Vogel's Approximation Method (VAM)

Bengal Steel has three factories that send products to four distribution centers (DC) as given the table below. The unit costs of material handling and delivery to the four DCs are given at the top-right corner of each cell in the table. The manager wants to have a feasible solution to minimize the total cost of transportation.

Solve the problem usingVogel's Approximation Method (VAM) and circle the solution (amount of materials) in the respective solutions or write the xij (i = 1,2,3; j = 1,2,3,4) values. Does theVogel's Approximation Method (VAM) provide an optimal solution in general? Why and why not?

Please show all work and provide any source files or calculations used.

To	Distribution Centers	Supply
	DC-1	DC-2	DC-3	DC-4
Factory 1	12	11	9	20	120
Factory 2	8	5	17	15	150
Factory 3	10	15	14	7	130
Demand:	90	70	100	140	400

To	Distribution Centers	Supply
From	DC-1	DC-2	DC-3	DC-4
Plant 1	12	11	9	20
Plant 2	8	5	17	15
Plant 3	10	15	14	7
Demand: