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.
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
Factory | Dealer | Capacity | |||
---|---|---|---|---|---|
A | B | C | D | ||
X | 13 | 7 | 19 | ||
Y | 7 | ||||
Z | 22 | 14 | |||
Demand |
The maximum net return is
25 X 200 + 8 X 80 + 7 X 320 + 10 X 100 + 14 X 100 + 20 X 200 = 14280.