# Transportation and Assignment Models in Operations Research

Transportation and assignment models are special purpose algorithms of the linear programming. The simplex method of Linear Programming Problems(LPP) proves to be inefficient is certain situations like determining optimum assignment of jobs to persons, supply of materials from several supply points to several destinations and the like. More effective solution models have been evolved and these are called assignment and transportation models.

The transportation model is concerned with selecting the routes between supply and demand points in order to minimize costs of transportation subject to constraints of supply at any supply point and demand at any demand point. Assume a company has 4 manufacturing plants with different capacity levels, and 5 regional distribution centres. 4 x 5 = 20 routes are possible. Given the transportation costs per load of each of 20 routes between the manufacturing (supply) plants and the regional distribution (demand) centres, and supply and demand constraints, how many loads can be transported through different routes so as to minimize transportation costs? The answer to this question is obtained easily through the transportation algorithm.

Similarly, how are we to assign different jobs to different persons/machines, given cost of job completion for each pair of job machine/person? The objective is minimizing total cost. This is best solved through assignment algorithm.

Uses of Transportation and Assignment Models in Decision Making

The broad purposes of Transportation and Assignment models in LPP are just mentioned above. Now we have just enumerated the different situations where we can make use of these models.

Transportation model is used in the following:

• To decide the transportation of new materials from various centres to different manufacturing plants. In the case of multi-plant company this is highly useful.
• To decide the transportation of finished goods from different manufacturing plants to the different distribution centres. For a multi-plant-multi-market company this is useful.
• To decide the transportation of finished goods from different manufacturing plants to the different distribution centres. For a multi-plant-multi-market company this is useful. These two are the uses of transportation model. The objective is minimizing transportation cost.

Assignment model is used in the following:

• To decide the assignment of jobs to persons/machines, the assignment model is used.
• To decide the route a traveling executive has to adopt (dealing with the order inn which he/she has to visit different places).
• To decide the order in which different activities performed on one and the same facility be taken up.

In the case of transportation model, the supply quantity may be less or more than the demand. Similarly the assignment model, the number of jobs may be equal to, less or more than the number of machines/persons available. In all these cases the simplex method of LPP can be adopted, but transportation and assignment models are more effective, less time consuming and easier than the LPP.