Midterm_1_Solutions (1)

Midterm_1_Solutions (1) - IEOR 150 Midterm I Fall 2009...

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IEOR 150 Midterm I Fall 2009 Problem 1 (25 points) A coffee shop in San Francisco sells Cappuccino at a fairly steady rate of 1000 pounds annually. Assume one pound of Cappuccino is made from 0.25 pound of some certain coffee beans. The beans are purchased from a local supplier for \$2.70 per pound. The setup cost for this coffee shop to place an order from its supplier is \$50. The holding cost for coffee beans is based on a 20 percent annual interest rate. a. Determine the optimal order quantity for the coffee beans. (10 points) b. If the replenishment lead time is three weeks, determine the recorder level based on the on-hand inventory. (5 points) c. The current reorder policy is to buy the coffee beans once a year, what is the additional cost incurred by this policy. (10 points) Solution a. 50 K = 1000 0.25 250 2.7 0.2 0.54 h λ = × = = × = So, the optimal order quantity should be 2 2 50 250 * 215 0.54 K Q h λ × × = = = b. The reorder point should be 250*3 / 52 14.42 15 R λτ = = = c. Average annual cost for setup cost and holding cost under optimal order policy is 50 250 0.54 215 * 116.19 2 215 2 K hQ C Q λ × × = + = + = Average annual cost for setup cost and holding cost under current order policy is 50 250 0.54 250 117.5 2 250 2 K hQ C Q λ × × = + = + = Additional cost is * 117.5 116.19 1.31 C C C Δ =

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