# hw4 - holding cost h is charged for per unit excess...

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HOMEWORK 4 Due April 9 For students registered for 3 credits: 5.5, 5.6 and 5.13. For students registered for 4 credits: 5.5, 5.6, 5.13, 5.10 and the following problem (a). (a) Consider n retailers each of which faces a Newsvendor problem. That is, each retailer faces uncertain demand and needs to place an order to fill it before its realization. The retailers’ demands depend on the state of the world ω . Let Ω be the sample space of ω with a finite number of scenarios and assume that ω takes the outcome j with probability p j (and thus j Ω p j = 1). Assume that ordering incurs a per unit cost c , a penalty l is incurred for per unit unfilled demand and a
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Unformatted text preview: holding cost h is charged for per unit excess inventory (for simplicity, we assume that these costs are the same for all retailers). The retailers may decide to collaborate by placing joint orders before observing the realization of uncertain demand and redistributing inventory among themselves after demand realization. Apparently, the whole system would be better oﬀ due to the risk pooling eﬀect. The question is how the retailers should share the cost. You are asked to formulate this question in a cooperative game framework and show that the core is nonempty. 1...
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