# Economic Order Quantity and Cycle Service Level

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• Published : November 18, 2010

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OPERATIONS MANAGEMENT B3401
ASSIGNMENT # 3 (Total 100 points)
Due on Nov 16 2010 (Tuesday)
(Write your name, student #, section # in which you are registered)

Q1. (Total 20 points)
The FS factory can produce wieners at a rate of 5,000 per day. FS supplies wieners to local stores at a steady rate of 250 per day. The cost of preparing the equipment for producing wieners is \$22. Annual holding costs are 15 cents per wiener. The factory operates 300 days a year. Find: 1) The optimal total production quantity per cycle and the corresponding maximal on-hand stock level. 2) The optimal number of cycles per year

3) The optimal length of each cycle.

Q2. (Total 30 points)
A manufacturer of exercise equipment purchases the pully section of the equipment from a supplier who lists these prices: less than 1000, \$5 each; 1,000 to 3,999, \$4.95 each; 4,000 to 5,999, \$4.9 each; and 6,000 or more, \$4.85 each. Ordering costs are \$50 per order, annual carrying costs are 40 percent of purchase cost, and annual usage is 4,900 pulleys. Determine an order quantity that will minimize the total cost (Ordering + Holding + Purchase).

Q3. (Total 50 points)
Harvey’s Specialty Shop is a popular spot that specializes in international gourmet foods. One of the items that Harvey sells is a popular mustard that he purchases from an English company. The mustard costs \$10 a jar and requires a 2-month lead time for replenishment of stock. The replenishment time is almost constant. Harvey uses a 20% annual interest rate to compute holding costs. Bookkeeping expenses for placing an order amount to about \$50. During the 2-month supply time, Harvey estimates that he sells an average of 100 jars but there is substantial variation. He estimates the standard deviation of demand for each 2-month period is 25. Assume that demand is described by a normal distribution. (3 + 3 + 4 + 8 + 12 + 20 = 50 points) a) What is the optimal order quantity?

b) What will be the average...