Reconsider Prob. 8.1-7. Now assume that distribution centers 1, 2, and 3 must receive exactly 10, 20, and 30 units per week, respectively. For administrative convenience, management has decided that each distribution center will be supplied totally by a single plant, so that one plant will supply one distribution center and the other plant will supply the other two distribution centers. The choice of these assignments of plants to distribution centers is to be made solely on the basis of minimizing total shipping cost.
(a) Formulate this problem as an assignment problem by constructing the appropriate cost table, including identifying the corresponding assignees and tasks.
(b) Obtain an optimal solution.
(c) Reformulate this assignment problem as an equivalent transportation problem (with four sources) by constructing the appropriate parameter table.
(d) Solve the problem as formulated in part (c).
(e) Repeat part (c) with just two sources.
(f) Solve the problem as formulated in part (e).
Prob. 8.1-7
The Move-It Company has two plants producing forklift trucks that then are shipped to three distribution centers. The production costs are the same at the two plants, and the cost of shipping for each truck is shown for each combination of plant and distribution center:
A total of 60 forklift trucks are produced and shipped per week. Each plant can produce and ship any amount up to a maximum of 50 trucks per week, so there is considerable flexibility on how to divide the total production between the two plants so as to reduce shipping costs. However, each distribution center must receive exactly 20 trucks per week. Management's objective is to determine how many forklift trucks should be produced at each plant, and then what the overall shipping pattern should be to minimize total shipping cost.
(a) Formulate this problem as a transportation problem by constructing the appropriate parameter table.
(b) Display the transportation problem on an Excel spreadsheet.
(c) Use the Excel Solver to obtain an optimal solution.