# Maximization 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: Maximization Problem in Transportation

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.

Factory Dealer Capacity
A B C D
X 12 18 6 25 200
Y 8 7 10 18 500
Z 14 3 11 20 300
Demand 180 320 100 400

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

Factory Dealer Capacity
A B C D
X 13 7 19 0 200
Y 17 18 15 7 500
Z 11 22 14 5 300
Demand 180 320 100 400

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

Final table

Use Horizontal Scrollbar to View Full Table Calculation.

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.