 1,300 1,300 1,300 938 1,146 1,190 1,300 1,300

Production

0 950 1100 1284 1404 1404 1404 1404 900 1100 1142 1404 1404

12

So, if the no layoffno hiring policy for the permanent employees can be relaxed, Skycell will be able to further reduce the total cost. However, the reduction from case (c) is marginal.

Minimize 800IH, + 1200IL, + 3200IW, + 30I 0 , + 3000II, + 20000Ip, t=l

6 7 8

# Temp 0

310

4

(c) IfSkycell only carries 1100 permanent employees but has 200 seasonal employees, the total cost will be reduced to $356,984,667, a 0.34% cost saving compared to (a)

Wt

# Laid off

1=1

Subject to: Problem 8-4:

Inventory constraints: 1'_1 + P, - I , = D" t = 1, .. ,12


10 =112 =50

Decision Variables:

Overtime constraints: 0 , - 20W,

<;

H, = # of workers hired in month t (t = 1, .. ,12) L, = # of workers laid-off in month t (t = 1, .. ,12) W, = # of workers employed in month t (t = 1,.. ,12) 0, = # of hours of overtime in month t (t = 1, .. ,12) IRt = # of routers (ODDs) held in inventory at the end of month t (t = 1, .. ,12) IS, = # of switches (ODDs) held in inventory at the end of month t (t = 1, .. ,12) CS, = # of switches (ODDs) subcontracted in month t (t = 1, .. ,12) P]{,= # of routers (ODDs) produced in month t (t = 1, .. ,12) PS, = # of switches (ODDs) produced in month t (t = 1,.. ,12)

0, t = 1, ... ,12

Production constraints: p _ ~ _ 960W, < 0

,

1000

1000 -

, t

I

= , ...

12

Full-Time Workforce constraints: W, - W'_1 - H, + L, = 0,

Parameters: DR, = # of routers (ODDs) demanded in time period t (t = 1, ... 12) DS, = # of switches (ODDs) demanded in time period t (t = 1, ... 12)

t = 1, ... ,12

Wo = 1250 W, <; 1300, t = 0, ... ,12


9-37


9-38

12

12

12

12

and (b) it can be observed that the production schedule of switches (PSt) is impacted, as is 1S t. On the other hand, the production plan for routers remains the same.

Minimize 1600LW, + 15LO, + 2000LIR, + 1000LIS, 1=1

t =l

1=1

t=l

Subject to: Inventory constraints: lRH + f'R, -lR, = DR"

t = 1, .. ,12

ISH + PS, - IS, = DS"

t = 1, .. ,12

(c) From the table below it is evident that as the number of employees increases, the value of increasing total number of overtime hours allowed per employee per month decreases. When the number of employees is 6700, there is no cost difference between using 20 and 40 hours of overtime per employee. Total cost

IRo = IR'2 = 100

# employees Overtime 20

ISo = IS'2 = 50


5900 6300

Overtime 40 Cost difference % chanQe 135,429,0001132,135,000 3,294,000 2.4323% 135,429,0001134,552,000 877,000 0.6476%

6700

138,302,0001138,302,000

0

0

0 , - 20W, oe; 0, t = 1, ... ,12 Problem 8-5:

Production constraints: In this case we add hiring and layoff options. 333PR, + 166.7 PS, - 0 , -160W, oe; 0,

t = 1, ... 12 12

12

12

12

12

12

Minimize 700LH, + 1000LL, + 1600LW, + 15LO, + 2000LIR, + 1000LIS,


t =l

t=l

t =l

1=1

1=1

t =l

Subject to: W, = 6300,

t = 0, ... ,12

(a) IT otal cost = $

135,429,000

t = 1, .. ,12

ISH + PS, - IS, = DS"

t = 1, .. ,12

IRo = IR'2 = 100

Router Switch Production Production

Period

Inventory constraints: IRH + PR, - IR, = DR"

ISo = IS'2 = 50

0 1

2 3

4 5

6 7

8 9 10 11 12

1700 1600 2600 2500 800 1800 1200 1400 2500 2800 1000

2648 2848 1150 1804 800 1800 2400 3248 1048 1204 1000

1100

1050

Overtime constraints: 0 , - 20W, oe; 0, t = 1, ... ,12 Production constraints: 333PR, + 166.7PS, - 0 , -160(W, - 0.5(H,_, + H , J Joe; 0,

Workforce constraints: W, -W,_, -H, + L, = 0,

(b) If the overtime allowed per employee per month is increased to 40, the total cost becomes $134,552,000. So, cost reduction is incurred as a result of such an action. Comparing the output of (a)


t = 1, ... 12

9-39

t= 1, ... ,12

Wo =6300


9-40

The solution to this problem is shown in Worksheet 8-5. Part (b) can be solved by replacing the production constraints in the above formulation by:

333PR, + 166.7 PS, - 0 , -160W, oe; O.

Problem 8-6:

t = 1•... 12

In this case we add the subcontract option Minimize

(a)

ITotal cost =

137,118,107

$

12

12

12

12

12

12

12

12

700LH , +IOOOLL, + 1600LW, + 15La, + 2000LIR, + lOOOLIS, + 6000LCR, + 4000LCS, Ht

Period

Lt

# Hired 0 1

Wt

11

0 0 0 0 671 0 0 0 0 0 0

12

431

0

3

4 5

6 7

8 9

10

Router

Switch

t =l

# #Laidofl Workforce Overtime Production Production 0 0 15 0

0 0 0 0 0 0 241 0 0 0 0

2

Ot

6,300 00 6,300 00 6,300 86500.0 6,300 126000.0 5,629 00 5,629 00 5,869 00 5,869 00 5,869 117385.9 5,869 117385.9 5,869 00

1700 1600 2600 2600 800 1800 1200 1400 2500 2800 1000

2645 2845 1362 1599 800 1800 3117 2716 1334 733 1000

6,300

1000

1050

00

t=l

Inventory constraints: IRH + PR, + CR, - IR, = DR"

Ht

0 1

2 3

4 5

6 7

8 9

10 11

12

Lt

Ht

0 0 0 0 671 0 0 0 0 0 0 0

0 0 1451 0 0 0 0 0 3718 0 0 0

t =l

t = 1, .. ,12


0 , - 20W, oe; 0, t = 1, ... ,12 Production constraints:

333PR, + 166.7PS, - 0 , -160(W, - 0.5(H,_, + H , J Joe; 0,

t = 1, ... 12


t= 1, ... ,12

Wo =6300

Lt

(a) FlexMan should use the subcontractor to produce 446,000 units of routers in period 4 and 1,446,000 units of routers in period 10. FlexMan should not use the subcontractor for switch

616 0 0 0 3069 0 0 0 0 0 1483 0


t =l

ISo = IS'2 = 50

# Laid off # Hired # Laid off 0 0 0 0 0 0 0 0 0 0 241 0 0 0 0 431

t =l

IRo = IR'2 = 100

b)

# Hired

1=1

ISH + PS, + CS, - IS, = DS" t = 1, .. ,12

W, -W,_, -H, + L, = 0, Period

1=1

Subject to:

(b) The total cost will be $131,256,258, a reduction of 4.275% from (a). Comparing the hiring and layoff results of (a) and (b), we fmd more hiring and layoff happens in (b). As can be seen, when a new employee is 100% productive when they are hired, FlexMan's cost will reduce. So, it is reasonable that FlexMan will use the option of more new hires and lay them off when appropriate. a)

t=l

(b) FlexMan should not use the subcontractor at all. (c) When the productivity of new employees is low, FlexMan suffers from loss of capacity. When the new employees have the full productivity, FlexMan can use the same amount of cost (of salary) in acquiring a higher output rate, thus reducing the average unit cost. Therefore, the choice of whether or not to use a subcontractor will vary with the productivity of new employees.

Problem 8-7:

9-41


9-42

We utilize the same fOl1Uulation as in Problem 8-4, but impose constraints on the ending inventory to allow for safety stock as shown below:

IR,

:2

0.15DR'+1

IS,

:2

0.15DS'+1

(a)

Parameters:

142,960,650

IT otal cost = $

L, ~ # of workers laid-off in month t (t ~ 1, .. ,12) W, ~ # of workers employed in month t (t ~ 1, .. ,12) 0, ~ # of hours of overtime in month t (t ~ 1, .. ,12) I,~ # of units held in inventory at the end of month t (t ~ 1, .. ,12) C,~ # of units subcontracted in month t (t ~ 1, .. ,12) P,~ # of units produced in montli t (t ~ 1, .. ,12)

D, Router

Period

~

# of units demanded in time period t (t ~ 1, ... 12)

Switch

Production Production

Problem 9-1:

0 1

2 3

4 5 6 7

8 9

10 11

12

1770 1750 2585 2245 950 1710 1230 1565 2545 2530 1000 950

2504 2545 1037 2310 770 1815 2308 2915 953 1739 865 1050

12

12

12

12

Minimize 2400L:W, + 22L:O, + 3L:I, + 40L:P, t =l

1=1

1=1

1=1

Subject to: Inventory constraints: IH + P, -I, ~ D" t ~ 1, .. ,12

10 ~ 112 ~ 4000 Overtime constraints: 0, - 20W, "' 0, t

~

1, ... ,12

Production constraints: (b) Comparing cost in (a) to cost in 8-4 (a), we observe an increase of$7,531,650 in total cost, an 5.56% of cost increase by providing this service contract.

2P' - 0, -160W, ",0, t

(c) From the table below we can see that keeping a safety stock of 5% of the following month's demand for routers will be the best policy for Flexl\1an.

Router 15%, Switch 15% Router 5%, Switch 15% Router 15%, Switch 5%

W,

Savings Total Cost 142.960.650 138.902.350 2.84% 142.125.650 0.58%

250,

t ~ 0, ... ,12

(b) From the table below we can see that it is better to promote in April than in July, as the profit is slightly higher. Price=$125

Total Cost

Promotion Promotion July) No promotion April) Total Cost$16.820.000 $17.059.400 $17.367.300 Total Revenue - $28.500.000 $28.916.625 $29.198.750 Profit = $11.680.000 $11.857.225 $11.831.450 Profit increase $177.225 $151.450

Decision Variables:

# of workers hired in month t (t ~ 1, .. ,12)


~

(a) Worksheet 9-1 provides the solution to this problem and the corresponding aggregate plan. The total cost of the plan is $16,820,000


~

1, ... 12


Chapter 9: Sales and Operations Planning

H,

~

9-43


9-44

Workforce constraints: (c) If a sink is sold at $250, then the profit associated with promotion in July is higher than in April. So, as the product margin increases it is more beneficial to offer the discount in high demand period. Price= $250 Total CostTotal Revenue Profit Profit increase -

Total Cost No promotion Promotion (April) Promotion (July) $16,820,000 $17,059,399.94 $17,367,299.95 $57,000,000 $57,833,250 $58,397,500 $40,180,000 $40,773,850.06 $41,030,200.05 $593,850.06 $850,200.05

W, -W'_l -H, + L,

(a) Total Cost = Total Revenue = Profit = Period

Problem 9-2: We now include hiring and layoff costs in the model. Note that the workforce level constraints also change. 12

12

12

12

12

12

Minimize 1000L:H, + 2000L:F, + 2400L:W, + 22L:O, + 3L:I, + 40L:P, Subject to: t =l

t =l

t =l

1=1

1=1

1=1

Inventory constraints: 1 H + 1', -1 , = iJ" t = 1, .. ,12

10 = 112 = 4000 Overtime constraints:

t= 1, ... ,12

I$ $ $

16,571,000 28,500,000 11,929,000

Production

0 1 2 3 4 5 6 7 8 9 10 11 12

20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 18,000 15,000 15,000

(b) Promotion in July is better. Profit increases to $218,900.1

0 , - 20W, "' 0, t = 1, ... ,12 Production constraints:

2P' - 0, -160W, ",0,

= 0,

Wo = 250

Total Cost = Total Revenue Profit = Profit increase-

t = 1, ... 12

Total Cost No Promotion Promotion July) promotion April) $16,571,000 $16,794,500 $17,050,850 $28,500,000 $28,916,625 $29,198,750 $11,929,000 $12,122,125 $12,147,900 0 $193,125.1 $218,900.1

(c) If the holding cost increases to $5/unitlmonth, then promotion should be held in April. Promotion in July will result in producing more units of product, which in turn results in a higher carrying cost. Although, the sales amount is also higher if promotion is in July, the incurred profit is lower due to the higher carrying cost.


9-45


9-46

Holding = $5/unitlmonth

Total Cost Promotion April)

Total Cost No Promotion Promotion Ipromotion April) July) $16,828,625 $17,038,361 $17,353,188 $28,500,000 $28,916,625 $29,198,750 $11,671,375 $11,878,264 $11,845,562 0 $206,889 $174,187.4

Total CostTotal Revenue Profit Profit increase=

Problem 9-3:

Total Cost-

Promotion Julv) $17,000,100 $17,251,400

Total Revenue = Profit =

$28,916,625 $11,916,525

9-4~

In this case we add the subcontract option to problem information given in 9-1 12

12

12

12

1=1

1=1

1=1

9-6


12

Minimize 2400LW, + 22LO, +3LI, + 40LP' + 74LC, t =l

$29,198,750 $11,947,350

Decision Variables:

1=1

Subject to:


H, = # of workers hired in month t (t = 1, .. ,12) L, = # of workers laid-off in month t (t = 1, .. ,12) W, = # of workers employed in month t (t = 1, .. ,12) 0, = # of hours of overtime in month t (t = 1, .. ,12) 1,= # of units held in inventory at the end of month t (t = 1, .. ,12) C,= # of units subcontracted in month t (t = 1, .. ,12) P,= # of units produced in month t (t = 1, .. ,12)

0 , - 20W, "' 0,

Parameters:

Inventory constraints:

I H +P,+C, -I, =D"

/=1, .. ,12

io = i'2 = 4000

/ = 1, ... ,12


D, = # of units demanded in time period t (t = 1, ... 12)

2P' - 0, -160W, ",0, / = 1, ... 12

Problem 9-4:


Minimize 1600LW, + ISLa, + 4Li , + 3SLi-;

W, = 250,

Subject to:

12

t =l

/ = 0, ... ,12

From worksheet 9-3, no units should be outsourced from the subcontractor. But with promotion, the subcontracting option should be used. Specifically, if the promotion is in Apri~ 2600 units and 1000 units should be outsourced from the subcontractor in August and September, respectively. If the promotion is in July, then 1000units and 6100 units should be outsourced in July and August, respectively. The need for subcontracting is because promotion induces additional demand, which will not be cost effective for Lavare to produce by itself, as the carrying cost will outweigh the costs paid to the subcontractor.


9-47

12

1=1

12

1=1

12

1=1

Inventory constraints: 1,_, + P, -I, = D" / = 1, .. ,12

10 = 1'2 = 4000 Overtime constraints:

0 , - 20W, "' 0, / = 1, ... ,12


9-48

CQ


2P' - 0, -160W, <; 0,

44 Period

t = 1, ... 12

0 1 2 3 4 5 6 7 8 9 10 11 12


W, = 250,

t = 0, ... ,12

(a) Total Cost = Total Revenue = Profit =

$12.013.000 $15.920.000 $3.907.000

Pt Period

66

46

64

Production Production Production Production

9,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 15,000 10,000 11,000 14,000

12,000 20,000 20,000 20,000 20,000 20,000 20,000 17,000 15,000 10,000 11,000 14,000

8,000 12,700 20,000 20,000 20,000 17,500 20,000 20,000 15,000 10,000 11,000 14,000

8,000 15,000 20,000 20,000 20,000 20,000 20,000 18,000 15,000 10,000 11,000 14,000

Production

0 1 2 3 4 5 6 7 8 9 10 11 12

(d) There are tbree strategies for both Jumbo and Sbrimpy, which leads to a total of9 combinations of strategies, as shown in the table below. Jumbo would achieve the highest profit if it promoted in June and Shirmpy did not promote at all, and it would receive the lowest profit if it promoted in June and Sbrimpy promoted in April. In order to achieve a middle ground, it would be beneficial for Jumbo to coordinate with Shirmpy so that they either don't promote at all or promote in the same month.

9,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000 15,000 10,000 11,000 14,000

Jumbo \ Shrimpy No promotion April June No promotion $3.907.000 $3.615.000 $3.594.600 April $4.103.000 $3.871.000 $3.513.800 June $4,008,400 $3,498,400 $3.760.600

Note: number in each cell represents Jumbo's profit

(b) Profit (Jumbo no promotion, Sbrimpypromotes in April)= $3,615,000 Profit (Jumbo no promotion, Sbrimpy promotes in June)= $3,594,600 Profit (Jumbo promotes in April, Sbrimpy no promotion)= $4,103,000 Profit (Jumbo promotes in June, Sbrimpy no promotion)= $4,008,400 Also, from (a), profit (both no promotion)= $3,907,000.

(e) We flfst identifY the minimum profit for each strategy for Jumbo, as indicated by the numbers in bold in the table below. The maximum of these tbree minimum profits is $3,594,600. So, Jumbo sliould not undertake any promotion at all tbrougliout tlie year.

Since both Jumbo and Sbrimpy have similar demand patterns, and maybe similar cost structure, it is reasonable to think that the profit gained by one party's promotion is the competitor's loss caused by not promoting. Often the market size for a specific product is steady. So, one firm's gain is likely corning from its competitors' loss.

Jumbo \ Shrimpy No promotion April June No promotion $3.907.000 $3.615.000 $3,594,600 April $4.103.000 $3.871.000 $3,513,800 June $4.008.400 $3,498,400 $3.760.600

Problem 9-5:

(c) Profit (both promote in ApriV44) = $3,871,000 Profit (both promote in June/66) =$3,760,600 Profit (Jumbo June, Sbrimpy April /64) = $3,498,400 Profit (Jumbo April, Sbrimpy June /46) = $3,513,800

Re-defme two variables: W, : workforce, in terms of # of shifts (per shift= 100 employees) 0 , : overtime (hours per shift)

The production plan is shown as follows:


9-49


9-50

12

12

12

12

Profit (Q&H promotes in April, Unilock no promotion)= $1,520,174 Profit (Q&H promotes in June, Unilock no promotion)= $1,611,294 Also, from (a), profit (both no promotion)= $1,607,850.

Minimize 160*1000~::rV, + 15*100L:O, +100L:I, +1000L:F; t=l

1=1

1=1

1=1

Subject to:

From the results, ifQ&H does not promote in the right month it tends to lose even ifUnilock does not promote. On the other hand, ifUnilock does promote, then Q&H would expect loss of profit.

Inventory constraints: 1 H + 1', -1 , = iJ" t = 1, .. ,12

10 = 112 = 150 (tons) I , ;2100, t= 1, ... ,11

(c) Profit (both promote in ApriV44) = $1,466,410 Profit (both promote in June/66) = $1,477,050 Profit (Q&H April, Unilock June /46) = $1,259,774 Profit (Q&H June, Unilock April /64) = $1,253,614

Overtime constraints: 0 , - 20W,

<;

The production plan is shown as follows:

0, t = 1, ... ,12

44


Period

0 1 2 3 4 5 6 7 8 9 10 11 12

F;-0,-160W, <;0, t=I, ... 12 Workforce constraints:

W, = 2,

t = 0, ... ,12

(a) Total Cost = Total Revenue = Profit =

$7,453,150 $9,061,000 $1,607,850

Pt Period

66

46

64

Production Production Production Production

291 320 320 320 214 209 291 277 304 291 320 329

230 305 320 320 320 320 218 208 304 291 320 329

263 320 320 320 228 83 291 277 304 291 320 329

230 301 277 188 320 320 233 222 304 291 320 329

Production

0 1 2 3 4 5 6 7 8 9 10 11 12

(d) There are three strategies for both Q&H and Unilock, which leads to a total of 9 combinations of strategies, as shown in the table below. Q&H would achieve the highest profit if it promoted in June and Unilock did not promote at al~ and it would receive the lowest profit if it promoted in June and Unilock promoted in April. In order to achieve a middle ground, it would be beneficial for Q&H to coordinate with Unilock so that they either don't promote at all or promote in the same month.

230 301 277 302 285 278 291 277 304 291 320 329

Q&H IUniiock No promotion April June

No promotion April

June

$1,607,850 $1,366,250 $1,385,450 $1,520,174 $1,466,410 $1,259,774 $1,611,294 $1,253,614 $1,477,050

Note: number in each cell represents Q&H's profit (b) Profit (Q&H no promotion, Unilock promotes in April)= $1,362,250 Profit (Q&H no promotion, Unilock promotes in June)= $1,385,450


9-51


9-52

(e) We frrst identifY the minimum profit for each strategy for Q&H, as indicated by the numbers in bold in the table below. The maximum of these three minimum profits is $1,366,250. SO, Q&H should not undertake any promotion at all throughout the year.

Q&H IUniiock No promotion April June

No promotion $1,607,850 $1,520,174 $1,611,294

April $1,366,250 $1,466,410 $1,253,614

2.

(a) If the order quantity is 100 then the number of orders placed in a year are: D/Q = 109500/100 = 1095. So, 1095 orders are placed each year at a cost of$1000/order. Thus, the total order cost is $1,095,000.

June $1,385,450 $1,259,774 $1,477,050

Cycle inventory = Q/2 = 100/2 = 50 and the annual inventory cost is (50)(0.2)(500) = $5,000 (b) If a load of 100 units has to be optimal then corresponding order cost can be computed by using the fo llowing expression:

Problem 9-6:

Q=~2DS

Fart of the formulation needs to revised 12

12

12

12

hC

12

Minimize 160* IOOOLW, + 15 *IOOL 0 , + IOOLl , + IOOOLf; + 2300L C, t =l

1=1

1=1

1=1

r=~-;:-:c::-::-:-::;-

100 =

1=1

Subject to:

S = (100)2 (0.2)(500) = $ 4.57 er order (2)(109500) p

Inventory constraints: IH+P,+C, -I,=D"

(2)(109500)S (0.2)(500)

This analysis is shown in worksheet 11-2.

/=1, .. ,12

C, ;:-0

3.

Other constraints remain the same as 9-5

(a) We first consider the case of ordering separately:

(a) to (e) are exactly the same as 9-5, as none of the promotion/no promotion strategy results in outsourcing anything from the third party.

For supplier A: 2(20000)( 400 + 100) = 4,472 units/order (0.2)(5) Total cost = order cost + holding cost = (20000/4472)(500) + (4472/2)(0.2)(5) = $4,472

Order quantity (Q) =

Chapter 11: Managing Economies of Scale in the Supply Chain: Cycle Inventory . order quantity . IS . given . l. The economic by

~2DS . problem: - - . In this

Similarly, for suppliers Band C the order quantities are 1768 and 949 and the associated total costs are $1,414 and $949, respectively.

hC

D = 109,500 (i.e., 300 units/day multiplied by 365 days/year)

So, the total cost is $6,835

S = $1000/order H = hC = (0.2)(500) = $100/unitlyear

(b) In using complete aggregation, we evaluate the order frequency (n*) as follows:

So, the EOQ value is 1480 units and the total yearly cost is $147,986

So, n* of the case is

=

D AhC A + DBhC B + DchCc 2S*

The cycle inventory value is EOQ/2 = 1480/2 =740 S* = 400 + 3(100) = $700 Worksheet 1l.1 provides the solution to this problem.


9-53


9-54

So, n* ~

20000(0,2)(5) + 2500(02)( 4) + 9000(0,2)(5) ~ 4 orders/year 2(700)

This analysis is shown in worksheet 11 -4

For supplier A: Q

~

5. We solve this problem using a similar approach as in the previous case except the equation used for computing the order quantity at a particular price level in the presence of marginal unit quantity discounts is as shown below:

D/n ~ 20000/4 ~ 5000 units/order

Total cost ~ order cost + holding cost ~ 4(500) + (5000/2)(0.2)(5)

~

$4,500

Similarly, for suppliers Band C the order quantities are 625 and 225 and the associated total costs are $650 and $513, respectively.

. level C Q at for a pnce

~

~2D(S+V-qC) " , hC,

For price ~ $1.00 per unit

So, the total cost is $5,663. Worksheet 11-3 provides the solution to this problem

Q~

2(20000)(12)(400+ 0- (0)(1)) (0.2)(1)

~

30 984 ,

4.

Since Q > 19,999, we adjust Q

(a) This is a quantity discount model and the decision is to identify the optimal order quantity in the presence of discounts. We evaluate the order quantities at different unit prices using the economic order quantity equation as shown below:

The same procedure is followed for the other unit prices and the optimal quantity is 63,246 at a total cost of $242,663.

~

20,000 and the corresponding total cost is $ 246,800

Worksheet 10 -5 shows the analysis and problem solution For, price

~

$1.00 per unit 6. In the case of no promotion, we can use the EOQ expression to compute the order quantity.

Q~EOQ~

2(20000)( 400)(12) ~ 30 984 (0.2)(1) ,

So,

Since Q > 19,999

2(1000)(52)(200) ~ 6450 units/order 0.25(2)

In the presence of discount,

We select Q ~ 20,000 (break point) and evaluate the corresponding total cost, which includes purchase cost + holding cost + order cost Total Cost ~ (20000)(12)(0.98) + (20000](0.2 KO.98) + (20000)(12) (400) 2 20000

Q~

Qd_~+ CQ'

~ $ 241,960

(C-d)h

Similarly we evaluate the EOQs at prices ofp ~ 0.98 (Q ~ 31298) and p ~ 0.96 (Q ~ 31623, which is not in the range so use Q ~ 40001). The corresponding total costs are $241,334 and $236,640.

C-d

Qd ~ 0.2(1000)(52) + 2(6450) ~ 30 277 units/order , (2 - 0.2)025 (2 - 0.2) Dominick's order given the short-term price reduction must be 30,277.

So, the optimal value ofQ

~

40001 and the total cost is $236,640

The cycle inventory is Q/2

~

40001/2 ~ 2000.5

Worksheet 11-6 shows the solution to this problem

(b) If the manufacturer did not offer a quantity discount but sold all plywood at $0.96 per square foot then Q ~ 31,623 and the total cost is $ 233,436


9-55


9-56

7. In this problem, the goal is to obtain an annual demand for which TL costs are equal to LTL costs. As the annual demand increases, the optimal batch size grows making TL more economical. Above the threshold

obtained, Flanger should use TL. Below the threshold they should use L TL. 8. Thus, we equate the two cost functions as shown below: (a) LTL costs with one supplier per truck:

Optimal order quantity QTL -

Optimal order quantity QTL ~ 1_2-,-(3-,-0-,-00--'-)(c..,1_00--,-) ~ 245 units (0.2)(50)

2(D)(500) (0.2)(50)

Annual order cost ~

Time between orders

~(100)

J

245 - 12 ( 3000

~

0.98 months

QTL

Annual trucking cost

~ ~(400)

Annual order cost ~ 3000 (100) ~ $1225 245 Annual trucking cost ~ 3000(1) ~ $3000

QTL

~

Annual holding cost

Total Cost for TL

~

QTL (10) 2

~ ~(100)+~(400)+ QTL QTL

~

Annual holding cost

Qn

(10)

Total Cost for TL

2

~

245 (10) ~ $1225

2

$5449

LTL Costs:

Optimal order quantity QLTL ~

Cbl TL costs with one supplier per truck:

2(D)(100) (0.2)(50)

Optimal order quantity QTL Annual order cost ~

~(100)

Annual trucking cost Annual holding cost

Total Cost for TL

QLTL ~

~

D(1)

. between orders TIme

~

2(3000)(1 000) ~ 775 units (0.2)(50)

J

(775 - 12 3000

~

3.1 months

QLTL (10) 2

~ ~(100)+ D(1)+ QLTL

Annual order cost ~ 3000 (100) ~ $387 775 (10)

Annual trucking cost

~

3000 (900) ~ $3486 775

Equating the TL and L TL costs results in a demand value of 3056. If the demand goes beyond this value then the TL option will prove economical and if the demand is below this value then LTL is the optimal choice.

Annual holding cost

~

775 (10) ~ $3873

Worksheet 10-7 solves this problem in EXCEL by using the solver option.

Total Cost for TL

(b) If the unit cost is increased to $100 then the new threshold is 6112. Thus, as unit cost increases the LTL

(c) TL costs with two suppliers per truck:

QLTL

2

~

2

$7746

option becomes preferable. In the presence of aggregation we solve for optimal order frequency n*

(c) If the L TL cost decreases to $0.8 per unit then the new threshold value becomes 4775.


9-57


9-58

(a) So, n* of the case of 2 suppliers is

~

Fast moving products:

S*

~

800 + 2(100) + 2(100)

Thus, n* =

~

$ 1200

EO

(3000)(10) + (3000)(10) ~ 5 orders/year 2(1200)

Optimal order quantity (Q) per supplier

~

_ _ Q- Q-

/2(30000)(200) 5(0.5)

3464 unitslbatch

Days of demand ~ 3464 (365) ~ 42 30000

D/n ~ 600 units Annual setup cost ~ 30000 (200) ~ $1732 3464

Order cost per product ~ 3000 (100) ~ $500 600 Annual trucking cost per product ~ 3000 (800 + 100(2)) / 2 ~ $2500 600

Annual holding cost

Annual holding cost per product ~ 600 (1 0) ~ $3000

~

3464 (0.5)(5)~ $1732 2

Total cost per product ~ $3464

2

Total cost for all fast moving products (5 products) Total Cost for TL

~

~

$17320

$6000 Similar analysis for the medium and slow products results in batch sizes of 2191 and 980, respectively.

(d) The optimal number of suppliers that need to be grouped is 4 with an order quantity of 490 units and total cost of $4,899. The truck capacity of 2000 units would not be sufficient if more than 4 suppliers are aggregated.

(b) The total costs for three product groups are:

(e) When demand is 3000 the aggregated TL option with four suppliers is optimal, and when the demand decreases to 1500 the L TL option is optimaL As demand increases to 1800, the aggregated TL option with four suppliers is optimaL

Fast moving ~ $17,320 Medium moving ~ $21,908 Slow moving ~ $34,292

Worksheet 11-8 shows the results and analysis for this problem So, the total cost across all products is $73,522. 9. We compute the total cost for the fast moving product and a similar approach can be utilized to evaluate the total costs for medium and slow moving products.

(c) For the fast moving products the total time required is:

30000 + 30000 (0.5) ~304.3 hours 100 3464 Similarly, for the medium and slow moving products the number of hours needed is 122.7 and 25.2, respectively.

Worksheet 11-9 demonstrates these computations.


9-59


9-60

10.


(a)

The days of inventory carried at the large customer are:

In situations where full truckloads are used the number of deliveries for large, medium, and small customers in a given year is 5, 2, and 0.7, respectively, which is obtained by dividing annual demand by truck capacity in each case.

(7.1/2)(365)/60

~

22 days of inventory

For the medium and small customers the total costs are $11,225 and $6,481, respectively, and the inventory carried by these customers is 34 and 59 units, respectively.

For the Large customer: Thus, the overall cost of this plan for the three customers is $35,454 Order quantity

~

Q

~

12 units/order (truck capacity) (c) In this case we utilize complete aggregation, i.e., each truck has products that are shipped to all customers.

The transportation cost for large customer is given by: In the presence of aggregation we solve for optimal order frequency n* nL(S+sL)

~

5(800+ 250)

~

$5250 So, n* of the case is

The holding cost is given by: (12/2)(10000)(0.25)

~

DLhC L +DMhCM + DshC s 2S*

=

$15,000 S*

~

800 + 3(250)

~

$1550


(12/2)(365)/60

~

60(0.25)(10000) + 24(0.25)(10000) + 8(0.25)(10000)

So, n* =


8.6 orders/year

2(1550)

37 days of inventory For the Large customer:

For the medium and small customers the total costs are $17,100 and $15,700, respectively, and the inventory carried by these customers is 91 and 274 units, respectively.

Order quantity

Thus, the overall cost of this plan for the three customers is $53,050

Transportation cost:

Worksheet 11-10 shows these evaluations.

nL(S+SL)

(b) In this case, we evaluate separate EOQs for each of three cases.

The holding cost is given by:

For the Large customer:

(6.97/2)(10000)(0.25)

Order quantity

~

Q

Number of orders (nL)

~

D/Q

~

6017.1

~

~

8.5(800+250)

~

~

~

~

~

60/8.6

~

6.97 units/order

$9,044

$8,707

~

21.2 days of inventory

For the medium and small customers the total costs are $5,636 and $3,314, respectively, and the inventory carried by these customers is 21.2 and 21.2 units, respectively.

$8874

Thus, the overall cost of this plan for the three customers is $26,702 (d) In the case of partial aggregation we evaluate relative delivery frequency. In this case not every customer is supplied with the product in every order.

$8,874


8.6(800+250)

(6.97/2)(365)/60

The holding cost is given by: (7.1/2)(10000)(0.25)

D/n*


8.5 orders/year

The transportation cost for large customer is given by: nL(S+SL)

~

Q


2(60)(800 + 250) ~ 7.1 units/order 0.25(10000)

~

~

~

9-61


9-62

Step 1 we identify most frequently ordered product assuming each product is ordered independently.

These evaluations are shown in different worksheets in 11-10

For the large customer:

11. (a) From the retailer's standpoint, the optimal order quantity is:

0.25(10000)(60) ~ 8.5 orders/year 2(800+ 250)

Q~

For the medium and small customers the order frequency is 5.3 and 3.1, respectively.

2(240000)(200) ~ 9798 units/order 0.2(5)

Thus, the most frequent ordering of the product comes from the large customer.

Retailer costs:

Step 2: We identify the frequency with which other customer orders are included into the most frequently ordered.

Order costs ~ (240000/9798)(200) ~ $4,899 Holding costs ~ (9798/2)(0.2)(5) ~ $4,899 Retailer total cost ~ $9,798

We evaluate

nM and nL

Crunchy's costs:

Since we are already accounting for the fixed cost for the large customer, we only consider the product specific costs for medium and small customers. Thus:

n ~ ~hCMLJM M

~

and similarly, n L

~

2s M

0.25(10000)(24) 2(250)

~

11

Total cost

~ ; ; /nM ~ 8.5111 ~ 0.77 ~> we

~

$37,232

(b) In jointly optimizing the order quantity is:

6.3

We now evaluate the frequency with which medium and small customers order relative to the large customer.

mM

Order costs ~ (240000/9798)(1000) ~ $24,495 Holding costs ~ (9798/2)(0.2)(3) ~ $2,939 Retailer total cost ~ $27,434

Q

2(240000)(200 + 1000) ~ 18974 units/order 0.2(5) + 0.2(3)

round up to the closest integer, i.e., 1 Retailer costs:

Similarly, m s

~

2

Step 3: Having decided the order frequency for each customer, we recalculate the order frequency for the most

Order costs ~ $2,530 Holding costs ~ $9,487 Retailer total cost ~ $12,017

frequently ordering customer, i.e., the large customer: Crunchy's costs:

DLhC L +DMhCM + DshC s

n~

~

60(0.25)(10000) + 24(0.25)(10000) + 8(0.25)(10000)

2(S+SM/mM +SL/mL) 9.37 orders/year

Order costs ~ $12,649 Holding costs ~ $5,692 Retailer total cost ~ $18,341 Total cost ~ $30,358

2(800 + (250/1) + (250/2))

Step 4: For medium and small customers, we evaluate the order frequency: nM

ns

~ ~

nimM

nims

9.3711 ~ 9.37 9.37/2 ~ 4.68

~

~

The total costs are evaluated as in the previous problem except for the fact that the order costs for medium and small customers only includes the product specific costs.

The total cost for tailored aggregation is $ 26,693


9-63


9-64

(c) In this case, we equate the total costs associated with ordering at the EOQ and the breakpoint levels for the retailer in determining the discount level. The goal seek option is utilized to obtain the discount per unit at

2.

break point, which is equal to $0. 00917. Worksheet 11-11 provides details of the analysis. Dr - (T+L) D

~

(2+3)(300)

~

1500

12. (a) Given that Demand is estimated to be equal to 2,000,000 - 2,000p and the production costs for Orange is $100 per unit, we get the optimal price by setting P equal to (2,000,000 + 2,000(100))/4000 giving Orange a wholesale price equal to $550. At this wholesale price Good Buy would set a retail price equal to (2,000,000 + 2,000(550))/4000 or $775.

SS -

hi (CSL)

OUL

~

X CYr -

D(T+L) + ss

hi (0.95) x 447 ~

1500 + 736

~ ~

736 (where, hi (0.95)

~

NORMSINV (0.95))

2236

Excel Workslieet 12-2 illustrates tliese computations

Profits for Orange at this price would be $202,500,000 and Good Buy would have a profit of $101,250,000.

3.

(b) If Orange offers a $40 discount to Good Buy, then the new price would be (2,000,000 + 2,000(510))/4000 or $755. Good Buy would pass along $20 or 50% of the discount offered by Orange. Worksheet 11-12 provides details of the analysis.

Dr CY L

~

-

LD

~

(2)(300)

JL CY D

~

600

../2(200) ~ 283

-

13. (a) Good Buy should purchase is lots equal to SQRT[(2DS)/hC] SQRT {(2x450000x10000)/(.2x550)] ~ 9,045

~

We use the following expression to determine the safety stock (ss): ESC ~ -ss[l- F s(~)]+ CY Lf s(~) O'L

(b) Given the $40 discount by Orange for the next two weeks, Good buy should adjust its lot size to (40)(450000)/(550-40)(.2) + (550x9045)/(550-40) ~ 16,814. Equation 11.15

O'L

ESC - -ssll -NORMDIST(ss/CYr, 0, 1, 1)] + 0rNORMDIST(ss/CYr, 0, 1, 0). We utilize the GOAL SEEK function in EXCEL in determining safety stock (ss) by using ss as the changing value that results in an ESC value of 5.

The lot size increase about 86%.

Worksheet 11-13 provides details of the analysis.

Excel Workslieet 12-3 illustrates tliese computations. Goal Seek set-up:

Chapter 12: Managing Uncertainty in a Supply Chain: Safety Inventory

SET CELL C29 TO VALUE 5

1. BY CHANGING CELL C27 D r ~ LD

~

(2)(300)

~

600 This results in a ss value of 477 and the reorder point of:

(JL -

SS

JL CY D

-

../2 (200) ~ 283

~ hi (CSL) X CYr ~ hi

ROP ~ DL + ss

~

ROP ~ DL + ss

(0.95) x 283

600 + 465

~

~

465 (where, hi (0.95)

~

NORMSINV (0.95))

~

600 + 477

~

1,077

4.

1065

D r ~ LD

~

(2)(250)

~

500

Excel Worksheet 12-1 illustrates these computations


9-65


9-66

DL SS -

ROP - ss

CSL

~

600 - 500

~

F(DL + SS, Do "L)

~

~

LD

~

(4)(800)

"L - Ji"D -

100

F(600, 500, 212)

~

NORMDIST (600, 500, 212, I)

~

~

3200

.J4(lOO)~200

Coefficient of variation - rs / 11

0.68

ss per store ~ Fs· i (CSL)

ESC~-ss[l- FS(~)]+"ds(~) O'L

~

O'L

Total safety inventory ESC

~

-ss[1 -NORMDIST(ss/"L, 0, I, I)] + 0LNORMDIST(ss/"L, 0, I, 0)

Fill rate (fr)

~

1- (ESC/Q)

~

1- (43.8611000)

~

~

43.86

X

~

100/800 ~ 0.13

"L ~ Fs· i (0.95) x 200 ~ 329 (where, Fs· i (0.95) ~ NORMSINV (0.95))

(329)(900)

Total value of safety inventory

0.96

~

~

~

296,074

(296,074)(30)

~

$8,882,210

Total annual safety inventory holding cost ~ (8,882,210)(0.25)

Excel Worksheet 12-4 illustrates these computations

Holding cost per unit sold ~ 2220552/(800)(900)

5.

~

~

$2,220,552

$308

Aggregated Option:

D L ~ LD

~

(2)(250)

~

500

- 'L "D+D sL - ,,I

0 L -"

SS -

2

2 2 -

hi (CSL)

X

DC ~ kD ~ (900)(800) ~ 720000

2x 150 + 2

250 x1.5 2

2

431 ~

"L - hi (0.95) x 431 ~ 709 (where, hi (0.95) ~ NORMSINV (0.95))

DL - LD c ~ (4)(800)(900) ~ 2,880,000

ESC~-ss[l- Fs(~)]+"ds(~) O'L

ESC

~

-ss[1 -NORMDIST(ss/"L, 0, I, I)] + 0LNORMDIST(ss/"L, 0, I, 0)

Fill rate (fr)

~

1- (ESC/Q)

~

"L

O'L

~

1- (911000)

~

~

"firs g ~

ss ~ Fs· i (CSL)

9

X

.J4 (3000) ~ 6000 "L ~ Fs· i (0.95) x 6000 ~ 9869 (where, Fs· i (0.95) ~ NORMSINV (0.95))

Total safety inventory

0.991

~

9869


Standard deviation of lead time

Required safety inventory

1.50 1.00 0.50 0.00

~

(9869)(30)

~

$296,070

Total annual safety inventory holding cost ~ (296070 )(0.25) Holding cost per unit sold ~ 74018/(800)(900)

709 539

~

~

$74,018

$0.1

Savings in the holding cost per unit sold from aggregation ~ $3.08 - $0.1

405

~

$2.98

349 Following are the evaluations for the Cashmere Sweaters:

Excel Worksheet 12-5 illustrates these computations Disaggregated Option: 6.

DL

~

LD

~

(4)(50)

~

200

Following are the evaluations for the Khaki pants:

"L - Ji"D -

Disaggregated Option:


9-67

.J4(50)~ 100


9-68

Coefficient of variation ~

CY / I-'


(IL ~ Fs· i (0.95) x 100 ~ 164 (where, Fs· i (0.95) ~ NORMSINV (0.95))


~

X

~

50/50 ~ 1

(164)(900)


~

~

France: D L ~ LD (I L -

147,600

(147,600 )(100)

~

$14,760,000

Total annual safety inventory holding cost ~ $14,760,000 )(0.25) Holding cost per unit sold ~ $3,690,000 1/(50)(900)

~

~

(8)(3000)

JL (I D

ss at France ~

$3,690,000

~

-

(CSL)

$82

The ss at the other five countries is evaluated in a similar manner, which results in a total ss for Europe of

48,384 Aggregated Option:

DC ~ kD ~ (900)(50) ~ 45000

DC =

DL ~ LD c ~ (4)(50)(900) ~ 180000

ss

~

hi (CSL)

X

(IL

4935


CY,2 -

~

.[iCY;

ss ~ Fs· i (CSL) ~

3000 + 4000 + 2000 + 2500+ 1000 + 4000

~ 16500

(4935)(100)

2

2

2

2

2

";2000 + 2200 + 1400 + 1600 + 800 + 2400

2

~ 4445.22

DL - LD c ~ (8)(16500) ~ 132,000

(IL ~ hi (0.95) x 3000 ~ 4935 (where, hi (0.95) ~ NORMSINV (0.95)) ~

~ = ~t

(J'

-!4(l500)~ 3000


i:D, ~ 1=1

~ ,jkCY - ,J9OO(50) ~ 1500

.[iCY; -

(IL - F S· i (0.95) x 5657 ~ 9305

X

(where, Fs· i (0.95) ~ NORMSINV (0.95))

Aggregated Option:

(I L -

24000

.J8 2000 ~ 5657

F S· i

Note: the above are also incorrect on the worksheet.

(J' ~

~

~

~ .J8(4445.22)~ 12573 X

(IL ~ Fs· i (0.95) x 12573 ~ 20,681 (where, Fs· i (0.95) ~ NORMSINV (0.95))

$493,456 Inventory savings from aggregation ~ 48,384 -

Total annual safety inventory holding cost ~ (493456)(0.25)

~

20,681~

27,704

$123,364 Excel Worksheet 12-7 illustrates these computations.

Holding cost per unit sold ~ 123364/(50)(900) ~ $2.74 8.

Savings in the holding cost per unit sold from aggregation ~ $82.84 - $2.74

~

$79.50

Centralization results in savings for both products, but it is evident that savings in holding cost per unit sold

(a) Disaggregated Option:

from aggregating Cashmere Sweaters is higher than Khaki pants. So, Cashmere Sweaters are better for centralization.

From the previous problem, we know that the total ss for Europe is 48,384

Excel Worksheet 12-6 illustrates these computations.

Holding cost ~ (200)(0.25)(48384)

7.

Aggregated Option: ss

~

~

$2,419,200

20,681

Disaggregated Option:


9-69


9-70

Holding cost ~ (200)(0.25)(20681)

~

$1,034,036

The following table shows the savings as the correlation coefficient increases from 0 to 1 with increments of

0.2 Savings from aggregation

~

$2,419,200 -$1,034,036

~

$1,385,164

(b) If the $5/unit additional cost of assembly from centralization then the total additional costs (132000)(52)(5) ~ Savings ~ $1,385,164 - So, it is not economical to aggregate

Corr.Coeff. 995876.3 0 0.2 0.4 0.6 0.8 1

~

(c) If the lead time changes to 4 weeks, we evaluate the safety stocks and associated costs in a similar manner.

The holding cost tram the dis aggregated option

~

(200)(0.25)(34213)

The holding cost from the aggregated option ~ (200)(0.25)(14623)

~

~

$1,710,650

Replenishment Lead Time (Weeks) 10 12 4 6 8 $979,474 $1,199,606 $1,385,185 $1,548,684 $1,696,498 $704,191 $862,454 $995,876 $1,113,424 $1,219,694 $489,462 $599,466 $692,203 $773,907 $847,772 $307,211 $376,255 $434,462 $485,743 $532,105 $146,047 $178,870 $206,542 $230,921 $252,961 $0 $0 $0 $0 $0

$731,150 Excel Worksheet 12-9 illustrates these computations.

Savings from aggregation

~

$1,710,650 - $731,150

~

$979,500 10.

Excel Worksheet 12-8 illustrates these computations. Using Sea Transportation: 9.

Average batch size ~ DT

~

(5000)(20)

~

100,000

Since the demand at various locations is not independent, we utilize the following expressions for the aggregated option:

ss k

var(Dc)~ LOT+2 L Pij"i" j

~

hi (CSL)

X "[

~

~

hi (0.99) x 24000

55832 (where, hi (0.99)

Days of safety inventory

~

55832/5000

~

11.17 days

Average cycle inventory

~

batch size/2

~

100000/2 ~ 50,000

~

NORMSINV (0.99))

i>j

i=l

Days of cycle inventory

~

50000/5000

For P ~ 0.2

Total inventory cost (cycle + safety)

"b ~ ~var(DC) ~~20002 + ... + 2400 2 + 2(0.2){(2000)(2200) + ... + (800)(2400)

Transportation cost per year

~

~

10 days

(50000 + 55832)(100)(0.2)

(0.5)(5000)(365)

~

~

~

$2,116,640

$912,500

Annual Holding Cost + Transportation Cost ~ $2,116,640 + $912,500 ~ $3,029,140 "L

~ .,[ieJ g ~ ~20002 + ... + 2400 2 + 2(0.2){ (2000)(2200) + ... + (800)(2400)} ,J8 ~

ss

In-Transit Inventory

17307

~ Fs· (CSL) i

~

DL

~

(5000)(36)

Cost of Holding In-Transit Inventory X "[

~ Fs·

i

(0.95) x 17307

~

i

28467 (where, Fs· (0.95)

Inventory savings from aggregation ~ 48,384 -

28,467~

~

NORMSINV (0.95))

~

~

180,000

(180000)(100)(0.2)

Total Costs (including in-transit inventory)

19,918

Holding cost savings from aggregation ~ (200)(0.25)(19918)

~

~

~

$3,600,000

$3,029,140 + $3,600,000 ~ $6,629,140

Using Air Transportation: $995,900


Average batch size ~ DT

9-71

~

(5000)(1)

~

5,000


9-72

11. (JL -

ss

JL" D - .J4( 4000) ~ 8,000

~ hi (CSL)

X "[

~ hi

(0.99)

X

Using Sea Transportation: ~

8000

18,611 (where, hi (0.99)


~

18611/5000

~

3.72 days


~

batch size/2

~

5000/2

~

"L -


~

2500/5000

Total inventory cost (cycle + safety) Transportation cost per year

~

~

~

~

ss - hi (CSL)

(2500 + 18611)(100)(0.2) ~

~

~

DL

~

(5000)(4)

Cost of Holding In-Transit Inventory

~

~

OUL

$2,737,500 ~

(20000)(100)(0.2) ~

X "[ -

~

(5000)(20)

hi (0.99) x 29933

~

D(T+L) + ss

~

Days of cycle inventory ~

~

~

100,000

69,635 (where, hi (0.99)

~

~

50000/5000

~

~

~

~

349,635

100000/2 ~ 50,000

10 days

(50000 + 69635)(100)(0.2)

(0.5)(5000)(365)

~

~

$2,392,700

$912,500

Annual Holding Cost + Transportation Cost ~ $2,392,700 + $912,500

Based on the results air transportation would be the optimal choice, but if Motorola does not have the ownership of in-transit inventory then sea transportation is the optimal choice.

~

In-Transit Inventory


~

DL

(5000)(36)


~

NORMSINV (0.99))

13.93 days

~

batch size/2

Transportation cost per year

$3,559,720

~

69635/5000

Total inventory cost (cycle + safety)

$400,000

$3,159,720 + $400,000

~

~

5000(36+20) + 69635


$3,159,720

20000


~

.J36 + 20( 4000) ~ 29,933

-


$422,220

Annual Holding Cost + Transportation Cost ~ $422,220 + $2,737,500 In-Transit Inventory

.JL + T (J'D

DT

2,500

0.5 days

(1.5)(5000)(365)

~

Average batch size

NORMSINV (0.99))

~

~

$3,305,200

180,000

(180000)(100)(0.2)


~

~

$3,600,000

$3,029,140 + $3,600,000

~

$6,905,200

Using Air Transportation: Average batch size

ss ~ Fs· i (CSL)

X "[

~

DT

~ Fs· i

Days of safety inventory OUL - D(T+L) + ss

~


9-73

(5000)(1)

~

~

~ ~

5,000

(0.99) x 8944 ~ 20,807 (where, Fs· i (0.99) ~ NORMSINV (0.99)) 20807/5000

~

4.16 days

5000(1+4) + 20807



~

batch size/2 2500/5000

~

~

~

45,807

5000/2

~

2,500

0.5 days


9-74

Total inventory cost (cycle + safety) Transportation cost per year

~

~

(2500 + 20807)(100)(0.2)

(1.5)(5000)(365)

~

~

$466,150

$2,737,500

Annual Holding Cost + Transportation Cost ~ $466,150 + $2,737,500 In-Transit Inventory

~

~

DL

(5000)(4)


~

~

We use the GOAL SEEK function in determining the safety stock (ss) by using ss as the changing value that results in an ESC value of IS

~

$3,203,650

Goal Seek set-up:

20000

SET CELL A15

(20000)(100)(0.2) ~


~

$400,000

$3,203,650 + $400,000

~

TO VALUE 1.5 $3,603,650

BY CHANGING CELL Dl2 This results in an ss value of 271 and a reorder point of ~ 300(2) + 271

Based on the results air transportation would be the optimal choice. Even if Motorola does not have the

~

871

ownership of in-transit inventory, air transportation is the optimal choice.

Excel Workslieet 12-13 illustrates tliese computations. Excel Worksheet 12-11 illustrates these computations. 14. 12.

(a) ss

~

ROP - DL

~

750 - 300(2)

~

750-600

~

150 Disaggregated Option:

(JL

~

JL CY D ~ ../2(100)

~ 141.42

F(DL + ss, DL CYr)

F(750, 600, 141.42)

CJL+T - .JL+T CJ D CSL

~

~

~

NORMDIST (SS/CYL, 0, 1,1)

~

-


ESC~-ss[l- Fs(~)]+cyds(~) O'L

~

1- (ESCIQ)

~

1- (1011500)

X

(where, hi (0.99)

O'L

ESC ~ -ss[l -NORMDIST(ssICYL, 0, 1, 1)] + C5LNORMDIST(ssICYL, 0, 1, 0) Fill rate (fr)

-J3+7(50)~ 158

85.56%

~

~


10

~

CYL ~ Fs· i (0.99) x 158 ~ 367.83 ~

NORMSINV (0.99))

(367.83)(25)

~

9195.7

Aggregated Option:

0.993

DC ~ kD ~ (25)(300) ~ 7500

If the ROP increased from 750 to 800 the fill rate will increase to 0.996

k


varCDc)~ LOT+2L Pij CY i CY j 1=1

l>j

13. Fill rate (fr) So, ESC

~

~

1- (ESCI1500)

~

0.999

CJ ~ ~ ../kcy - m(50) ~ 250 (we are assuming that p ~ O. If P is not 0 then the covariance terms have to be

1.5

included)

ESC~-ss[l- Fs(~)]+cyds(~)l O'L

O'L

ESC ~ -ss[l -NORMDIST(ssICYL, 0, 1, 1)] + C5 LNORMDIST(ssICYL, 0, 1, 0)


~

ss ~ Fs· i (CSL)

1.5

9-75

X

CYL ~ Fs· i (0.99) x 791 ~ 1839.14 (where, Fs· i (0.99) ~ NORMSINV (0.99))


9-76

Units savings from aggregation ~ 9195.7 - 1839.14 ~ 7356.56 Popular Variant all Inventories Centralized: Inventory savings

~

(7356.56) (10)

Annual holding cost savings Increase in delivery cost

~

~

~

$73,566

(73,566 )(0.2)

Demand per period

$14,712

~

(300)(25)(365)(0.02)

~

demand at large dealers + demand at small dealers (50)(5) + (10)(30) ~ 550

~

~

Standard deviation of demand per period ~

$54,750

..;r5-(1-5-)2;;--+-3-0-(5-)"'2 ~ 43.30

Since the increase in transportation costs outweighs the savings received from aggregation, we do not recommend aggregation for this case.

ss (at regional warehouse) ~ Fs· 1 (CSL)

(b) We utilize the same approach as in (a) by changing the daily demand mean and standard deviation to 5 and 4, respectively

reduction in safety inventory from complete aggregation

Units savings from aggregation ~ 735.66 - 147.13

production + transportation cost increase per year

Inventory savings

~

(588.52) (10)

Annual holding cost savings Increase in delivery cost

~

~

~

~

588.52

$ 5885.2

~

,fL

(J

D

~ Fs· 1 (0.95)

(597.74)(20000)(0.2) ~

~

~

x

J4( 43.30) ~ 142.45

246.73 + 493.46 - 142.45

~

597.74

$2,390,942.52

(550)(100)(52)

~

$2,860,000

(c)

($5885.2 )(0.2)

(5)(25)(365)(0.02)

holding cost savings per year

x

~

~

$1177

Popular Variant only Small Dealer Inventories Centralized:

$913

Demand per period

~

~

demand at small dealers (10)(30) ~ 300

Since the increase in transportation costs does not outweigh the savings received from aggregation, we recommend aggregation for this case.

Standard deviation of demand per period ~ ~30(5)2 ~ 27.39

(c) Yes. The benefit from aggregation decreases as p increases. When p aggregation in both cases.

ss (at regional warehouse) ~ F S · 1 (CSL)

~

0.5, we do not recommend

F S· 1 (0.95)

x

J4(27.39) ~ 90.09


reduction in safety inventory from small dealer centralization

~

493.46 - 90.09

15. (a)

holding cost savings per year

~

x

,fL

(J

D -

(403.36)(20000)(0.2)

production + transportation cost increase per year

~

~

~

403.36

$1,613,440

(300)(100)(52)

~

$1,560,000

Popular Variant at Large Dealer: (d) Centralizing inventories from small dealers and decentralizing at large dealers is the optimal strategy

Decentralized: ss (at each large dealer) ~ Fs· 1 (CSL) x ,fL (J D ~ Fs· 1 (0.95) ss (across all large dealers) ~ (5)(49.35) ~ 246.73

x

J4(15) ~ 49.35

(e) Similar analysis can be performed for the uncommon variant (See EXCEL Worksheet 12-15 for more details)

Popular Variant at Small Dealer:

(f) For the popular variant, centralize inventories from small dealers and decentralize at large dealers. For the uncommon variant, centralize all inventories.

Decentralized: ss (at each small dealer) ~ Fs· (CSL) x ,fL (J D ~ Fs· (0.95) ss (across all small dealers) ~ (30)(16.45) ~ 493.46 1

1

x

J4(5) ~ 16.45

Excel Worksheet 12-15 illustrates these computations. 16.

(b)


9-77


9-78

(394.76)(1000)(0.2)

~

$78,952.97

component cost increase per period ~ (252)(25)(52)

~

$327,600

liolding cost savings per year ss (tor the variant) ~ f<'s-l (CSL) x JL (J D - f<'s-l (0.95) x ..[4(200) ~ 657.94 ss (across all high volume variants) ~ (1)(657.94) ~ 657.94

~

additional cost at wliicli complete commonality is justified ~ 78952.97/(252)(52)

Low volume variant without component commonality:

~

$6.03

Commonality is not justified across low vo lume variants because of increased costs. Excel Worksheet 12-16 illustrates these computations.

ss (tor the variant) ~ f<'s-l (CSL) x JL (J D - f<'s-l (0.95) x ..[4(20) ~ 65.79 ss (across all low volume variants) ~ (9)(65.79) ~ 592.15

Chapter 13: Determining Optimal Level of Product Availability

(b&c)

Exercise Solutions

With complete commonality: l. Demand per period ~ demand for high volume variant + demand for low volume variant ~ (1000)(1) + (28)(9) ~ 12,52_--;;-_----::-

CS'L • ~ ~ ~ _50_ ~ 0.2941

Standard deviation of demand per period ~ Jl(200)2 + 9(20)2 ~ 208.81

C"+Cc

50+120

Optirnallot-size ~ O· ~ NORMINV ss ~ F S - 1 (CSL)

x

JL

(J

D

CCS'L . f'.J) ~ NORMINV(0.2941,100,40) ~ 78.34

~ F S- 1 (0.95) x 8686.91

Given that p reduction in safety inventory from complete commonality ~ 657.94 + 592.15 - 686.91

~

~

Expected profits holding cost savings per year

~

(563.18)(1000)(0.2)

~

$200, s

~

$30, c

~

$150:

563.18 ~

(p - s)f' NORMDIST«O - f')/(J. O. 1. 1)

$ll2,635.54 - (p - s)(J NORMDIST((O - f')/'0 O. 1. 0) - 0 (c - s) NORMDIST(O.

component cost increase per period ~ (1252)(25)(52)

~

f', '0

1)

$1,627,600

+ 0 (p - c) [I -NORMDIST(O. additional cost at which complete commonality is justified ~ ll2635.54/(1252)(52)

~

f', '0

I)] ~ $2.657

$l. 73 Expected overstock ~ (0 - f')NORMDIST«(O - f')/(J. O. 1. 1) + (J NORMDIST«(O - f')/(J. O. 1. 0)

Commonality is not justified across all variants because of increased costs.

~741

(d&e)

Expected understock ~

Only low vo lume variant uses commonality

(f'- 0)[1 -NORMDIST«(O - f')/(J. O. 1. 1)] + (J NORMDIST«(O - f')/(J. O. 1. 0)

Demand per period ~ demand for low volume variant ~ (28)(9) ~ 252

~

29.07

EXCEL worksheet 13-1 illustrates these computations

Standard deviation of demand per period ~ J9(20)2 ~ 60 ss ~ Fs- 1 (CSL)

x

JL (J D ~ Fs- 1 (0.95) x

2.

..[4(60) ~ 197.38

With revised forecasting: reduction in safety inventory from low volume variant using commonality ~ 592.15 -197.38 ~ 394.76


9-79


9-80

CSL ' = ~ = _50_ = 0.2941 C " +C,

4.

50+120

Optimallot-size =0' = NORMINV

CC::-'L

.f'.J) = NORMINV(0.2941,100,15) = 9l.88

Using the current policy:

""<'L' - ~ __ 30 __ 075 L0 C " + C, 30 + 10

Given that p = $200, s = $30, c = $150: Expected profits = (p - s)f' NORMDIST«O - f')/CY, 0, 1, 1)

Optimal lot-size =0' = NORMINV

CC::-'L

,f',J) = NORMINV(0.75,20000,10000) = 26,745

- (p - s)CY NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O, J.'. '0 1)

Given that p = $60, s = $20, c = $30:

+ 0 (p - c) [I -NORMDIST(O, J.'. (01)] = $4,121 Expected profits

=

(p - s)f' NORMDIST«O - f')/CY, 0, I, 1)

Expected overstock = (0 - f')NORMDIST«(O - f')/CY, 0, I, 1) + CY NORMDIST«(O - f')/CY, 0, I, 0) - (p - s)CY NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O, J.'. '0 1) =

2.78

+ 0 (p - c) [I -NORMDIST(O, J.'. (01)] = $472,889

Expected understock =

Expected overstock = (0 - f')NORMDIST«(O - f')/CY, 0, I, 1) + CY NORMDIST«(O - f')/CY, 0, I, 0)

(f'- 0)[1 -NORMDIST«(O - f')/CY, 0, I, 1)] + CY NORMDIST«(O - f')/CY, 0, 1,0) = 10.9

=


8,236

Using South America option:

3.

C"~ "C , = 3;~ 5 = 0.857

Mean demand during lead time =DL= (2000)(2) = 4000

CSL • =

Standard deviation of demand during lead time = (JL = CY DJL = 500.[i = 707

Optimal lot-size = 0' = NORMINV

CC::-'L

,f',J) = NORMINV(0.857,20000,10000)

= 30,676 Safety inventory = ROP - DL = 6000 - 4000 = 2000 Given that p = $60, s = $25, c = $30:

CSL = NORMDIST (6000, 4000, 707, 1) = 0.9977

Expected profits

Cost of overstocking = (0.25)(40) = $10 Justifying cost of under stocking: C U

OptimalCSL

=

HQ (1- CSL) D y ,",

~= _8_0_= C" + C, 80 +10

=

(p - s)f' NORMDIST«O - f')/CY, 0, I, 1)

- (p - s)CY NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O, J.'. '0 1)

10 x 10000 = $4ll (1- 0.9977) x 2000 x 52

+ 0 (p - c) [I -NORMDIST(O, J.'. (01)] = $521,024 Expected overstock = (0 - f')NORMDIST«(O - f')/CY, 0, I, 1) + CY NORMDIST«(O - f')/CY, 0, I, 0)

0.8889

=

11,407

Optimal safety stock = (NORMSINV (0.8889» (707) = 863 units

So, it is evident that using South America option results in increased expected profits, but also increases the


production capacity requirements needed at Champion.



9-81


9-82

Thus, it is benefical to utilize the tailored sourcing option due to increased expected profits. This option increases the optimal production lot size for Reguplo and decreases the lot sizes for each of the other three options.

5. Current sourcing (one line):

EXCEL worksheet 13-5 illustrates these computations Reguplo: 6.

CSL ' = ~ = ~ =0.8333 C"+ C, 100 + 20 Optimal lot-size =0' = NORMINV

CC::-'L

IBM: .f'.J) = NORMINV(0.8333, 10000, 1000) =

CS'L '=~=_35_=0.7447 C " +C, 35+12

= 10,967 Given that p = $200, s = $80, c = $100:


Expected profits = (p - s)f' NORMDIST«O - f')/", 0, 1, 1)

Given that p = $50, s = $3, c = $15:

- (p - s)" NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O,

+ 0 (p - c) [I -NORMDIST(O,

f',

f', '0

,f',J) = NORMINV(0.7447,5000,2000) = 6,316

Expected profits = (p - s)f' NORMDIST«O - f')/", 0, 1, 1)

1)

- (p - s)" NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O,

(01)] = $970,018


Each ofthe other models:

CSL ' = ~ = _11_0_ C" + C, 110 + 30

CC::-'L

f',

f', '0

1)

(01)] = $144,796

Expected overstock = (0 - f')NORMDIST«(O - f')/", 0, 1, 1) + "NORMDIST«(O - f')/", 0, 1, 0)

= 0.7857

= 1,622


CC::-'L

,f',J) = NORMINV(0.7857,1000,700) =

Similarly, the other three are evaluated and the results are summarized below:

= 1,554 Given that p = $220, s = $80, c = $llO:

Outputs Optimal cycle service level Optimal production size

Expected profits = (p - s)f' NORMDIST«O - f')/", 0, 1, 1) - (p - s)" NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O,


f',

f', '0

1)

Expected profits

(01)] = $81,421

Total expected profits = $970,018 + 3($81,421) = $1,214,280

Expected overstock

Tailored sourcing policy: The computations are exactly the same with revised data for Reguplo (c = $90) and for each of the other three models (c= $120) Total expected profits = $1,281,670


AT&T 0.7447 8,645

HP 0.7447 5,316

Cisco 0.7447 5447

-$207,245

-$109,796

- $106,776

2,028

1,622

1,785

Total production lot size = 6316 + 8,645 + 5,316 + 5,447 = 25,723 Total expected profits = $144,796 + $207,245 + $109,796 + $106,776 = $568,612 Total expected overstock = 1,622 + 2,028 + 1,622 + 1,785 = 7,057 (= amount donated to charity on average) EXCEL worksheet 13-6 illustrates these computations

9-83


9-84

7.

(b)

With aggregation: Cost of overstocking, Co =

$

0.50

Standard deviation ~ J2000 + 2500 + 2000 + 2200 ~ 4369

Cost of understocking, Cu =

$

5.00

CS'L ' ~ ~ ~ ~ ~ 0.8889

Mean demand Standard deviation of demand =

50,000

Anticipated demand

~

5,000 + 7,000 + 4,000 + 4,000 2

2

C"+C, 32+4 Optimal lot-size ~ 0' ~ NORMINV ~ 25,333 Given that p

~

~

2

20,000

2

CCSL ' ",J) ~ NORMINV(0.8889,20000,4369)

. CSL ~ Optunal

~

15,000

- C" - - ~ -5- ~ 0.91 C"+C, 5+0.5

$50, s ~ $14, c ~ $18: Optimal order quantity ~ (NORMSINV (0.91»(15,000) + 50,000 ~ 70,028

Expected profits

~

(p - s)" NORMDIST«O - ,,)/CY, 0, 1, 1) EXCEL worksheet 13-8 illustrates these computations

- (p - s)CY NORMDIST((O - ")/'0 0, 1, 0) - 0 (c - s) NORMDIST(O,


f',

'0 1)]

~

f',

'0 1)

$610,210

Expected overstock ~ (0 - ,,)NORMDIST«(O - ,,)/CY, 0, 1, 1) + CY NORMDIST«(O - ,,)/CY, 0, 1, 0) ~

5,568

As can be seen from the results above, postponement increases the expected profit and decreases the amount of overstock.

EXCEL worksheet 13-7 illustrates these computations 8.

(a)

Cost of overstocking, Co =

$

0.50

Cost of understocking, Cu =

$

100

Mean demand Standard deviation of demand =

50,000

Optimal CSL ~

15,000

~ ~ ~ _1_ ~ 0.67 C"+C,

1+0.5

Optimal order quantity ~ (NORMSINV (0.67»(15,000) + 50,000 ~ 56,461


9-85


9-86

9.


(a)

Expected overstock ~ (0 - f')NORMDIST«(O - f')/CY, 0, I, I) + CY NORMDIST«(O - f')/CY, 0, I, 0) ~

Mean demand =

5.000

Standard deviation of demand =

2.000

Cost of overstockinq. Co

$ 40.00

Order size =

6.000

1)] ~ $140,001

f', '0

1,224

Southern Hemisphere option:

~

CSL (implied by the order size)

CS'L ' ~ ~ ~ ~ ~ 0.90 C" + Cc 45 +5 ~

(Co)(CSL)/(l-CSL)

~

,f',J) ~ NORMINV(0.9,4000, 1750) ~ 6243

0.691 Given that p

~

Implied cost of understocking, Cu

CCS'L

Optimal lot-size ~O' ~ NORMINV

NORMDIST (6000-5000/2000)

(40)(0.691)/(1-0.691)

~

~

$125, s

~

$75, c

~

$80:

$89.64 Expected profits

~

(p - s)f' NORMDIST«O - f')/CY, 0, I, I)

(b) - (p - s)CY NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O, Mean demand =


Expected overstock ~ (0 - f')NORMDIST«(O - f')/CY, 0, I, I) + CY NORMDIST«(O - f')/CY, 0, I, 0)

Standard deviation of demand =

2,000

$ 40.00

Order size =

8,000 ~

~

~

1)] ~ $164,644

f', '0

2,326


NORMDIST (8000-5000/2000)

Implied cost of understocking, C u

(Co)(CSL)/(l-CSL)

~

~

0.933

(40)(0.933)/(1-0.933)

II. ~

$558.74

(a)


Mean demand during lead time

~DL~

(40)(1)

~

40

Standard deviation of demand during lead time ~

10.

Safety inventory

Current policy:

CSL

CS'L ' ~ ~ ~ _45_ ~ 0.6923 C" + C,

CCS'L

~

~

ROP - DL

~

45 - 40

NORMDIST (45, 40, 5, I)

~

~

Expected profits

$125, s ~

~

$60, c

~

~ CY DJL ~ 5.Jl ~ 5

5

~

(0.25)(4)

~

HQ (1- CSL)

Dr,",

$1

,f',J) ~ NORMINV(0.6923,4000, 1750) ~ 4879 Justifying cost of under stocking: C U

Given that p

~

(JL

0.8413

Cost of holding one unit for one year

45 + 20

Optimal lot-size ~O' ~ NORMINV

1)

5,000

Cost of overstockinq, Co

CSL (implied by the order size)

f', '0

$80:

1 x 200 (1- 0.8413) x 40 x 365

$0.086

(p - s)f' NORMDIST«O - f')/CY, 0, I, I)

- (p - s)CY NORMDIST((O - f')/'0 0, 1, 0) - 0 (c - s) NORMDIST(O,

f', '0


1)

9-87


9-88

(b)

With postponement:

HQ(CSL)

Justifying cost of understocking: C u

1 x 200 x 0.8413

(1- 0.8413) x 40 x 365

Anticipated demand ~ 20,000 + 20,000 + 20,000 + 20,000 ~ 80,000

$0.073

Standard deviation

~ .J8000 2 + 8000 2 + 8000 2 + 8000 2

= 16000

CSL . = ~ = _8_ = 0.6154

(c)

DesiredCSL~I-~-ICu

D

y

,",

C u+C u lx200 l.5 x 40 x 365

0.9909

8+5

Optima11ot-size ~ 0' ~ NORMINV ~

Desired safety stock ~ (NORMSINV(0.9909))(5)

~

11.8

CCS'L . f'.0") ~ NORMINV(0.6154,80000,16000)

84,694

Given tliat p ~ $20, s ~ $7, c ~ $12:

Desired reorder point ~ 40 + 11. 8 ~ 51. 8 Expected profits

~

(p - s)f' NORMDIST((O - f')/CY. O. 1. 1)


- (p - s)CY NORMDIST((O - f')/'0 O. 1. 0) - 0 (c - s) NORMDIST(O.

f', '0

1)

12.

+ 0 (p - c) [I -NORMDIST(O.

f', '0

I)]

~

$560.515

Without postponement: Expected overstock ~ (0 - f')NORMDIST((O - f')/CY. O. 1. 1) + CY NORMDIST((O - f')/CY. O. 1. 0) F or each box: ~

CS'L • = ~ = _1_0_ = 0.7692 C u+C u 10+3 Optima11ot-size ~ O· ~ NORMINV CCS'L . fl. 0") ~ NORMINV(0.7692,20000,8000) ~

Indifferent: At a unit cost of$IO.7 the two options. i.e .. postponement and no postponement would be indifferent. This unit cost is obtained by using the solver option in EXCEL by considering cell 21 as the changing cell while cell 35 is utilized as the target cell with a value of $673.446.

25,891

Given that p ~ $20, s ~ $7, c ~ $10: Expected profits

~


(p - s)f' NORMDIST((O - f')/CY. O. 1. 1)

- (p - s)CY NORMDIST((O - f')/'0 O. 1. 0) - 0 (c - s) NORMDIST(O.

+ 0 (p - c) [I -NORMDIST(O.

f', '0

I)]

~

13. f', '0

1)

The with and without postponement calculations are similar to problem 12 (EXCEL worksheet 13-13 illustrates these computations). but what is new in this problem is the tailored postponement which is discussed below:

$168.362

Expected overstock ~ (0 - f')NORMDIST((O - f')/CY. O. 1. 1) + CY NORMDIST((O - f')/CY. O. 1. 0) ~

Total expected profits

~

Tailored postponement:

6.965

4(168.362)

9.003

Popular style without postponement: ~

""<''L' = ~= _1_5_=0.6818 L0 C +C u 15 +7 Optima11ot-size ~ 0' ~ NORMINV CCS'L . f'.0") ~ NORMINV(0.6818,30000,5000)

$673.446

U

Total expected overstock ~ 4(6.965) Total production quantity

~

~

4(25.891)

27.860 ~

~

103.564


9-89

32,364


9-90

Given that p

~

Expected profits

$35, s ~ $13, c ~

~

Optimal lot-size ~ 0' ~ NORMINV

$20:

~

(p - s)1' NORMDIST((O -1')/", 0, 1, 1)

Given that p

- (p - s)" NORMDIST((O - 1')1'0 0, 1, 0) - 0 (c - s) NORMDIST(O, J1, '0 1)


J1, '0 1)] ~

Expected profits

$410,757

Standard deviation ~

J4000

~

8,000 + 8,000 + 8,000 2

~

+ 4000 + 4000 = 6928

~

Expected profits

~

~

Given that p

,1',0") ~ NORMINV(0,6182,24000,6928)

$21,4:

J1, '0 I)} ~

~

~

~

$28:

(p - s)1' NORMDIST((O -1')/", 0, 1, 1)

J1, '0 1)] ~

$268,281

~

6,295

Expected profits increase with discount.


$410,757 + $268,281 ~

~

$679,038

15.

21,479

Without discount:


1"<'1' - ~- _7__ 0 7 L0 C"+C, 7+3

14.

Optimal lot-size ~ 0' ~ NORMINV Without discount:

~

CS'L ' ~ ~ ~ _6_5_ ~ 0.6842 C" + C c

$1,076,941

Expected overstock ~ (0 -I')NORMDIST((O -1')1",0, 1, 1) + "NORMDIST((O -1')1",0, 1, 0)

18,083

Total expected overstock ~ 3,396 + 18,083

$95, s ~ $0, c



Total expected profit

5,470



~

~

Expected profits

(p - s)1' NORMDIST((O -1')/", 0, 1, 1)


$1,029,731

With discount:

26,083

$35, s ~ $13, c

J1, '0 1)] ~

Optimal lot-size ~ 0' ~ 25,000

C" + C, 14 + 8 Optimal lot-size ~ 0' ~ NORMINV CCSL Given that p

(p - s)1' NORMDIST((O -1')/", 0, 1, 1)

~

24,000

2

CS'L • = ~ = ~ = 0,6182 ~

$30:


Other three styles with postponement:

2

~


3,396

Aggregated expected demand

$95, s ~ $0, c ~

,1',0") ~ NORMINV(0.6842,20000,8000)


Expected overstock ~ (0 -I')NORMDIST((O -1')1",0, 1, 1) + "NORMDIST((O -1')1",0, 1, 0) ~

~

CCS'L

23,836

Given that p

~

CCSL

,1',0") ~ NORMINV(O. 7, 70000,25000)

83,110

$10, s ~ $0, c

~

$3:

65 +30


9-91


9-92

Expected profits

~

(p - s)1' NORMDIST((O -1')/", 0, 1, 1)

40-Gb

26,1'72



J1, '0 1)] ~

$403,077 expected profits would be: 40-Gb 20-Gb $1,790,125 $2,072,482

Expected overstock ~ (0 -I')NORMDIST((O -1')1",0, 1, 1) + "NORMDIST((O -1')1",0, 1, 0) ~

17,869

6-Gb $2,002,170

With discount: EXCEL worksheet 13-16 illustrates these computations.

Optimal lot-size ~ 0' ~ 100,000

Chapter 14: Transportation in a Supply Chain Given that p

~

Expected profits

$10, s ~ $0, c ~

~

$2,75:

(p - s)1' NORMDIST((O -1')/", 0, 1, 1)

Exercise Solutions



J1, '0 1)] ~

1.

$410,974 Coal:

Expected overstock ~ (0 -I')NORMDIST((O -1')1",0, 1, 1) + "NORMDIST((O -1')1",0, 1, 0) We evaluate the total cost per day for each ofthe options and select the one with the lowest cost. For ~

31,403 the carload option the calculations are shown below:

Expected profits increase with discount.

EXCEL worksheet 13-15 illustrates these computations Safety inventory held

~

2(lead time)(daily consumption rate)

~

2(15)(100000)

~

3,000,000 Ibs

16. a. the manufacturer should order

40-Gb 26,772

20-Gb 47,419

Safety inventory cost per day

6-Gb 84,054

b. The expected profits for the units are:

40-Gb $1,664,888

20-Gb $2,048,931

Cycle inventory ~ Q/2

~

~

(3000000)(0.25)(0.01)/365

I 00000/2

~

~

$20.55

50000 units

6-Gb $2,080,846 Cycle inventory cost per day ~ (50000)(0.25)(0.01)/365

c. !fthe available capacity is limited to 140,000 units the manufacturer should order:


9-93

~

$0.34


9-94

Transportation cost per day ~ 400(100000/10000)

~

One warehouse is built in either the eastern or western zone (by symmetry, the costs will be the same) One warehouse is built in the central zone A warehouse is built in each zone

$4000

One warehouse is built in the Eastern Zone This implies that an average of50,000 books are shipped from the Eastern to each of the three zone weekly. Weekly transportation cost ~ 50000*4/4 (to Western) + 50000*3/4 (to Central) + 50000*214 (to Eastern) ~ $112,500 Average batch size ~ weekly demand ~ 3*50000 ~ 150,000 Safety inventory ~ norrnsinv(.997)*,JI+i.J3 *25000 ~ 168,267 Annual fIxed cost of warehouse ~ 200,000 + l.5*(150000 + 168267) ~ $677,400 Weekly fIxed cost of warehouse ~ 677400/52 ~ $13,027 Weekly operating cost of warehouse ~ 0.01 *150,000 ~ $1,500 Weekly cost of cycle stock ~ (150000/2)*10*25/52 ~ $3,606 Weekly cost of safety stock ~ 168267* 10*25/52 ~ $8,090 Weekly cost of this option ~ Transport cost + facility cost + cost of inventory ~ $112,500 + $13,027 + $1,500 + $3,606 + $8,090 ~ $138,722

Total cost per day ~ $420.89

Other options can be evaluated in a similar manner

Worksheet 14-1 provides the results for all the options. Based on these results, using a full train results in the lowest cost per day of$258.8l

One warehouse is built in the Central Zone This implies that an average of50,000 books are shipped from the Central to each of the three zone weekly. Weekly transportation cost ~ 50000*3/4 (to Western) + 50000*214 (to Central) + 50000*3/4 (to Eastern) ~ $100,000 Average batch size ~ weekly demand ~ 3*50000 ~ 150,000 Safety inventory ~ norrnsinv(.997)*,JI+i.J3 *25000 ~ 168,267 Annual fIxed cost of warehouse ~ 200,000 + l.5*(150000 + 168267) ~ $677,400 Weekly fIxed cost of warehouse ~ 677400/52 ~ $13,027 Weekly operating cost of warehouse ~ 0.01 *150,000 ~ $1,500 Weekly cost of cycle stock ~ (150000/2)*10*25/52 ~ $3,606 Weekly cost of safety stock ~ 168267* 10*25/52 ~ $8,090 Weekly cost of this option ~ Transport cost + facility cost + cost of inventory ~ $100,000 + $13,027 + $1,500 + $3,606 + $8,090 ~ $126,222

l\1RO:

Similar analysis can be undertaken for the l\1RO option and using a truck at the smallest shipment size of 1250 results in the lowest cost of $139 per day.

Worksheet 14-1 depicts these results

The idea of this exercise is to evaluate the change in facility, inventory and transportation costs on centralization. We evaluate the costs for the following three options:

One warehouse is built in each Zone This implies that an average of 50,000 books are shipped from each warehouse to its own zone weekly. We frrst calculate all costs at a single warehouse and then multiply by 3. For each warehouse, we have: Weekly transportation cost ~ 50000*214 ~ $25,000 Average batch size ~ weekly demand ~ 50000



2.

9-95

9-96

Safety inventory ~ normsinv(.997)*.JI;i *25000 ~ 97,149 Annual fIxed cost of warehouse ~ 200,000 + 1.5*(50000 + 97,149) ~ $420,723 Weekly fIxed cost of warehouse ~ 420,723/52 ~ $8,091 Weekly operating cost of warehouse ~ 0.01 *50,000 ~ $500 Weekly cost of cycle stock ~ (50000/2)* 10*25/52 ~ $1,202 Weekly cost of safety stock ~ 168267* 10*25/52 ~ $6,599 Weekly cost of this option ~ 3*(Transport cost + facility cost + cost of inventory at each warehouse) ~ 3*($25,000 + $8,091 + $500 + $1,202 + $6,599) ~ $124,174

Thus, cost per ton ~ 360 / 75 ~ 4.80 Cost of two medium trucks every three days Thus, cost per ton ~ 410 / 75 ~ 5.47 Cost of one large truck ~ 230 Euros Thus, cost per ton ~ 230 / 75 ~ 3.07

~

2*205

~

410 Euros

Tlius, if Milan is to be replenished every three days, it is best to use one large truck The optimal trucking option and associated cost for each replenishment frequency is shown in the table. Below we show the optimal shipment options for each city.

The cost with a warehouse in each zone is the lowest (it is very close to the cost of having only one warehouse in the central zone).

3. We detail the analysis for one ofthe cities (l\1ilan) and provide the results in the other cases. Milan has daily demand of25,000 kg. If the Milan warehouse is replenished every k days, the quantity to be shipped will be 25,000k kg. Thus, the number of trucks and the cost per ton for different replenishment intervals is as shown below. MILAN 1 2 3 4 Replenishment Interval Load Size No of Trucks (Small) Cost per ton (Small) No of Trucks (Medium) Cost per ton (medium) No of Trucks (Large) Cost Der ton (Laroe)

25000 1 720 1 8.20 1 9.20

50000 2 720 1 4.10 1 4.60

75000 2 4.80 2 5.47 1 3.07

100000 3 5.40 2 4.10 2 4.60

With daily replenishment, the load size is 25,000 kg. Daily cost of small truck ~ (100 + 0.1 *800) ~ 180 Euros. Thus, cost per ton ~ 180/ 25 ~ 7.2 Daily cost of medium truck ~ (125 + 0.1 *800) ~ 205 Euros. Thus, cost per ton ~ 205 / 25 ~ 8.2 Daily cost oflarge truck ~ (150 + 0.1 *800) ~ 230 Euros. Thus, cost per ton ~ 230 / 25 ~ 9.2 Thus, if Milan is to be replenished daily, a small truck should be used. In contrast, ifwe consider a replenishment every three days, the load size ~ 25,000*3

~

75,000 kg.

The use of small or medium trucks will require two trucks each, whereas the use of a large truck will only require one truck With replenishment every three days, Cost of2 small trucks every three days

~

2* 180

~

360 Euros


9-97


9-98

PARIS Paris

Daily Demand

Chapter 15: Sourcing Decisions in a Supply Chain

35000 1000

Distance

Replenishment Interval Load Size No of Trucks (Small) Cost per ton shipped (Small) No of Trucks (Medium) Cost per ton (medium) No of Trucks (Large) Cost per ton (Larqe)

1.

1

2

3

4

35000 1 5.71 1 6.43 1 7.14

70000 2 5.71 2 6.43 1

105000 3 5.71 2 4.29 2 4.76

140000 4 5.71 3 4.82 2

3.57

With no buyback:

CSL' = C":"C,

Optirnallot-size = O' = NORMINV

Daily Demand Distance

Replenishment Interval Load Size No of Trucks (Small) Cost per ton (Small) No of Trucks (Medium) Cost per ton (medium) No of Trucks (Large) Cost per ton (Larqe)

3.57

Given that: Barnes & Noble's sale price (p) = $24 Barnes & Noble's salvage value (s = b) = $3 Barnes & Noble's cost (c) = $12:

20000 600

1

2

3

4

20000 1 8.00 1 9.25 1 10.5

40000 1 4.00 1 4.63 1 5.25

60000 2 5.33 1 308 1 3.50

80000 2 4.00 2 4.63 1

Expected profits for Barnes & Noble's

Distance

Replenishment Interval Load Size No of Trucks (Small) Cost per ton (Small) No of Trucks (Medium) Cost per ton (medium) No of Trucks (Large) Cost per ton (Larqe)

Ip - s)1" NORMDIST«O -1")/", 0, I, I)

+ 0 (p - e) [I -NORMDIST(O, I-" (01)] = $198,784

2.63

Expected overstock = (0 -I")NORMDIST«(O -1")1",0, I, I) + "NORMDIST«(O -1")1",0, I, 0) 2,477

=

Daily Demand

=

-Ip - s)" NORMDIST((O - 1")1'0 0, 1, 0) - 0 (e - s) NORMDIST(O, I-" '0 1)

MADRID Madrid

CC::-'L ' I",a) = NORMINV(0.571,20000,5000)

= 20,900

COPENHAGEN CopenH

= 121!9 =0.571

20000 1300

Expected understock =

1

2

3

4

20000 1 11.50 1 12.75 1 14.00

40000 1 5.75 1 6.38 1 7.00

60000 2 7.67 1 4.25 1 4.67

80000 2 5.75 2 6.38 1

(1"- 0)[1 -NORMDIST«(O -1")1",0, I, I)] + "NORMDIST«(O -1")1",0, 1,0) = 1,577

Given that: Publisher's sale price (c) = $12 Publisher's buyback price (b) = $0 Publisher's cost (v) = $1

3.50

The above tables assume that only one type of truck will be used. We can also do the analysis assuming that a combination (e.g small + large) can also be used.

Publisher's expected profit

=

Total supply chain profit

$198,784 + $229,901

=

O(c-v) - (overstock)(b) =

=

$229,901

$428,685

With buyback:

Other factors that should be considered before making this decision are: 1. How does the replenishment interval affect the safety stock requirement at the warehouses? 2. How does the replenishment interval affect the level of inventory (and thus the size of the warehouses )? 3. How does the replenishment interval affect other warehouse costs (such as labor cost)?


9-99

We reevaluate the profits for Barnes & Noble's (with c

=

b

=

8) and the publisher (with b

=

5)

23372 4118 746


9-100

Expected profit for Barnes & Noble's Expected profit for publisher Total supply chain profit

~

~

~

We reevaluate the profits for VideosRUs (with c

$214,578

$236,506

~

b

~

8.99) and the Studio (with b

~

4)

16648 6862 214

$451,084

EXCEL Worksheet 15-1 illustrates these computations Expected profit for VideosRUs

~

$90,835

2. ~

Expected profit for Studio

$122,386

With no buyback: Total supply chain profit

I"<''L' L0

~

Cu Cu+C u~

9.99 999+501

Optima110t-size ~ 0' ~ NORMINV ~

0.666

(C8L ' f', (J") ~ NORMINV(0.666, 10000,5000)

3.

Topgun's response:

Given that: VideosRUs' sale price (p) ~ $19.99 VideosRUs' salvage value (s ~ b) ~ $4.99 VideosRUs' cost (c) ~ $10: ~

CSL~~= (1-f)p-c

C+C

f', '0

~

~

1,752

Expected studio profit ~ (c - v) 0' + /P(O' - expected overstock at retailer)

Expected understock ~

~

(f'- 0)[1 -NORMDIST«(O - f')lcy, 0, 1, 1)] + CYNORMDIST«(O - f')lcy, 0,1, 0)

~

1,103

~

(I - j)p(O' - expected overstock at retailer) +

~

(1-0.35)(15)(6487-1752) + (1)(1752)-(3)(6487)

Total supply chain profits

Total supply chain profit

~

O(c-v) - (overstock)(b)

$72,609 + $109,300

~

~

(3-2)6487 + 0.35(15)(6487-1752)

~

$31,344

Expected retailer profit

Given that: Studio's sale price (c) ~ $10 Studio's buyback price (b) ~ $0 Studio's cost (v) ~ $1 ~

(C8L ' f', (J") ~ NORMINV(0.771,5000,2000)

6,487

Expected sales at Topgun ~ 6,487 - 1,752 ~ 4,735

3,248

Publisher's expected profit

(1- 0.35)(15 - 3) ~ 0771 (1- 0.35)(15 -1)

Expected overstock ~ (0 - f')NORMDIST«(O - f')lcy, 0, 1, 1) + CY NORMDIST«(O - f')lcy, 0, 1, 0)

1)] ~ $72,609

Expected overstock ~ (0 - f')NORMDIST«(O - f')lcy, 0, 1, 1) + CY NORMDIST«(O - f')lcy, 0, 1, 0) ~

(1-f)P-SR

Optima110t-size = 0' ~ NORMINV

(p - s)f' NORMDIST«O - f')/CY, 0, 1, 1)

- (p - s)CY NORMDIST((O - f')I'0 0, 1, 0) - 0 (c - s) NORMDIST(O, f', '0 1)


$213,221

EXCEL Worksheet 15-2 illustrates these computations

12,144

Expected profits for VideosRUs

~

~

$31,344 + $28, 455

SR

~

x expected overstock at retailer - cO'. ~

$28,455

$59,799

$109,300

$181,909

With buyback:


9-101


9-102

We reevaluate the problem with the revised contract; the solution is shown below:

Expected manufacturer profit ~ QRX C + (Q - QR)SM- Q x v.

Inputs Whole sale price, c = Production cost, v = Retail price, p =

Discount price,

$ $ $ $

SR

2 2 15

We solve for the optimal order quantity 0 using Solver by maximizing the retailer ' s profit function shown above. The results are shown below:

1

Inputs

0.43

Revenue share fraction, f = Mean demand = SO of demand =

5000 2000

Mean Demand

4,000

Standard Deviation of Demand

1,600

Benetton's Sale Price, c=

36.00

Benetton's Cost, v= salvage value for Benetton, Sm

20.00

$

Topgun's Response O ptim al cycle service lev el O ptim al order quanti ty, O· = Expected overstock = Expected sales =

0 .868 7230 2363 4867

$ $ 1000

$ Output

Expected Topgun profit = Supply Chain profit .

60 905

Q - 0 (1+ 0.35) 0 (1- 0)

~

3931

0.35

Q=

5,307

q=

393 1

Output

4.

Expected quantity purchased by retailer, QR

2500

alpha = beta =

EXCEL Worksheet 15-3 illustrates these computations

~

salvage value, Sc = Order size, 0 =

Contract

It is evident that the second contract results in higher profits for both parties.

q

55.00

$

$ 31,391 $ 29,514 $

Expected studio proFit =

Retailers Sale Price, p=

.u{FS( Q:.u J- FS( q:.u J} -

qF(q) + Q(1 - F(Q))+

Retailers Expected purchase =

4,41 8

Retailers Expected sales =

3,8 13

Manufacturers profits =

$ 61 ,791 $

Retailers proFits =

65 804 $

Supply chain profit .

127,595

EXCEL Worksheet 15-4 illustrates these computations 5.

~

Expected quantity sold by retailer D R Q(1 -F(Q)) + flF s( Q :fl

J-

(J

f

s( Q: fl

J,

Average demand/week ~ 100 SD demand/week ~ 50 Holding cost ~ 0.25 Cycle Service Level ~ 0.95

Expected overstock at manufacturer = QR- D1\,


9-103


9-104

We reevaluate the total costs associated with supplier 2 based on the three options provided in the problem; the costs are show below:

Supplier 1: Reliable Cost/unit ~ $5000 Min batch size ~ 100 Lead time (wks) ~ 1 SD Lead time (wks) ~ 0.1

Material Cost ~ (52)(100)(5000) ~ $26,000,000 Cycle inventory ~ 100/2 ~ 50 Cycle inventory cost ~ (50)(5000)(0.25) ~ $62,500 Standard deviation of demand during lead time is:

Option

Total Cost

LT=4

26,373,828.55

min batch=800

26,259,790.75

SD of LT=3

26,191,932.07

All three

26,064,178.01

$ $ ss

~ hi (CSL)

x (h

~ hi

Safety inventory cost Total cost

~

~

(0.95) x 50.99

~

83.87 (where, hi (0.95)

(83.87)(5000)(0.25)

~

~

NORMSINV (0.95))

$

$104,839

$26,000,000 + $62,500+ $104,839

~

$26,167,339

$

Supplier 2: Value

If all three options are in place then it is profitable to consider supplier 2.

Cost/unit ~ $4800 Min batch size ~ 1000 Lead time (wks) ~ 5 SD Lead time (wks) ~ 4

EXCEL Worksheet 15-6 illustrates these computations 7 and 8. The setup for these two problems is same as problem 4 except that 0 is given in the problem and we need to identify the following:

Material Cost ~ (52)(100)(4800) ~ $24,960,000 Cycle inventory ~ 1000/2 ~ 500 Cycle inventory cost ~ (500)(4800)(0.25) ~ $600,000 Standard deviation of demand during lead time is:

Q

~

q ~ 0 (1- 0.2) F(q)

ss - hi (CSL) x (h - hi (0.95) x 415.33 Safety inventory cost Total cost

~

~

~

683.16 (where, hi (0.95)

(683.16)(4800)(0.25)

~

~NORMSINV

F(Q)

(0.95))

~

~

~

~

1000(1.2)

1000(0. 8)

~

~

1200

800

NORMDIST (800,1000,300,1)

~

0.2525

~NORMDIST(1200,1000,300,1) ~

Q-I-l

$819,791

$24,960,000 + $600,000+ $819,791

0 (1+ 0.2)

1200 -1000 300

0.7475

0.67

$26,379,790

800-1000 It is evident that supplier 1 is the preferred supplier due to lower costs

300

- 0.67

EXCEL Worksheet 15-5 illustrates these computations 6.


9-105


9-106

Expected quantity purchased by retailer, QR - qF(q) + Q(1 - F(Q))+

.u{FS(Q:.u]-FS( q:.u]} -

Q' ~ pi (p', fl, (J)

~

NORMINV(p', fl, (J)

p' ~ 1-(4/8) ~ 0.5

NORMINV(O.S, 400000,150000)

Expected quantity sold by retailer DR - Q(1 -F(Q)) + fl FS( Q :fl Expected overstock at manufacturer

~

~

400,000

But since the manufacturer only sends 100,000 to the retailer, the amount to be sent to the high service channel is the minimum of 100,000 and 400,000. So only 100,000 units are sent to the high service channel.

J- (J f s( Q: fl J~ 954.66

Worksheet 16-2 presents this solution. 3. (a)

QR -DR ~ 45.34

s*~~~_3_~0.S Expected manufacturer profit ~ QRX

C

Cw+C s 3+3 0' ~ NORMINV(s', fl" (J,) ~ NORMINV(O.S, 20000, 10000) ~ 20000

+ (Q - QR)SM- Q x v ~ $4,800

With change in alpha and beta values the revised profits are:

alpha & beta

So, the total size of the contracts that the manager should sign is 20,000 square feet

Retail profit

(b)

$ alpha=.5

o ~ NORMINV(O.S, 0 15(100000 + 0), (0.6(0.15)(10000 + 0)).

3,704.18

$ beta=.5

The problem is solved by using solver by maximizing 0 subject to the restriction that 0

3,782.96

~

NORMINV(O.S,

o 15(100000 + 0), (0.6(0.15)(10000 + 0)).

EXCEL Worksheet 15-7&8 illustrates these computations

o ~ 17,647 square feet

Chapter 16: Pricing and Revenue Management in a Supply Chain

So, the total space that the manager should sign contracts for is 17,647 square feet Worksheet 16-3 presents this solution 4.

Exercise Solutions

The amount of trucking capacity the manager should save for the spot market is given by:

1.

Q' - pi (p', fl, (J)

The amount of production capacity to reserve is:

Q' - pi (p', fl, (J)

~NORMINV(p',

NORMINV(p', fl, (J)

p' ~ 1-(0.1/0.13) ~ 0.23

fl, (J)

NORMINV(0.23, 60000, 20000)

p' ~ 1-(5/10) ~ 0.5

NORMINV(O.S, 250, 100)

~

~

45,274 units

Worksheet 16-4 presents this solution. ~

250 units

5.

Worksheet 16-1 presents this solution.

The size of the annual contract the manager should sign is given by:

2.

Just as in the case of the previous problem:


9-107


9-108

p' ~ 1-(0.5/0.7) ~ 0.29

Maximize profit (P1-300)(20000-1O pI) + (p2-200)(40000-30 p2)

NORMINV(0.29, 500000, 150000) ~ 415,108 square feet

Subject to:

Worksheet 16-5 presents this solution.

(20000-10 pI) +(40000-30 p2)

6.

PI, P2 >~ 0

Unconstrained case:

Solving this problem results in PI

Decision variables:

Worksheet 16-7 presents the solution to this problem using Solver. Note that this is a non-linear modeL

<~

400000 (this capacity will solve the unconstrained problem)

~

$1,150 and P2

~

$766.7 and a profit of $16,858,333

Constrained case:

PI

~

price that NatBike should charge customized segment

P2

~

price that NatBike should charge standard segment

The only difference for the constrained case is that we change the capacity constraint as shown below:

(20000-10 PI) +(40000-30 P2)

<~

20000

Objective: Solving this problem results in PI

~

$1,287.5 and P2

~

$904.2 and a profit of $16,102,083

Maximize profit (P1-200)(20000-1O PI) + (p2-200)(40000-30 P2) Worksheet 16-7 presents the solution to this problem using Solver. Note that this is a nonlinear modeL Subject to: (20000-10 pI) +(40000-30 p2)

<~

400000 (this capacity will solve the unconstrained problem)

PI, P2 >~ 0 Solving this problem results in PI

~

$1,100 and P2

~

$766.7 and a profit of $17,733,333

Worksheet 16-6 presents the solution to this problem using Solver. Note that this is a nonlinear modeL

8.

Constrained case: In this case we allow for acquiring additional capacity at a cost The only difference for the constrained case is that we change the capacity constraint as shown below: Decision variables:

(20000-10 PI) +(40000-30 P2)

<~


20000 ~

$1,250 and P2

~

PI

~


P2

~


$916.7 and a profit of $16,833,333

7. c

=

additional capacity to acquire

The only change that we make here is with respect to the production costs as shown in bold. Objective: Unconstrained case:

Maximize profit (P1-200)(20000-1O pI) + (p2-200)(40000-30 p2) - 25c Decision variables:

Subject to: PI

~


P2

~


(20000-10 PI) +(40000-30 P2) PI, P2,

c>~

<~

20000 + c

0

Objective:


9-109


9-110

~


$1,112.5 and P2

~

$779.2 and a profit of $17,589,583

Decision variables:

Worksheet 16-8 presents the solution to this problem using Solver. Note that this is a nonlinear modeL

PI

~

pz

= price charged during the second month for each swimsuit

Pl

~

price charged during the first month for each swimsuit

9.

price charged during the third month for each swimsuit

Fixed price model:

q ~ quantity to purchase at the beginning of the season Decision variables:

Objective: p

=

price charged during entire season for each swimsuit

Maximize profit pI(2000-1OpI) + p2(2000-20p2) + pl(2000-30pl) - 40q Objective: Subject to: Maximize revenue p(2000-1Op) + p(2000-20p) + p(2000-30p)

~

p(6000-60p) (2000-1OpI) +(2000-20pI) +(2000-30pI)

<~

q

Subject to: PI, P2, Pl, (2000-1Op) + (2000-20p) + (2000-30p)

<~

q>~

0

5000 Solving this problem results in PI

P

>~

~

$120, P2

~

$70, Pl

~

$53.33 and the total revenue is $87,333.

0

Worksheet 16-9 presents the solution to this problem using Solver. Note that this is a nonlinear modeL Solving this problem results in p

~

$50 and total revenue of $150,000

Dynamic price model: Decision variables:

PI

~

pz

= price charged during the second month for each swimsuit

Pl

~

price charged during the first month for each swimsuit

price charged during the third month for each swimsuit

Objective: Maximize revenue: pI(2000-1OpI) + p2(2000-20p2) + pl(2000-30pl) Subject to: (2000-1OpI) +(2000-20pI) + (2000-30pI) PI, P2, Pl

>~

<~

5000

0

Solving this problem results in pI

~

$100, p2

~

$50, p3

~

$33.33 and the total revenue is $183,333.

Quantity model:


9-111


9-112

Discussion QA 9to17

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