# Optimization Models Question

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1-A general property of the EOQ inventory model is that total inventory holding and total ordering costs are equal at the optimal solution. Use the data in Problem 1 to show that this result is true. Use equations (10.1), (10.2), and (10.3) to show that, in general, total holding costs and total ordering costs are equal whenever Q* is used

2-Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside’s generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year (12,000 units annually). Assume that the ordering costs are \$25 per order, the unit cost is \$2.50 per compo-nent, and annual holding costs are 20% of the value of the inventory. Westside has 250 work-ing days per year and a lead time of 5 days. Answer the following inventory policy questions:

a. What is the EOQ for this component?

b. What is the reorder point?

c. What is the cycle time?

d. What are the total annual holding and ordering costs associated with your recom-mended EOQ?

3- The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC \$250 per order to cover the expenses of delivering and transferring the fuel to MBC’s storage tanks. The lead time for a new shipment from American Petroleum is 10 days; the cost of holding a gallon of fuel in the storage tanks is \$0.04 per month, or \$0.48 per year; and annual fuel usage is 150,000 gallons. MBC buses operate 300 days a year.

a. What is the optimal order quantity for MBC?

b. How frequently should MBC order to replenish the gasoline supply?

c. The MBC storage tanks have a capacity of 15,000 gallons. Should MBC consider expanding the capacity of its storage tanks?

d. What is the reorder point?

4-All-Star Bat Manufacturing, Inc., supplies baseball bats to major and minor league base-ball teams. After an initial order in January, demand over the six-month baseball season is approximately constant at 1000 bats per month. Assuming that the bat production process can handle up to 4000 bats per month, the bat production setup costs are \$150 per setup, the production cost is \$10 per bat, and the holding costs have a monthly rate of 2%, what production lot size would you recommend to meet the demand during the baseball season? If All-Star operates 20 days per month, how often will the production process operate, and what is the length of a production run?

5-Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is \$14.50. The holding cost is based on an 18% annual rate, and production setup costs are \$150 per setup. The equipment with which the book is produced has an annual production volume of 25,000 copies. Wilson has 250 working days per year, and the lead time for a production run is 15 days.

Use the production lot size model to compute the following values:

a. Minimum cost production lot size

b. Number of production runs per year

c. Cycle timed. Length of a production rune. Maximum inventory

f. Total annual cost

g. Reorder poin

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