Stepping stone method

After computing the initial solution by using any of the three methods explained above, the solution needs to be tested to see whether the solution is optimum or not, by using the stepping stone method. In this method, the decision-maker calculates the net cost change obtained by introducing a unit of quantity in any of the unoccupied cells and checks for the possibility of improving the solution. This method describes the unused cells as 'water' and used cells as 'stones,' and the transportation refers to walking on a path of stones half submerged in water. The procedure of this method is explained below:

Step 1: Determine the initial basic solution by using any of the three methods: north-west method, least cost method or the Vogel approximation method. Then check the solution for feasibility.

Step 2: Select an unoccupied cell and trace a closed path starting from that cell using the most direct route through at least three occupied cells by making only horizontal or vertical moves.

Step 3: Starting from the selected cell, assign + and - signs alternatively to the corner cells of the closed path.

Step 4: Calculate the 'net cost change' of the selected cell by adding the unit cost values (with the signs assigned) along the closed path.

Step 5: If the 'net cost change' is positive for all the unoccupied cells, we can conclude that optimum solution has been arrived at.

Step 6: If the 'net cost change' of an unoccupied cell is negative, the quantity of products to be assigned to that cell is equal to the minimum quantity of those cells with the minus sign in the closed path.

Step 7: Repeat the same procedure till the optimum solution has been reached.   

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