Quantitativetechniquesinmanagement

Prof Vinay Pandit ASSIGNMENT AND TRANSPORTATION THEORY 1) What is an Assignment Problem? • The assignment problem can be stated as a problem where different jobs are to be assigned to different machines on the basis of the cost of doing these jobs. The objective is to minimize the total cost of doing all the jobs on different machines • The peculiarity of the assignment problem is only one job can be assigned to one machine i.e., it should be a one-to-one assignment • The cost data is given as a matrix where rows correspond to jobs and columns to machines and there are as many rows as the number of columns i.e. the number of jobs and number of Machines should be equal • This can be compared to demand equals supply condition in a balanced transportation problem. In the optimal solution there should be only one assignment in each row and columns of the given assignment table. one can observe various situations where assignment problem can exist e.g., assignment of workers to jobs like assigning clerks to different counters in a bank or salesman to different areas for sales, different contracts to bidders. • Assignment becomes a problem because each job requires different skills and the capacity or efficiency of each person with respect to these jobs can be different. This gives rise to cost differences. If each person is able to do all jobs equally efficiently then all costs will be the same and each job can be assigned to any person. • When assignment is a problem it becomes a typical optimization problem it can therefore be compared to a transportation problem. The cost elements are given and is a square matrix and requirement at each destination is one and availability at each origin is also one. OR MMS

Prof Vinay Pandit ASSIGNMENT AND TRANSPORTATION THEORY •

In addition we have number of origins which equals the number of destinations hence the total demand equals total supply . There is only one assignment in each row and each column .However If we...