IEOR150F10_Midterm2_Solution - IEOR 150 Fall 2010 Suggested...

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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 stock-out. However, for an inventory problem with zero lead time, it is possible to achieve no stock-out. (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 β = 0 . 7, we will order 1 unit; if β = 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 power-of-two restriction are the same because the total purchasing quantities are the same. If a > b > 0 and a b ≤ 1 + γ where γ ∈ (0 , 1), then certainly a + c b + c ≤ γ for any c > 0....
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IEOR150F10_Midterm2_Solution - IEOR 150 Fall 2010 Suggested...

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