Question

Create a transportation problem
Select an initial feasible solution ( any method).
Solve the transportation problem using the method of multipliers.

Answer 1

PROBLEM :

A company has factories at F1 and F2 which supply to warehouses at W1 and W2. Weekly factory capacities are 190 and 130 units, respectively. Weekly warehouse requirement are 180 and 140 units, respectively. Unit shipping costs ( in dollars ) are as follows :

	W1	W2	Supply
F1	16	20	190
F2	14	8	130
Demand	180	140

Determine the optimal distribution for this company to minimize total shipping cost.

INITIAL FEASIBLE SOLUTION USING VOGEL'S APPROXIMATION METHOD :

In this method we calculate row and column penalties. For row penalties we calculate the difference between the two least cost cells which have not been allocated, for both rows and columns.

SOLVING THE TRANSPORTATION PROBLEM USING THE METHOD OF MULTIPLIERS :

In the method of multipliers, we associate the multipliers Ui and Vj with row i and column j of the transportation tableau.

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