IEOR150F10_hw01_sol

# IEOR150F10_hw01_sol - IEOR 150 Fall 2010 Suggested Solution...

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Unformatted text preview: IEOR 150, Fall 2010 Suggested Solution to Homework 1 1. (Problem 4.10 in the textbook; 20 points) For this problem, we have the following parameters: The fixed ordering cost K = 45 dollars per pound, the demand rate λ = 280 pounds per year, and the holding cost h = 2 . 40 × . 2 = 0 . 48 dollars per pound per year. (a) The optimal order quantity is Q * = r 2 Kλ h = r 2 × 45 × 280 . 48 = r 25200 . 48 = 229 . 13 pounds . (b) If we order Q * pounds, it takes Q * λ years to consume this amount. The optimal order cycle is thus T * = Q * λ = 229 . 13 280 = 0 . 82 year . (c) The average annual cost of holding and setup is G * = √ 2 Kλh = √ 2 × 45 × 280 × . 48 = \$109 . 98 . (d) Because we assume there are 52 weeks in one year, three weeks is τ = 3 52 years. Note that τ = 3 52 < . 82 = T * , so the lead time is shorter than the optimal order cycle. Therefore, the reorder quantity should be R = τλ = 3 52 × 280 = 16 . 15 pounds . This is the amount we consume during the lead time. 2. (Problem 4.13 in the textbook; 10 points) Under the true fixed ordering cost K = 15 dollars, the “wrong” total cost calculated in using the “wrong” order quantity Q *...
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IEOR150F10_hw01_sol - IEOR 150 Fall 2010 Suggested Solution...

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