OIDD615 sample final exam - solutions

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 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 7 of 16 Q11. On average they have 2.5 units of a drill press. The drill press sells for $200 and it is purchased for $125. Average weekly demand is 0.25 units. On average what is the holding cost they incur per item (i.e., per drill press)? (Q12-16) Enrico Scalia has been put in charge of Barilla’s JITD program to manage the inventory of their pasta in the Cortese Distribution Center. They use order upto policies to manage inventory. They place orders daily and each order is received after 4 days. Q12. The 1kg box of fettuccine sells 1.25 cases per day on average. They currently have 6 cases on order and 2 cases on-hand and they operate with a base stock level of 11. They are about to place an order for today. What was demand yesterday (in cases)? On average, the drill press stays in the store for 2.5/0.25 = 10 weeks. The cost of the item is $125. The holding cost is: $125 * 0.60/year * 10/52 year = $14.42 The inventory position is 6 + 2 = 8 cases. Since the base-stock level is 11, the previous period’s demand was 11 – 8 = 3 cases.

OIDD 615 Sample Final Exam. Page 8 of 16 Q13. The 500gr box of penne pasta is one of their top sellers – on average they sell 1.25 pallets per day. (A pallet contains 100 cases, each case has 12 of the 500 gr boxes.) What order upto level (in pallets) should they choose to ensure a 0.9915 in-stock probability? Q14. They sell 0.5 cases of tagliatelle each day. If they operate with a base stock level of 6 cases, what would be their average on-hand inventory? Assume demand can be modeled with a Poisson distribution. Q15. They sell 250 cases of spaghetti each day, with a standard deviation of 100 cases. If they want their in-stock probability to be at least 0.995, what order up-to level should they choose (in cases)? The average demand over l+1 = 4 + 1 = 5 days is 5 * 1.25 = 6.25 Assume Poisson distribution for demand with mean 6.25. F(12) = 0.99117 and F(13) = 0.99637 The order upto level should be 13 pallets. The average demand over l + 1 = 5 days is 5 * 0.5 = 2.5 cases. From the Poisson Inventory Function Table with a mean of 2.5, I(6) = 3.5199 From the standard normal distribution table, z = 2.58 to achieve in-stock probability of 0.995. The mean demand over l + 1 = 5 days is 5 * 250 = 1250 cases and the standard deviation is sqrt(5) * 100 = 223.6. The order upto level should be: S = mu + z * sigma = 1250 + 2.58 * 223.6 = 1826.89

OIDD 615 Sample Final Exam. Page 10 of 16 Q19. Suppose a retailer operates 40 stores in California and currently receive deliveries directly from a supplier (left panel in figure below). They are considering to add a distribution center (DC) to their supply chain so that the supplier will deliver to the DC and then product will be sent from the DC to the stores (right panel in figure below). Adding the DC will not change the lead time from the supplier. Under which of the following eight conditions (A, B,…,H) would adding a DC be most beneficial to the supply chain? Supplier lead +me DC Supplier Stores . . . Supplier . . . Supplier lead +me Stores Current Proposed change Supply chain Supplier lead time Store holding costs Store in4stock requirement A Short (1 week) Low (20%) Low (0.950) B Short (1 week) High (60%) Low (0.950) C Short (1 week) Low (20%) High (0.999) D Short (1 week) High (60%) High (0.999) E Long (10 weeks) Low (20%) Low (0.950) F Long (10 weeks) High (60%) Low (0.950) G Long (10 weeks) Low (20%) High (0.999) H Long (10 weeks) High (60%) High (0.999) Pooling is most beneficial when: In-stock requirement is HIGH Store holding costs are HIGH Supplier lead time is LONG Answer: H

OIDD 615 Sample Final Exam. Page 11 of 16 Q20. Which of the following five graphs (A,…,E) best describes the relationship between the amount of cross training provided to a team of consultants (x-axis) and the value/benefit of that cross training (y-axis)? Q21. JetFree Air sells seats on their airplanes for less than all of their competitors. However, they do not allow refunds or ticket changes – if a customer purchases a ticket but doesn’t use the ticket for the designated flight, then the customer loses the entire purchase price. Despite not allowing refunds or ticket changes (even for a fee), JetFree overbooks their flights – they sell more tickets than they have seats on the aircraft. From the point of view of maximizing revenue in the short run (i.e., ignore long run customer retention issues), is this a rational strategy? a) No – Given that they don’t have refunds, there is no need to risk having more passengers arrive for a flight than there are seats on the plane. b) No – It is not optimal to overbook when ticket prices are low. c) No – Overbooking increases the chances of departure delays. d) Yes – Given that some customers do not arrive for the flight, this allows them to effectively sell some seats twice. e) Yes – Whenever there are different customer classes, such as “business travelers” willing to book “last minute” at a higher price, and “leisure travelers” that book well in advance, it is advantageous to reserve some seats for the business travelers. Cross training Benefit Cross training Benefit Cross training Benefit Cross training Benefit Cross training Benefit A B C D E A little cross-training can provide a huge improvement in efficiency. Answer: D Answer: D

OIDD 615 Sample Final Exam. Page 13 of 16 Q24 (1pt) A firm uses an order up-to model to manage inventory. Suppose they increase their target in-stock probability and therefore raise the order upto level for the product. Nothing else changes. For example, they continue to order with the same frequency, the lead time remains the same and the demand distribution remains the same. Would the coefficient of variation of this firm’s orders to their supplier increase, decrease or stay the same (once they have adjusted to the new order upto level)? Explain your choice. Q25 (2pt) Operations strategy involves decisions on process timing, location, and control. The higher the level of control, the more standardized a firm can make its processes. Give an example of a company that adopted a more standardized process relative to the rest of the industry and identify the two key benefits of that decision for the company. A 1pt answer only gives one benefit or no example. A 2pt answer gives an example and two benefits. The classic example is McDonalds. By standardizing the cooking process they could increase conformance quality (i.e., the consistency of the product across locations) and they could higher less expensive/lower skilled labor. Stay the same. With an order upto policy the amount ordered each period equals demand in the previous period, no matter what the order upto level is. As demand doesn’t change, it follows that the variability of the ordering process doesn’t change either.

OIDD 615 Sample Final Exam. Page 14 of 16 Q26 (2pt) Suppose a firm would try to compete with Amazon by charging customers a lower price (including shipping). To make this a viable business, explain what else the firm would have to do – in terms of operations as well as what it offers customers – to make this a potentially viable strategy (i.e., a strategy that may lead to a successful business in the long run). Given that Amazon is barely profitable, to lower price and still be viable (i.e., make a profit), the firm would have to sacrifice some costly feature. For example, they could use cheaper/slower shipping, or they could stock inventory is fewer locations (which would reduce inventory costs but increase shipping times), or they could offer less variety (which would reduce inventory costs). A 1 pt answer identifies that there is a tradeoff but doesn’t provide details.

OIDD 615 Sample Final Exam. Page 16 of 16 purchases the tray from you (Tovolo) and sends the product to one or more of Amazon’s warehouses. When the 3 rd party seller makes a sale to a customer, Amazon ships the product to the customer (because Amazon is the one that is physically holding the product). As the article mentions, Amazon may commingle (i.e., pool) identical items (as determined by their bar codes) stored in the same warehouse from multiple 3 rd party sellers. The article discusses a limitation of this program – it might result in a customer receiving a counterfeit item when they thought they were purchasing the original item. One benefit of the program is that 3 rd party sellers don’t have to go through “ … the trouble of having to label individual items sent to the Amazon warehouse.” Besides the labeling advantage (which can’t be too big), why would Amazon do this? In other words, what are the advantages of such an idea? (Note, don’t explain why Amazon offers order- fulfillment services to 3 rd party sellers. Instead, given that they offer order-fulfillment services, explain the rationale for commingling identical inventory.) By pooling inventory Amazon can avoid delaying shipping an item from one seller that is out of inventory when the same item is available from another seller. It also means that Amazon can choose to ship from the nearest DC (to lower shipping costs) even though the seller’s items may be stocked in another DC.