MANAGEMENT MANA GEMENT SCIENCE MODELS Cases Author: Prof. Subhash Datta
CASE 1: FINANCIAL PLANNING AT HEWLETT ............................................................................................ 2 CASE 2: MOSSAIC M OSSAIC TILES ........................... ............. ........................... .......................... ........................... .......................... .......................... ........................... .......................... ................. .... 3 CASE 3: DISTRIBUTION SYSTEM DESIGN ................................................................................................... 5 MANAGERIAL REPORT ................................................................................................................................
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CASE 4: NATIONAL BANK ......................................................................................................................... 7 CASE 5: SEERVADA PARK ......................................................................................................................... 8 CASE 6: COUNTRY BEVERAGE DRIVE-THRU ............................................................................................ 10 MANAGERIAL REPORT ..............................................................................................................................
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Case 1: Financial Planning at Hewlett Linear Programming has been used for a variety of financial planning applications. Hewlett Corporation has established an early voluntary retirement program as part of its corporate restructuring. At the close of the voluntary sign-up period, 78 employees had elected early retirement. As a result of these early retirements, the company has incurred the following obligations over the next 8-years. Cash requirements (in Lakhs of rupees) are due at the beginning of each year.
Year
1
2
3
4
5
6
7
8
Cash Requirement
195
95
100
105
110
90
108
120
The corporate treasurer must determine how much money must be set aside today to meet the 8-year financial obligations as they come due. The financing plan for the retirement program includes investments in government bonds as well as savings. The investments in government bonds are limited to three choices as follows:
Bond
Price (Rs.)
Rate
Years to Maturity
1
50000
9
5
2
40000
6
6
3
60000
11
7
The government bonds have a par value of Rs. 40000, which means that even with different prices each bond pays Rs. 40000 at maturity. The rates shown are based on the par value. For purposes of planning, the treasurer has assumed that any funds not invested in bonds will be placed in savings and earns interest at an annual rate of 5%.
i. ii.
Formulate the Problem Solve by Excel Solver
iii.
Solve using QM for Windows
iv.
Present a report.
Case 2: Mossaic Tiles Gautam Ghose and Anjali Agarwal spent several summers during their college years working at different archaeological sites. During the period they learned how to make ceramic tiles from local artisans. After college they started a tile manufacturing firm called Mossaic Tiles. They opened their Plant at NOIDA, where they would have convenient access to special clay to make a derivative for their tiles. Their manufacturing operation consists of a few simple but precarious steps, including molding the tiles, baking and glazing.
Gautam and Anjali plan to produce two basic types of tiles for use in bathrooms, kitchens and other living rooms: a larger simple coloured tile and a smaller patterned tile. In the manufacturing process the colour or pattern is added before a tile is glazed. Either a single colour is sprayed over the top of a newly baked set of tiles or a stenciled pattern is sprayed on the top of a baked set of tiles.
The tiles are produced in batches of 100. The first step is to pour the clay derivative into specially constructed molds. It takes 18 minutes to prepare a mold for a batch of 100 larger tiles and 15 minutes to prepare a mold for a batch of 100 smaller tiles. The company has 60 hours available each week for molding. After the tiles are molded they are baked in a kiln: 0.3 hour for a batch of 100 larger tiles and 0.6 hour for a batch of 100 smaller tiles. The company has 105 hours available each week for baking. After baking, the tiles are either coloured or patterned and glazed. This process takes 0.1 hour for a batch of 100 larger tiles and 0.2 hour for a batch of 100 smaller tiles. Forty hours are available each week for the glazing process. Each batch of 100 large tiles requires 32.8 kg. Of the clay derivative to produce, while each batch of smaller tiles requires 20 kg. The company has 6000 kg. of the clay derivative available each week.
Mossaic earns a profit of Rs.10,000 for each batch of 100 of the larger tiles and Rs.15,000 for each batch of 100 smaller tiles. Mossaic Tiles want to know how many batches of each type of tile to produce each week in order to maximise profit. They also have some questions about resource usage they would like to answer:
a) Formulate a LP model for the Mossaic Tiles to determine the mix of the tiles it should manufacture each week. b) Solve graphically c) Determine the resources left over and not used at the optimal solution point. d) In the long run, Gautam and Anjali want to produce only the smaller patterned tiles. What must be the profit in order for the company to produce only the smaller tiles?
e) Mossaic believes it may be possible to reduce the time required for molding to 15 minutes for a batch of larger tiles and 12 minutes for a batch of smaller tiles. How will this affect the solution? f) The company which provides Mossaic with clay has indicated that it can deliver an additional 100 kg. Of clay each week. Should Mossaic agree to this offer? g) Mossaic is considering adding capacity to one of its kilns to provide 20 additional glazing hours per week at a cost of Rs.400,000. Should it make the investment? h) If the Kiln for glazing had to be shut down for 3 hours, reducing the available Kiln hours from 40 to 37. What effect will this have on the optimal solution?
Case 3: DISTRIBUTION SYSTEM DESIGN The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in El Paso and gradually built a customer base throughout Texas. A distribution centre was established in Ft. Worth, Texas, and later, as business expanded to the north, a second distribution centre was established in Santa Fe, New Mexico. The El Paso plant was expanded when the company began marketing its meters in Arizona, California, Nevada, and Utah. With the growth of the West Coast business, the Darby Company opened a third distribution centre in Las Vegas and just two years ago opened a second production plant in San Bernardino, California. Manufacturing cost differ between the companys production plants. The cost of each meter produced at the El Paso plant is $10.50. The San Bernardino plant utilizes newer and more efficient equipment; as a result, manufacturing costs are $0.50 per meter less than at the El Paso plant. Due to the companys rapid growth, not much attention had been paid to the efficiency of the distribution system, but Darbys management has decided that it is time to address this issue. The cost of shipping a meter from each of the two plants to each of the three distribution centers is shown in Table 1. The quarterly production capacity is 30,000 meters at the older El Paso plant and 20,000 meters at the St. Bernardino plant. Note that no shipments are allowed from the St. Bernardino plant to the Ft. Worth distribution center. The company serves nine customer zones from the three distribution centers. The forecast of the number of meters needed in each customer zone for the next quarter is shown in Table 2. The cost per unit of shipping from each distribution centre to each customer zone is given in Table 3; note that some of the distribution centers cannot serve certain customer zones. Table 1: Shipping Cost Per Unit from Production Plants to Distribution Centers ($). Distribution Center PLANT
Ft. Worth
Santa Fe
Las Vegas
El Paso
3.20
2.20
4.20
San Bernardino
-
3.90
1.20
Table 2: Quarterly Demand Forecast Customer Zone Demand (meters)
Dallas
6300
San Antonio
Wichita
4880
2130
Kansas City 1210
Denver
6120
Salt Lake City 4830
Phoenix
Los Angeles
2750
8580
San Diego 4460
In the current distribution system, demand at the Dallas, San Antonio, Wichita, and Kansas City customer zones is satisfied by shipments from the Ft. Worth distribution center. In a similar manner, the Denver, Salt Lake City, and Phoenix customer zones are served by the Santa Fe distribution centre and the Los Angeles and San Diego customer zones are served by the Las Vegas distribution center. To determine how many units to ship from each plant, the quarterly customer demand forecasts are aggregated at the distribution centers, and a transportation model is used to minimize the cost of shipping from the production plants to the distribution centers.
Managerial Report You have been called in to make recommendations for improving the distribution system. Your report should address, but not be limited to the following issues. 1. If the company does not change its current distribution strategy, what will its manufacturing and distribution costs be for the following quarter? 2. Suppose that the company is willing to consider dropping the distribution center Iimtations; that is, customers could be served by any of the distribution centers for which costs are available. Can costs be reduced? By how much? 3. The company wants to explore the possibility of satisfying some of the customer demand directly from the production plants. In particular, the shipping cost is $30 per unit from San Bernardino to Los Angeles and $0.70 from San Bernardino to San Diego. The cost for direct shipments from El Paso to San Antonio is $3.50 per unit. Can distribution costs be further reduced by considering these direct plant customer shipments? 4. Over the next five years, Darby is anticipating moderate growth (5000 meters) to the North and West. Would you recommend that they consider plant expansion at this time? TABLE 3: Shipping Cost From The Distribution Centers To The Customer Zones ($)
Distribution Center
Dallas San Antonio
Wichita Kansas Denver Salt City Lake City
Phoenix Los San Angeles Diego
Ft. Worth Santa Fe Las Vegas
0.3 5.2
3.1 4.5
-3.4 2.4
2.1 5.4
4.4 6.0
6.0 2.7 5.4
-4.7 3.3
-3.3 2.1
-2.7 2.5
Case 4: National Bank Using mail promotion with low introductory interest rates, the National Bank has built a large base of credit card customers throughout India. Currently all customers send their regular payments to the banks corporate office located in Mumbai. Daily collections from customers making their regular payments are substantial, with an average of approximately Rs. 3.5 crores. The bank estimates that it makes about 15% on its funds, and would like to ensure that customer payments are credited to the banks account as soon as possible. For example, if it takes 5 days for a customers payment to be sent through the mail, processed, and credited to the banks account, the bank has potentially lost 5 days worth of interest income. Although the time for this collection process cannot be completely eliminated, it is possible to reduce it for substantial benefits since a large sum of money is involved. Instead of sending all customers payments to Mumbai, the bank is considering having customers send their payments to one or more regional collection centres (lockboxes). Four potential lockbox locations have been proposed: Nagpur, Kanpur, Patna and Bangalore. To determine which lockboxes to open and where lockbox customers should send their payments, the bank has divided its customer base into 5 geographical regions: North, South, Central, East and West. Every customer in the same region will be instructed to send his or her payment to the same lockbox. The following table shows the average number of days it takes before a customers payment is credited to the banks account when the p ayment is sent from each of the regions to each of the potential lockboxes. Customer Zone
Location of Lockbox
Daily Collection (Rs. in Lakhs)
Nagpur
Kanpur
Patna
Bangalore
North
3
2
3
4
40
South
3
4
6
2
80
Central
2
3
3
4
60
East
3
4
2
5
70
West
3
4
4
3
100
Mr. George, the GM for cash management, has asked you to prepare a report containing your recommendations for the number of lockboxes and the best lockbox locations. The primary objective is to minimize the lost interest income, but you would also like to consider the effect of an annual fee charged for maintaining a lockbox at any location. Assume the range of fees to be in the range of Rs. 10000 to Rs. 20000 per location.
Case 5: SEERVADA PARK Seervada Park has recently been set aside for a limited amount of sightseeing and backpack hiking. Cars are not allowed into the park, but there is a narrow winding road system for trams and for jeeps driven by the park rangers. This road system is shown (without the curves) in Fig. 1, where location 0 is the entrance into the park; other letters designate the locations of ranger stations (and other limited facilities). The numbers give the distances of these winding roads in miles. The park contains a scenic wonder at station T. A small number of trams are used to transport sightseers from the park entrance to station T and back. The park management currently faces three problems. One is to determine which route from the park entrance to station T has the smallest total distance for the operation of the trams. (This is an example of the shortest-route problem) A second problem is that telephone lines must be installed under the roads to establish telephone communication between all the stations (including the park entrance). Because the installation is both expensive and disruptive to the natural environment, lines will be installed under just enough roads to provide some connection between every pair of stations. The question is where the lines should be laid to accomplish this with a minimum total number of miles of line installed. (This is an example of the minimal spanning tree problem)
The third problem is that more people want to take the tram ride from the park entrance to station T than can be accommodated during the peak season. To avoid unduly disturbing the ecology and wildlife of the region, a strict ration has been placed on the number of tram trips that can be made on each of the roads per day. (These limits differ for the different roads). Therefore, during the peak season, various routes might be followed regardless of distance to increase the number of tram trips that can be made each day. The question is how to route the various trips to maximize the number of trips that can be made per day without violating the limits on any individual road. (This is an example of the maximal flow problem).
Diagram 1:The Road System for Seervada Park
7 2
2 4
5
0
B 3
4
1
C
Diagram2
T
5
4
7 1
CASE 6: COUNTRY BEVERAGE DRIVE-THRU Country Beverage Drive-Thru, Inc., operates a chain of beverage supply stores in Northern Illinois. Each store has a single service lane; cars enter at one end of the store and exit at the other end. Customers pick up soft drinks, beer snacks, and party supplies without getting out of their cars. When a new customer arrives at the store, the customer waits until the preceding customers order is complete and then drives into the store for service. Typically, three employees operate each store during peak periods; two clerks take and fill orders; and a third clerk serves as cashier and store supervisor. Country Beverage is considering a revised store design in which computerized order-taking and payment are integrated with specialized warehousing equipment. Management hopes that the new design will permit operating each store with one clerk. To determine whether the new design is beneficial, management has decided to build a new store using the revised design. Country Beverages new store will be located near a major shopping center. Based on experience at other locations, management believes that during the peak late afternoon and evening hours, the time between arrivals follows an exponential probability distribution with a mean of 6 minutes. These peak hours are the most critical time period for the company; most of their profit is generated during these peak hours. An extensive study of times required to fill orders with a single clerk has led to the following probability distribution of service times. Service Time (minutes) 2 3 4 5 6 7 8 9
Probability 0.24 0.20 0.15 0.14 0.12 0.08 0.05 0.02 ------Total 1.00
In case customer wait times prove too long with just a single clerk, Country Beverages management is considering two alternatives: add a second clerk to help with bagging, taking orders, etc., or enlarge the drive-thru area so that two cars can be served at one (a two-channel system). With either of these options, two clerks will be needed. With the two-channel option, service times are expected to be the same for each channel. With the second clerk helping with a single channel, service times will be reduced. The following probability distribution describes service time given that option.
Service Time (minutes)
Probability
1 2 3 4 5
0.20 0.35 0.30 0.10 0.05 ------Total 1.00
Country Beverages management would like you to develop a spreadsheet simulation model of the new system and use it to compare the operation of the system using the following three designs: Design Alternatives A One channel, one clerk B One channel, two clerks C Two channels, each with one clerk
Management is especially concerned with how long customers have to wait for service. Research has shown that 30% of the customers will wait no longer than 6 minutes and that 90% will wait no longer than 10 minutes. As a guideline, management requires the average wait time to be less than 1.5 minutes.
Managerial Report Prepare a report that discusses the general development of the spreadsheet simulation model, and make any recommendations that you have regarding the best store design and staffing plan for Country Beverage. One additional consideration is that the design allowing for a twochannel system will cost an additional $10,000 to build. i.
List the information the spreadsheet simulation model should generate so that a decision can be made on the store design and the desired number of clerks.
ii.
Run the simulation for 1000 customers for each alternative considered. You may want to consider making more than one run with each alternative. [Note: Values from an exponential probability distribution with mean µ can be generated in Excel using the following function: = µ*LN(RAND())]
iii.
Be sure to note the number of customers Country Beverage is likely to lose due to long customer wait times with each design alternative.
