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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 Section A J. G. Dai Test 1 (February 24, 2011) This is a closed book test. No calculator is allowed. There are a total of 4 problems. The full score is 100. 1. (30 points) A warranty department manages the after-sale service for a critical part of a product. The department has an obligation to replace any damaged parts in the next 6 months. The number of damaged parts X in the next 6 months is assumed to be a random variable that follows the following distribution x 100 200 300 400 P ( X = x ) .1 .2 .5 .2 The department currently has 200 parts in stock. The department needs to decide if it should make one last production run for the part to be used for the next 6 months. To start the production run, the fixed cost is $2000. The unit cost to produce a part is $50. During the warranty period of next 6 months, if a replacement request comes and the department does not have a part available in house, it has to buy a part from the spot-market at the cost of $100 per part. Any part left at the end of 6 month sells at $10. (There is no holding cost.) Should the department make the production run? If so, how many items should it produce? (You will not receive any credit by guessing an answer. You must produce your calculations.) Solution. Note that 100- 50 100- 10 = 5 9 . Therefore, the optimal order up to quantity is 300. Assume the department makes a production run. The total expected cost is 2000 + 100(50) + 100 E ( X- 300) +- 10 E (300- X ) + = 2000 + 5000 + 100(100)( . 2)- 10[200( .....
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