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Stepping Stone Method

The Stepping Stone Method is an iterative procedure used to improve an initial feasible solution for the transportation problem. It involves examining the adjacent cells in a solution and evaluating the effect of transferring units of the shipment from one cell to another on the total cost. The method works as follows:

Begin with an initial feasible solution obtained using a heuristic method such as the North-West Corner Method, Least Cost Method, or Vogel’s Approximation Method.

Identify the set of occupied cells in the solution, i.e., cells with non-zero allocation.

Select an unoccupied cell and draw a closed path that starts and ends in the same row or column.

Determine the net change in the cost if one unit of shipment is moved from an occupied cell to the unoccupied cell, following the closed path.

Repeat step 4 for all other closed paths containing the unoccupied cell.

Select the closed path that results in the largest reduction in the total cost, and adjust the allocation by transferring one unit of shipment along the closed path.

Repeat steps 3 to 6 until no further improvement can be made.