Discussion
Consider the following tansportation problem :
| F1 | F2 | F3 | F4 | ||
|---|---|---|---|---|---|
| W1 | 19 | 30 | 30 | 10 | 7 |
| W2 | 70 | 30 | 40 | 60 | 9 |
| W3 | 40 | 8 | 70 | 30 | 18 |
| 5 | 8 | 7 | 14 | 34 |
(Columns: Factory F1 to F4; rows: Warehouse W1 to W3.)
Let Xij be the allocation in the (i, j)th cell. The solution (x11 = 5, x14 = 2, x22 = 2, x23 = 7, x32 = 6, x34 = 12) is :
Answer: B
The given allocation is the Optimal solution.
It uses 6 cells, equal to m + n - 1 = 3 + 4 - 1, so it is a basic solution. Test it with the u-v (MODI) method, setting \(u_{1} = 0\) and using \(u_{i} + v_{j} = c_{ij}\) in the occupied cells:
\[ \begin{aligned} v_{1} &= 19,\ v_{4} = 10,\ u_{3} = 20 \\ v_{2} &= -12,\ u_{2} = 42,\ v_{3} = -2 \end{aligned} \]
The reduced costs \(c_{ij} - u_{i} - v_{j}\) of the empty cells are 42, 32, 9, 8, 1 and 52, all positive, so no reallocation can lower the cost and the solution is optimal (total cost 863). It is not the Vogel or least cost starting solution: both of those first fill cell (3, 2), the lowest-cost cell at 8, with all 8 units, not 6.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development