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# Assignment Problem

The assignment problem is a special case of transportation problem where the number of sources and destinations are equal.

Assignment Problem:

Introduction:

The assignment problem is a particular case of transportation problem for which more efficient (less-time consuming) solution method has been devised by KUHN (1956) and FLOOD (1956). The justification of the steps leading to the solution is based on theorems proved by Hungarian Mathematicians KONEIG (1950) and EGERVARY (1953), hence the method is named Hungarian Method.

Suppose that we have ŌĆśmŌĆÖ jobs to be performed on ŌĆśnŌĆÖ machines . The cost of assigning each job to each machine is Cij (i =1,2,ŌĆ”,n and j = 1,2,ŌĆ”,n).Our objective is to assign the different jobs to the different machines(one job per machine) to minimize the overall cost. This is known as assignment problem.

The assignment problem is a special case of transportation problem where the number of sources and destinations are equal. Supply at each source and demand at each destination must be one. It means that there is exactly one occupied cell in each row and each column of the transportation table . Jobs represent sources and machines represent destinations.

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12th Business Maths and Statistics : Chapter 10 : Operations Research : Assignment Problem | Introduction | Operations Research