Assignment Model In Operational Research Notes


Many practical problems in operations research can be broadly formulated as linear programming

problems, for which the simplex this is a general method and cannot be used for specific types of problems like,

(i) transportation models, (ii) transshipment models and

(iii) the assignment models.

The above models are also basically allocation models. We can adopt the simplex technique to solve them,

but easier algorithms have been developed for solution of such problems. The following sections deal with the

transportation problems and their streamlined procedures for solution.


In a transportation problem, we have certain origins, which may represent factories where we produce

items and supply a required quantity of the products to a certain number of destinations. This must be done in such a

way as to maximize the profit or minimize the cost. Thus we have the places of production as origins and the places

of supply as destinations. Sometimes the origins and destinations are also termed as sources and sinks.

To illustrate a typical transportation model, suppose m factories supply certain items to n warehouses. Let

factory i (i = 1, 2, ..., m) produce ai units and the warehouse j (j = 1, 2, ..., n) requires bj units. Suppose the cost of

transportation from factory i to warehouse j is cij. Let us define the decision variables xij being the amount transported from the factory i to the warehouse j. Our objective is to find the transportation pattern that will

minimize the total transportation cost.

The model of a transportation problem can be represented in a concise tabular form with all the relevant

parameters mentioned above. See table 1

Table 1






1 2 ........ n

1 c11 c12 c1n a1

2 c21 c22 c2n a2

... ... ... ... ...

m cm1 cm2 cmn am

Required b1 b2 bn

The pattern of distribution of items in the form of transportation matrix is separately given below in table 2.



It makes use of Scientific methods to solve problems.•OR increases the effectiveness of a management Decision making ability.•It makes use of computer to solve large and complex problems.•It gives Quantitative solution.•It considers the human factors also.

The first and the most important requirement is that the root problem should be identifiedand understood. The problem should be identified properly, this indicates three major aspects:

A description of the goal or the objective of the study.

An identification of the decision alternative to the system.

Recognition of the limitations, restrictions and requirements of the system.

Limitations of OR:

The limitations are more related to the problems of model building, time and money factors.

Magnitude of computation: Modern problem involve large number of variables andhence to find interrelationship, among makes it difficult.

 Non – quantitative factors and Human emotional factor cannot be taken into account.

There is a wide gap between the managers and the operation researches.

Time and Money factors when the basic data is subjected to frequent changes thenincorporation of them into OR models are a costly affair.

Implementation of decisions involves human relations and behavior 

Q 2: What are the characteristics of the standard form of L.P.P.? What is the standard form of L.P.P.? State thefundamental theorem of L.P.P?








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