Abstract

So many researchers introduced variant problems for assignment model. In this Problem there is a set of n jobs, m machines and r periods. This is three dimensional problem. Number of jobs to be completed is n0 . The total number of assigned jobs should be 2 n0 . D(i,j,k) be the cost array of assignment of ith Job on jth machine at kth period. Each job requires two processes among A,B and C Processes and there are given. Any machine can do process A in 1st or 3rd period, process B in 2nd or 4th period and process C in any one of the four periods. For our convenience we consider processes A, B and C .as 1,2 and 3. One machine can do a job process in one period .i.e different jobs processes can be done on a machine in different periods. Each n0 job has to be assigned twice to machines for the two processes, hence the total number of assignment is 2 n0 . The objective of the problem is to assign each n0 job twice to the machines such that the total processing cost is minimum subject to conditions.

Keywords

References

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