A New Algorithm of Solving the Flow — Shop Problem
The general flow — shop problem indicated by n|m|F|Cmax, can be formulated as follows. Each of n jobs J,…,Jn has to be processed on m machines M1,…,Mm in that order. Job Jj, j=1,…,n, thus consists of a sequence of m operations oj1..,,…,0. jm0jk corresponds to the processing of Jj on Mk during a processing time Pjk We want to find a processing order on each machine Mk such that the time required to complete all jobs is minimized. If the processing order is assumed to be the same on each machine, the resulting problem is called the permutation flow — shop problem, and indicated by n|m|F|Cmax.
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