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Kappa Tile Company

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Mr. H.D. Johnson is president and majority stockholder of the Kappa Tile Company, a large manufacturer of high-quality bathroom and patio tile. Mr. Johnson purchased the company a approximately 20 years ago. At that time, the company had only one manufacturing plant, which was located in a small town in Tennessee. Kappa Tile Company has grown rapidly during the past 20 years. It is now one of the top five manufacturers of bathroom tile in the United States. Its Tennessee plant has quadrupled in size, and it has built two large new plants, one in Texas and one in the Midwestern area of the United States.

The company is concerned with a logistics problem that involves its major product line, white bathroom tile. This product accounts for 37% of the company's total sales volume. It is produced at all three of Kappa's manufacturing locations. The company's total volume of bathroom tile is sold to four major distributors located throughout the central part of the United States. The monthly requirements of the four distributors are 1500, 2000, 2500, and 3500 units. Each of the four distributors can be supplied from any of the company's manufacturing plants. There are production limitations, however, in that the Tennessee plant (plant 1), the Southwest plant, (plant 2), and the Midwest plant (plant 3) are limited to monthly production of 3000, 2750, and 3750 units respectively.

The Kappa Company must pay shipping cost on all tile, and Mr. Johnson believes that the company can save money by better allocating plant production. He has asked the chief accountant for an estimate of the per-unit shipping cost from each manufacturing plant to each distributor. These costs in dollars are as follows:


1 2 3 4

1 $15 $18 $22 $26

Plants 2 21 25 16 23

3 14 19 20 24

After receiving the cost data, Mr. Johnson discussed his logistics problem with the chief engineer. He knows that the firm has been quite successful in utilizing managerial decision techniques such as linear programming to reduce production costs and hopes that a similar tool of analysis will help him reduce distribution costs.


Mr. Johnson has been encouraging Kappa Tile's four distributors to install new inventory control systems,



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