OIDD615 practice questions - solutions

3 Q5. For the less popular players (“Other Players”) the CM ships a blank jersey to Nike’s DC at a cost of $11. After receiving the orders from retailers, Nike prints the name of the player and number on the blank jersey, which costs Nike $2 per jersey. Assume the selling price of jerseys with the names is still the same. If Nike runs out of blank jerseys, they can order more blank jerseys from a local supplier with essentially an immediate response time. But that supplier charges $14 per blank jersey. If Nike has blank jerseys left over at the end of the season, they sell them blank for $7 each. Demand for “Other Players” is Normally distributed with a mean of 60,000 and a standard deviation of 30,000. How many blank jerseys should Nike purchase from the CM (for $11 each) to maximize their expected profit from selling “Other Players”? (Q6-7) (Simplified Hosting Problem) Vmail is a service provider of free email. It hosts all emails on servers on “the cloud”. The typical usage on Mondays is normally distributed with mean 300 million minutes and standard deviation 75 million minutes. For a particular Monday, Vmail can buy cloud capacity well in advance for $0.01 per minute. If it purchases more capacity than it needs, the capacity goes unused (and they cannot get a refund for the capacity they purchased). If demand on Monday exceeds the capacity they purchased in advance, they must purchase additional capacity as needed from a company called Mackspace. However, Mackspace charges $0.03 per minute. Q6. How much capacity should Vmail purchase in advance (at $0.01 per minute) to minimize its total expected capacity expense? Give your answer in units of million minutes. Answer: 54,600. Cu= 14-11=3. If they order one jersey fewer than demand, they order from the more expensive supplier which costs $14 (instead of $11 from the regular supplier). The $2 printing cost doesn’t matter because it is incurred whether $11 or $14 is paid for a blank jersey. Co = Cost – salvage = $11-$7 = $4. If they over order by one unit, it must be salvaged (but there is no printing on this blank jersey). The Critical Ratio = Cu / (Co + Cu) = 0.4286 From the Normal Distribution Function Table we obtain z = -0.18. Then Q = µ + z*σ = 54,600. Answer: 333. Cu= 0.03-0.01 = 0.02 because if you had known you would use the minute of capacity, you would have purchased it for $0.01 rather than having to buy it from Mackspace for $0.03. Co=0.01 because if you buy the minute of capacity but don’t use it, you would have just not purchased the capacity and saved yourself 0.01. Critical Ratio = 0.6667 From the Standard Normal distribution function table, z = 0.44. Then Q = µ + z*σ = 333M.

6 Q10. Suppose the forecast for the May issue of National Geographic is normally distributed with a mean of 160 and a standard deviation of 45. The Penn Bookstore plans to stock 200 copies. What is the probability that they stockout (i.e., do not satisfy all demand)? Q11. BASF sells customized petrochemical catalysts that are produced in a plant in Germany. Many of their customers are in North America and transportation is done via ocean carrier. They can purchase container capacity in advance at the price of $2,250 per container. However, if they advance purchase containers, they bear the risk of not knowing their exact needs for containers. In particular, here is a forecast of their needs for June (i.e., a density and distribution function): If they purchase a container in advance and don’t actually need it, then they will fill it with some excess product and store that product in North America until it will be sold (i.e., the product is neither perishable nor at risk of obsolescence). The expected extra storage cost is $350 per container. For example, if their needs are for 2 containers but they advanced purchased 3 containers, then they ship all three containers and incur an extra $350 charge for the 1 container filled with excess product. Containers purchased on the spot market (after they learn their needs) are expected to cost $3000 per container. For example, they may advance purchase 1 container but discover that they need 3 containers, in which case they would purchase an additional 2 containers at $3000 each. How many containers should they advance purchase to minimize their costs? Q f(Q) F(Q) Q f(Q) F(Q) 0 0.0952 0.0952 11 0.0222 0.8997 1 0.1640 0.2592 12 0.0182 0.9179 2 0.1343 0.3935 13 0.0149 0.9328 3 0.1099 0.5034 14 0.0122 0.9450 4 0.0900 0.5934 15 0.0100 0.9550 5 0.0737 0.6671 16 0.0082 0.9631 6 0.0603 0.7275 17 0.0067 0.9698 7 0.0494 0.7769 18 0.0055 0.9753 8 0.0404 0.8173 19 0.0045 0.9798 9 0.0331 0.8504 20 0.0037 0.9834 10 0.0271 0.8775 Answer: 0.187. Q=200. Normalize the order quantity: z= (Q-µ)/σ = 0.89. From the Standard Normal Distribution Table the outcome of a standard normal is 0.89 or lower with probability 0.813. So the stockout prob is 1-0.813 = 0.187 Answer: 6 containers Co = $350. If they reserve one too many containers, they incur a cost of $350 that they would not have occurred otherwise. The product would have been shipped eventually, so the shipping costs do not factor into the overage cost. Cu = $750. If they reserve one too few containers, then they need to purchase a container on the spot for $3000. Had they known that they would need the container, they could have purchased it for $2,250. Hence, they incur $750 in additional charges. Critical ratio = 750 / (350 + 750) = 0.6818 From the table above, F(5) = 0.6671 and F(6) = 0.7275, so they should advance purchase 6 containers.

9 Q14. Which of the following statements is most likely to correctly characterize the difference between make-to-order and make-to-stock production? a) There is no work-in-process inventory with make-to-order whereas there can be a considerable amount with make-to-stock. b) When firms move production from high labor cost countries to lower labor cost countries they usually switch from make-to-stock to make-to-order production. c) Make-to-stock production copes with seasonal demand by building and drawing down inventory whereas make-to-order production copes with seasonal demand by adding and reducing labor. d) Firms that offer a narrow product line are more likely to implement make-to-order production. e) None of the above is correct. f) All of the above are correct. Order Upto Q15. Maxter Healthcare manages inventory of medical supplies at the Hospital of the University of Pennsylvania. In the emergency ward, their daily need of saline solution is normally distributed with a mean of 100 units and standard deviation 50 units. Orders are placed daily and received the next day (i.e. the lead time is one day). What order up-to level should Maxter use if they want to ensure a 99.5% in-stock probability while minimizing inventory? Answer c. (a) is incorrect because there is WIP with make-to-order. (b) is incorrect because it is not the case that high labor cost countries operate with make-to-stock and low-labor cost countries operate make-to-order (if anything, the pattern would probably be reversed). (d) make-to-order is done to provide variety, not to reduce it. (c) is correct because make-to-stock makes product in advance of demand, so if there is seasonality, then make-to-stock must build inventory in advance of a peak. As make-to-order cannot make product in advance of demand, when demand is high, it either makes customers wait a long time or it hires labor to cope with the surge. Answer: 382 We want instock probability of 0.9950. Looking up the Standard Normal distribution function table, we find z-score corresponding to the probability 0.995 is 2.58. Mu = The mean over L+1 periods is 100*2 = 200; Sigma = The standard deviation over L+1 periods is sqrt(2)*50 = 70.7, S= mu + z * sigma = 382

12 Q21. Aldi sells its private label granola cereal. Daily demand is Poisson with mean 3.5. Aldi replenishes stores daily, and the lead time to receive an order is 1 day. If they manage inventory of this product using a base stock level of 10, then what would be their average end-of-the-day on- hand inventory? Q22. Weekly demand for a wrench kit at Ace Hardware is Poisson with mean 0.2. They have a one week replenishment lead time and operate with a basestock level of 1. What is their weeks-of-supply for this wrench kit? Q23. Lowes sells the Sunburst Rose for $25 per unit and they buy it for $10 per unit. There is a short season for this product and they get to place a single order with their supplier. Demand during the selling season is expected to be Poisson with mean 8.25. Roses that are left over at the end of the season are thrown away. If they purchase 12 of the Sunburst Roses, what is the probability that Lowes makes a positive profit on this purchase? Answer: 3.2 Demand over l+1 days is (1+1)x3.5 = 7.0 S = 10 From the Poisson Inventory Function Table, I(S) = 3.2 Answer: 3.35 weeks Demand over l+1 weeks is (1+1) x 0.2 = 0.4 S = 1 From the Poisson Inventory Function table, I(S) = 0.67 Weeks of supply = 0.67 / 0.2 = 3.35 Answer: 0.914 If they purchase 12 at $10 each, their total cost is 12 x $10 = 120. At $25 per sale, they need 120/$25 = 4.8 sales to break even. As they cannot get 4.8 sales, they break even if they sell 5 or more. The probability to sell 5 or more is equal to 1 - Prob(Sell 4 or fewer). From the Poisson Distribution Function Table with mean 8.25, F(4) = 0.086 So they get a positive profit with probability 1-0.086= 0.914