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Sequencing Three-Stage Flexible Flowshops with Identical Machines to Minimize Makespan

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(n log 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.