Transportation Models

Operations Management – Transportation Models

Transportation models are a special type of linear programming models. These models are applicable not only for solving problems of transportation but also for solving a variety of industrial problems. Usually such problems have a large number of variables and constraints. Though possible, the computational effort required to solve such problems by the simplex technique is prohibitive. However, these problems have some special features and we can solve them by simpler methods.

Suppose a company has m plants which meet the demand at n market areas where

S_i is the plant capacity of plant i

D_j is the demand at market j

C_ij is the cost of transportation of unit product from plant i to market j.

There is a need to design a schedule of shipment of the products from various plants to meet the demand at all the market areas so as to minimize the total cost of transportation. We can formulate a mathematical model to solve the problem as

Let x_ijbe the number of units applied from plant i to market j . Then the total cost of transportation can be written as

Z = ^mΣ_i=1 ⁿΣ_j=1 C_ij x_ij

We have to minimize Z subject to the following constraints

The total supply from any plant will not exceed the plant capacity.

The total supply to any market will not be less than the associated demand.

Method of Solution

The solution of the Transportation model comprises the following steps:

• Start with an initial feasible solution
• Check if the current solution is optimal
• Improve upon the current solution in case there is a scope for further improvement

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