21. The Marengo Machine Company is a job shop that produces a great variety of items.

Flow within its plant is varied. Some departments deal with heavy items that are expensive to transport. The materials usually transported between some departments require only hand trucks, while a large industrial truck is usually required for the items moved in other parts of the plant. The costs for moving between various pairs of departments are shown in Table A. The expected number of trips between the departments is shown in Table B.

a. Develop a matrix of nearness priorities by computing the cost the company will incur for each unit of distance between the various departments.

b. Assume the departments are equal-size squares, and arrange them in a 2 X 3 grid so that the transportation costs will be minimized.

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TABLE A Cost per Unit of Distance between Departments (Dollars) FROM TO LATHE MILLS DRILLS CASTING FINISHING ASSEMBLY Lathe - 0.02 0.02 0.02 0.02 0.02 Mills 0.05 0.05 0.05 0.05 0.05 Drills 0.03 0.03 - 0.03 0.08 0.03 Casting 0.08 0.08 0.08 - 0.08 0.08 Finishing 0.05 0.05 0.05 0.05 0.05 Assembly 0.10 0.10 0.10 0.10 0.10 TABLE B Expected Number of Trips between Departments per Week FROM TO LATHE MILLS DRILLS CASTING FINISHING ASSEMBLY Lathe 300 100 Mills 200 300 Drills 50 150 - Casting 50 350 300 - Finishing 20 20 20 Assembly 10 10 10 292199 10 100 100 10 150 150 10 200 300 50 100 10 - 500 0 0