A NEW PARALLEL ALGORITHM FOR THE N-JOB, M-MACHINE FLOWSHOP SCHEDULING PROBLEM

This paper describes a new parallel algorithm for solving the m-machines, n-jobs flow-shop scheduling problem as well as its implementation on a distributed memory multiprocessor. The algorithm is basically a parallelization of the usual branch-and-bound method. It also takes advantage of the all-search method to keep the efficiency of parallel processing reasonably high when subproblems become smaller than a certain size. The performance evaluation is done by comparing the parallel execution of this algorithm on the nCUBE2 multiprocessor and the sequential execution of the branch-and-bound with depth-first search algorithm. The result shows that the mean speedup ratio for some conditions of the problem is more than the number of processors, and the mean speedup ratio for the conditions on which the sequential executions complete quickly is not smaller than 1.