Solution procedure for transportation problems

We now turn our attention to the solution procedure for a transportation problem known as transportation method. Conceptually, the transportation method is similar to the simplex method. We begin with an initial feasible solution. This initial feasible solution may or may not be optimum. The only way one can find it out is to test it. If the solution is not optimum it is revised and the test is repeated. Each iteration should bring close to the optimum solution.

   The problem is solved in general, by using the following procedure.

Steps 1. Define the objective function to be minimized with the constraints imposed on the problem.

2. set up the transportation table with m rows representing the sources (plants, factories etc.) and n columns representing the destinations (warehouses, stores, markets, etc.,)

3. Develop an initial feasible solution to the problem.

4. Examine whether the initial solution is feasible or not. The solution is said to be feasible if the solution has allocations in (m + n-1) cells with independent positions. (The positions are said independent if it is not possible to alter any individual allocation without either changing the positions of allocations or violating the supply and demand constraints.) The cells having allocation are known as occupied cells and the remaining cells are known as empty (or unoccupied) cells.

5. Test whether the solution obtained in step 4 is optimum or not. This is done by computing opportunity costs associated with the empty cells. Positive opportunity costs for all the empty cells signify optimum solution. (By opportunity cost of an empty cell, we mean that what will be the cost reduction if this particular cell is included in the solution).

6. if the solution is non-optimum modify the shipping schedule by including that empty cell whose inclusion in the programme results in largest savings.

7. Repeat steps 5 and 6 units an optimum solution is obtained.

Applications

Few applications of transportation model are given below:

-          To minimize shipping costs from factories to warehouses or from warehouses to retail outlets.

-          To determine lowest cost location for new factory warehouse or sales office.

-          To determine minimum cost production schedule that satisfies firm s demand and production limitations (called production smoothing)

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