Step1:

Set up a dummy column (dummy destination) if total supply > total demand or a dummy row (dummy source) if total demand > total supply by introducing any constant unit cost (k). The supply or demand at the dummy origin as a rim requirement is equal to the absolute difference of total supply and total demand. Hence an unbalanced transportation problem is converted into a balanced transportation problem.

Step 2:

Find an initial basic feasible solution (IBFS) by applying any transportation heuristics, namely North-West Corner Rule, least cost method, Vogel’s approximation method, Russell’s approximation method etc.

Step 3:

Following the determination of IBFS, obtain the optimum solution by using Modified distribution (MODI) method or Stepping stone method.

Step 4:

Calculate total transportation cost for the balanced transportation problem (BTP) with the feasible allocations obtained in step 3.

Step 5:

Compute total transportation cost for the original unbalanced transportation problem (UTP) as follows:

Total cost for UTP = Total cost for BTP − k × supply at dummy source or k × demand at dummy destination.