hmwk10 - ISyE 3232 Stochastic Manufacturing and Service...

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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 Drs. Hayriye Ayhan and Jim Dai Homework 10 March 31, 2011 (Do NOT hand in; please finish it before the 2nd test) 1. Suppose we agree to deliver an order in one day. The contract states that if we deliver the order within one day we receive $1000. However, if the order is late, we lose money proportional to the tardiness until we receive nothing if the order is two days late. The length of time for us to complete the order is exponentially distributed with mean 0 . 7 days. For notation, let T be the length of time until delivery. (a) What are the probabilities that we will deliver the order within one day and within two days? (b) What is the expected tardiness? (c) Notice that this contract is the one in the Littlefield simulation game 1. We now add two more contracts (which similarly have the rule of losing money proportional to tardiness): price = $750; quoted lead time = 7 days; maximum lead time = 14 days. price = $1250; quoted lead time = 0 . 5 day; maximum lead time = 1 days. Notice that in the $1000 contract, quoted lead time = 1 day; maximum lead time = 2 days. What are the expected revenues for these three contracts? Which contract would be the most lucrative assuming the mean time to delivery is 0...
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This note was uploaded on 01/16/2012 for the course ISYE 3232 taught by Professor Billings during the Spring '07 term at Georgia Institute of Technology.

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hmwk10 - ISyE 3232 Stochastic Manufacturing and Service...

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