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Definition: Assignment problems are specials class of linear programming problems which involve determining most efficient assignment of people to projects, jobs to machines etc. The desired objective is to minimize total costs or time required to perform the task at hand. The assignment is made on a one-to-one basis.

Comparison with Transportation Model: Assignment model may be regarded as a special case of transportation model. Here facilities represent the “sources” while the jobs represent the “destinations”. The supply available at each source is 1 i.e. ai = 1 for all i. Similarly, the demand at each destination is 1 i.e. bj = 1 for all j. The cost of transport ting (assigning) facility i to job j is cij.

Distinction between assignment problem and transportation problem: Assignment problem is a variation of transportation problem with two characteristics:
i) The cost matrix of an assignment problem is a square matrix and
ii) The optimum solution for the problem would always be such that there would be only one assignment in a given row or column of the cost matrix.

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