Page 113 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
Table 5.12: Balanced TP Model
Source Destination
1 2 3 4 Supply
1 10 16 9 12 200
2 12 12 13 5 300
3 14 8 13 4 300
4 0 0 0 0 200
Demand 100 200 450 250 1000/1000

5.7 Initial Feasible Solution

Step 1: Formulate the Problem

Formulate the given problem and set up in a matrix form. Check whether the problem is a
balanced or unbalanced transportation problem. If unbalanced, add dummy source (row) or
dummy destination (column) as required.

Step 2: Obtain the Initial Feasible Solution

The initial feasible solution can be obtained by any of the following three methods.
1. Northwest Corner Method (NWC)
2. Row and Column Minima Method (RCMM)
3. Vogel’s Approximation Method (VAM)

The transportation cost of the initial basic feasible solution through Vogel’s approximation
method, VAM will be the least when compared to the other two methods which gives the value
nearer to the optimal solution or optimal solution itself. Algorithms for all the three methods to
find the initial basic feasible solution are given.

5.7.1 Algorithm for North-West Corner Method (NWC)

1. Select the North-west (i.e., upper left) corner cell of the table and allocate the maximum
possible units between the supply and demand requirements. During allocation, the
transportation cost is completely discarded (not taken into consideration).

2. Delete that row or column which has no values (fully exhausted) for supply or demand.
3. Now, with the new reduced table, again select the North-west corner cell and allocate the
available values.

4. Repeat steps (2) and (3) until all the supply and demand values are zero.
5. Obtain the initial basic feasible solution.

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