OIDD615 sample final exam - solutions

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Apr 3, 2024

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OIDD 615 Sample Final Exam. Page 1 of 16 University of Pennsylvania The Wharton School Department of Operations and Information Management OIDD 615 SAMPLE EXAM - SOLUTIONS Professor Cachon Instructions: You are to complete this exam on your own. You may use any of the OIDD 615 materials from this term to work on this exam. There are 27 questions and 30 points available on this exam. No partial credit is given for 1-point questions. There is no penalty for guessing. Place your response in the box provided. You may use a calculator but no electronic device that can communicate with another device (e.g., iPad, Kindle, mobile phone, laptop, etc.) You have two hours to complete the exam. First Name: Last Name: Penn Id: My signature below certifies that I have complied with the University of Pennsylvania's Code of Academic Integrity in completing this final examination. ___________________________ Signature Date
OIDD 615 Sample Final Exam. Page 2 of 16 (Q1-Q5) Rifugio Bolzano in the Italian Dolomites is located at the top of one of the large peaks in the Catinaccio Park (see photo below). Most hikers take at least 5 hours to reach the rifugio, but once there, they are treated to excellent food and the option of a warm bed. The rifugio uses a large basket attached to a cable from a local village to resupply its inventory. It is Saturday morning and Marco Fruscalzo, the director of Rifugio Bolzano, is about to place the one order they can make to resupply their stocks to cover demand for this weekend (i.e., the basket will make one trip up the mountain from the village). Q1. Marco estimates that this weekend’s demand for bread has a mean of 40kgs and a standard deviation of 15kgs. Bread left over at the end of the weekend is too stale to serve, and so has no value. They currently do not have any bread in stock. Marco wants to be 99.5% sure that they will be able to cover all of their demand. How many kgs of bread should he order? From the standard normal distribution, F(2.58) = 0.9951 so the desired z-score is 2.58. 40kg + 2.58 * 15kg = 78.7kg
OIDD 615 Sample Final Exam. Page 3 of 16 Q2. Suppose Marco orders 70 kgs of bread. Continue to assume demand has a mean of 40kgs and a standard deviation of 15kgs and they currently have no bread. What is the expected amount of left over bread at the end of the weekend (in kgs)? Q3. In their gift shop the Rifugio sells small bottles of Grappa. Demand for this weekend is expected to be Poisson distributed with a mean of 4.5. Marco wants to be able to satisfy all demand with a 0.92 probability. They currently do not have any bottles in inventory. How many bottles should they order? Q4. Suppose Marco orders 4 bottles of Grappa. Continue to assume demand is Poisson with mean 4.5. How many bottles can he expect to sell during the weekend? Check the Poisson Inventory function table with mean = 4.5 I(4) = 0.58808 Expected sales = Q – Expected leftover inventory = 4 – 0.58808 = 3.4 Check the Poisson distribution table with mean = 4.5 F(7) = 0.91341 and F(8) = 0.95974 8 bottles are needed z-score of 70kg is (70-40)/15 = 2 I(z) = I(2) = 2.0085 Expected leftover inventory = 15 x 2.0085 = 30.1275
OIDD 615 Sample Final Exam. Page 4 of 16 Q5. Marco also needs to order some Arborio rice to be sure that they can make their famous mushroom risotto. They currently don’t have any rice but they want to include the risotto on the menu for this weekend. Suppose he orders 20 kgs of rice. Demand is normally distributed with a mean of 12kgs and a standard deviation of 4 kgs. What is the probability he will stock out of rice during this weekend? (Q6-Q7) Holiday Pop Inc specializes in “pop-up” stores – each 4 th quarter they open stores in several thousand locations throughout the country and then close them all at the end of the holiday season. They specialize in selling holiday gifts and related items, mostly purchased from overseas suppliers. One of their stores this season will be located in the Granite Run Mall. One of their items is a musical, spinning, miniature Christmas tree. Each one sells for $20 and they purchase them for $8 per unit. If there is inventory left over at the end of the season, they discount each unit to $4. Expected demand at this store has a mean of 200 and a standard deviation of 50. Q6. If they want to maximize their expected profit, how many units should they order for this store? z-score fo 20kg is (20-12)/4 = 2 From the standard normal distribution table: 1 – F(2) = 1 – 0.9772 = 0.0228 Probability of stockout is 0.0228 Overage cost is $8 - $4 = $4 Underage cost is $20 - $8 = $12 The newsvendor critical ratio is 12/(12 + 4) = 0.75 From the standard normal distribution table, z-score is 0.68 Q* = 200 + 0.68 * 50 = 234
OIDD 615 Sample Final Exam. Page 5 of 16 Q7. Holiday Pop finds that sales in the first two weeks of the season are highly correlated with final demand (i.e., once they observe demand in the first two weeks, there will be little remaining uncertainty in their forecast for total sales for the season). Although they don’t like to do this, they can place a second order after observing early season sales, but they need to use air shipments with that order. As a result, each unit placed with the 2 nd order costs them $17 (i.e., air adds $9 to the unit cost). Continue to assume they sell each unit for $20 and discount to $4. Given the possibility to place a 2 nd order, what quantity should they select for their 1 st order? Q8. A company collects the following data regarding last season’s performance of 5 items (labeled A to E) in one of their product categories: This season they have a product with a forecast of 500 units. If they use the A/F method to forecast, what mean should they use for the product’s demand model? Product Forecast Q* Sales Demand** A 100 200 150 150 B 200 300 150 150 C 400 500 500 800 D 600 700 300 300 E 800 900 900 1200 * Quantity ordered ** An estimate of demand The possibility of second order changes the underage cost. If they must use air, then they earn $3, but they earn $12 if they had ordered the unit in advance. So the underage cost is $12 - $3 = $9. The newsvendor critical ratio is 9/(9+4) = 0.6923 From the standard normal distribution table, z-score is 0.51 Q* = 200 + 0.51 * 50 = 225.5 The A/F ratio of each product are: A: 1.5 B: 0.75 C: 2 D: 0.5 E: 1.5 The average A/F ratio is (1.5 + 0.75 + 2 + 0.5 + 1.5)/5 = 1.25 Expected actual demand is 1.25 * 500 = 625
OIDD 615 Sample Final Exam. Page 6 of 16 Q9. The table below provides data for 6 products, named A to F. Assume a newsvendor model is appropriate for deciding an order quantity. Each product may experience either the cost of left over inventory or the cost of running out of inventory. For which product is the total of those two costs the highest percentage of its maximum profit? (Q10-Q11) The Home Depot in Conshohocken sells a wide array of tools. The annual holding cost for this store is 60% (e.g., an item purchased for $10 would cost $6 to hold in inventory for one year). Assume they operate 52 weeks per year. Q10. They sell a four-piece screwdriver set in that store. On average they have 8.5 units and this item has annual inventory turns equal to 10. They purchase the item for $11.5 and sell it for $18. On average what is the holding cost they incur per item (i.e., per four-piece screwdriver set)? Product Critical Ratio Mean Standard deviation A 0.4 200 200 B 0.4 400 300 C 0.5 600 400 D 0.5 800 500 E 0.6 1000 600 F 0.6 1200 700 Mismatch costs are high when coeff of variation is high and the critical ratio is low. The coeff of variation are: A: 1 B: 0.75 C: 0.67 D: 0.625 E: 0.6 F: 0.58 Product A has the highest coefficient of variation and the lowest critical ratio. An item stays in the store for 52/10 = 5.2 weeks The cost of the item is $11.5 The holding cost is: $11.5 * 0.60/year * 5.2/52 year = $0.69
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