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Unformatted text preview: IEOR 150, Fall 2010 Suggested Solution to Midterm 1 1. (a) False. For example, an inventory problem with normally distributed demands and a pos itive lead time must have a positive probability of stockout. However, for an inventory problem with zero lead time, it is possible to achieve no stockout. (b) False. If a ( Q,R ) policy is applied in a periodic review system, all the order quantities will still be the same. It is impossible to construct an ( s,S ) policy in a periodic environment so that the order quantities are all the same. (c) True. Because in a continuous review system, we will place an order whenever the inventory level (or position if appropriate) hits s . This follows from the fact that the inventory level decreases continuously. Therefore, we will always order S s units. An ( s,S ) policy applied in a continuous review system is equivalent to a ( Q,R ) policy with Q = S s and R = s . (d) False. This may not be true when the demand is discrete. For example, consider a demand D following a Bernoulli distribution: P ( D = 0) = P ( D = 1) = 0 . 5. If = 0 . 7, we will order 1 unit; if = 0 . 8, we will still order 1 unit. The resulting expected holding and setup costs are the same. (e) True. Note that the annual purchasing costs with or without the poweroftwo restriction are the same because the total purchasing quantities are the same. If a > b > 0 and a b 1 + where (0 , 1), then certainly a + c b + c for any c > 0....
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 Fall '09

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