Transportation Problem

Maximization In A Transportation Problem

There are certain types of transportation problems where the objective function is to be maximized instead of being minimized. These problems can be solved by converting the maximization problem into a minimization problem.

"Profit maximization is the single universal objective for most commercial organizations." -Vinay Chhabra & Manish Dewan

Example

Surya Roshni Ltd. has three factories - X, Y, and Z. It supplies goods to four dealers spread all over the country. The production capacities of these factories are 200, 500 and 300 per month respectively.

Determine a suitable allocation to maximize the total net return.

Solution.

Maximization transportation problem can be converted into minimization transportation problem by subtracting each transportation cost from maximum transportation cost.

Here, the maximum transportation cost is 25. So subtract each value from 25. The revised transportation problem is shown below.

Table 1

An initial basic feasible solution is obtained by matrix-minimum method and is shown in the final table.

Final table

Factory	Dealer				Capacity
	A	B	C	D
X	13	7	19		200
Y				7	500
Z		22	14		300
Demand	180	320	100	400

The maximum net return is

25 X 200 + 8 X 80 + 7 X 320 + 10 X 100 + 14 X 100 + 20 X 200 = 14280.