Uncertainty at Dog Co _ Week 1 Practice Problems _ CTL

3/15/2016

Practice Problem 7: Uncertainty at Dog Co | Week 1 Practice Problems | CTL.SC1x Courseware | edX

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Supply Chain Fundamentals

Week 1: Overview of Supply Chain Management & Logistics > Week 1 Practice Problems > Practice Problem 7: Uncertainty at Dog Co

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Course Overview & Logistics

PRACTICE PROBLEM 7: UNCERTAINTY AT DOG CO You have joined the supply chain group at Dog Co - the leading dog supplies and food store operating in the United States. You discover that

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Entrance Survey

prior to your arrival all inventory and stocking decisions were being made on just the average weekly demand. demand. The distribution of the the demand was being tracked, but it was not being used at all in any of the inventory

 Week 1:

Overview of Supply Chain Management & Logistics Welcome to Week 1 Lesson 1: Supply Chain Perspectives Lesson 2: Core Concepts & Approaches

calculations. Your manager, Hank, however, does not think you need to consider the distribution of demand. demand. "The average has always been good good enough for me!" he proclaims often and loudly. loudly. He prefers to use the average demand and then add add in 10% on top, "Just "Just to be safe". This is known as "Hank's Rule" at Dog Co. You do not want to get fired, but you would like to demonstrate to Hank that the distribution of demand does matter and perhaps "Hank's Rule" should be changed. Please enter all your numerical answers with at least 4 significant figures.

Week 1 Practice Problems

Supplemental Materials Materials for MicroMasters MicroMasters

Part 1

Week 1 Graded Assignment

You identified two SKUs that have common average weekly demand, but very different standard deviations.

Homework due Feb 24, 2016 at 15:00 UTC

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Week 2: Forecasting I Introduction Week 3:

SKU #87990_A (Wilson Chew Toys) cost $5.95 each and you sell them for $9.99. The weekly demand is distributed normally with a mean of 625 units and a standard deviation of 225 units. SKU #333_99_J_4 (Dexter Delight Dog Treats) cost $4.25 and you sell them for $8.00. The weekly demand is distributed normally with a mean of 630 units and a standard deviation of 50 units.

https:// https://cours courses.ed es.edx.or x.org/cou g/courses/ rses/cours course-v1: e-v1:MITx+ MITx+CTL.S CTL.SC1x_ C1x_2+1T 2+1T2016 2016/cou /coursewar rseware/eb6 e/eb6a807a a807af032 f0324d9ca 4d9caaaab9 aaab90813 08133f3e7 3f3e7c/63b c/63b1fbb 1fbbfbc1b fbc1b4438 4438b2bd b2bd073b 073bb398 b398f635 f635//

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Forecasting II Exponential Smoothing 

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If you stocked exactly the mean of the demand for any one of the items (that is 625 of the Wilson Chew Toys or 630 of the Dexter Delights), what is the probability that your demand will exceed what you have in stock for that item? Just enter a number from 0 to 1.00 for the probability.

Week 4: Forecasting III Special Cases & Extensions Week 5: Inventory Management I - Deterministic Demand

 Answer: .50

EXPLANATION

Exactly 50% of the time! The Normal distribution is symmetric. If we have the mean value, then 50% of the time we will have demand below the average and 50% of the time we will have demand above the average.

You have used 3 of 3 submissions

Part 2 Using the same two SKUs, you want to see how Hank's Rule applies to each of the products and how it impacts the probability of stocking out. What is the probability that the weekly demand for the Wilson Chew Toys (only one SKU not both) will exceed the level set by Hanks Rule, that is setting the inventory level at 688 (= 625 + 62.5)? Just enter a number from 0 to 1.00 for the probability.

 Answer: 0.390

EXPLANATION

We need to transform this value into the unit normal function and use the Unit Normal Tables or your spreadsheet NORMDIST functions. For the Wilson Chew Toys this gives us the following, k=(x-mean)/(Std Dev) = (688-625)/225 = 0.28. Using the tables, we get Probability of Demand being less than 688 = 0.6103 so that the Probability of Stocking out (demand exceeding this value) = 1 - 0.6103 = 0.3887 or 0.39.

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I also could have used the NORMDIST function, where stocking out = 1 - NORMDIST(688, 625, 225, 1) = 1- 0.6103 = 0.3897 = 0.39. Or, I could use the NORMSDIST function once I had already transformed it to the Unit Normal and found the k value. Stocking out = 1 NORMSDIST(0.28) = 0.3897 = 0.39. There are many ways to get to the same answer.


Part 3 Using the same two SKUs, you want to see how Hank's Rule applies to each of the products and how it impacts the probability of stocking out. What is the probability that the weekly demand for the Dexter Delights Dog Treats will exceed the level set by Hanks Rule, that is setting the inventory level at 693 (= 630 + 63)? Just enter a number from 0 to 1.00 for the probability. Note: the solution to this problem will not be posted until after the deadline.

 Answer: 0.104

EXPLANATION

We need to transform this value into the unit normal function and use the Unit Normal Tables or your spreadsheet NORMDIST functions. For the Dexter Delights this gives us the following, k=(x-mean)/(Std Dev) = (693-630)/50 = 1.26. Using the tables, we get Probability of Demand being less than 693 = 0.8962 so that the Probability of Stocking out (demand exceeding this value) = 1 - 0.8962 = 0.1038 or 0.104. So, the Wilson Chew Toys will stock out almost 40% of the time while the Dexter Delights will only stock out 10% of the time - with the same amount of extra "Hank Rule" inventory of 10% of average! We will learn more in later weeks about how to set inventory levels using service levels such as this. But this simple analysis shows that the shape of the distribution matters!


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Part 4 Hank kind of believes you, but he says that that only works on the fast moving items. He applies a different rule to slow moving items called "Hank's Slow Mover Rule." This rule says that if average weekly demand is less than 10, then stock the average, plus 1 unit. You pick two slow moving items for a test: SKU #11_9 (Griffin's Dog Bed) cost $195.95 each and you sell them for $275. The weekly demand is Poisson distributed with a mean of 3 units. SKU #3765 (Cody Indestructible Chewables) cost $35.50 and you sell them for $78.00. The weekly demand is Poisson distributed with a mean of 6 units. What is the probability that your demand for Griffin Beds will exceed the level set by Hank of 4 units (=3+1)? Just enter a number from 0 to 1.00 for the probability.

 Answer: 0.18

EXPLANATION

Using the Poisson Distribution tables, looking at lambda = 3, we can see the the probability that there are no more than 4 units of demand is equal to 0.81526. So, the probability of having too little inventory and stocking out = 1-0.81526 = 0.18474 = 0.18.


Part 5 What is the probability that your demand for Cody Indestructible Chewables will exceed the level set by Hank of 7 units (=6+1)? Just enter a number from 0 to 1.00 for the probability.


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 Answer: 0.26

EXPLANATION

Using the Poisson Distribution tables, looking at lambda = 6, we can see the probability that there are no more than 7 units of demand is equal to 0.74398. So, the probability of having too little inventory and stocking out = 1-0.74398 = 0.25702 = 0.26 Alternatively, you could use the POISSON function in your spreadsheet. So, Hank's "add 1 unit" rule does not have the same effect. You can see that it might over protect really slow movers and under protect faster movers. We will learn later how to set these inventory levels.


Part 6 Even after presenting your analysis, Hank is hesitant to change his rules. What should you do?

Quit Dog Co and get a job at Zaragoza Auto Supply or Boston Arts

Suggest that Hank take CTL.SC1x

Create a presentation that demonstrates how the lost sales and/or extra inventory costs impact Hank's bonus

Create a presentation that demonstrates how the lost sales and/or extra inventory costs impact Dog Co for Hank to use in a presentation to his boss

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EXPLANATION

We did not include points for this one - it is just for you to think about. As we will learn later, sometimes the form of the message and how it is delivered matters as much (if not more) than the actual message. Perhaps Hank feels threatened by you and perhaps he does not know how to translate the inventory savings into bottom line impacts to the overall company.


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Uncertainty at Dog Co _ Week 1 Practice Problems _ CTL

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