We study the problem of sequencing n jobs on a three-stage flowshop with multiple identical machines at each stage (a flexible flowshop), The objective is to minimize the makespan. Since the problem is strongly NP-complete. we develop and compare several heuristic procedures of time complexity O(nlog n). We were successful in deriving the worst case performance bound of one procedure. We have also developed several lower bounds that serve as datum for comparison; the lower bound used in the evaluation is always the best among them. Extensive experiments were conducted to evaluate the performance of the proposed procedures, and preferences are concluded based on their average performance.

No abstract

We study the problem of sequencing n simultaneously available jobs on a two-stage hybrid flowshop with uniform machines at each stage. The objective is to minimize the makespan. This problem belongs to the class of strongly NP-complete problems. We develop three heuristic procedures with time complexity of O n log n ð Þ. We derive the worst-case performance bound for heuristic 1 which ignores the dependence of the start time of the second stage on the completion time of the first stage. Heuristics 2 and 3 take such a dependence into account. Several lower bounds are derived, and the best among them serves as the benchmark for evaluation. Extensive computational experiments have been conducted to evaluate the performance of the proposed procedures. They demonstrate the efficacy of the first heuristic in the case of symmetric processing times. The last two heuristics are significantly better in the case of nonsymmetric processing times.

No abstract

~c consider a h~'o-~achine sc~cduling problem in an openshop with blocking. We are given the processln~ times ofnJobs on both machines, and the objective is to minimize the makespan. Symbolically, we are dealing with the problem 02lblockIC .. aa • Four approaches are ~roposed: (I) A nowshop-based heuristic that is based on the Gilmore-Gomory algo~I,!,~ fo~ the ~lb~~.lIC~, problem; (2) Two heuristics bascd on the idca of 'matching' to mlnlmlZC pot~nual Idle time on either machine, and (3) A random search algorithm that em~lates some Important characteristics of other 'softcomputing' meta-heuristics. We de~v~ some lo~cr and u~per bounds on the optimal objective value that should assist the d~clslon maker In evaluating the. result of a particular application. Numerical experiments with the procedures compare theIr performance under varying conditions and demonstrate the efficacy of the ,ondo", searrh algorithm.