Sequencing three-stage flexible flowshops with identical machines to minimize makespan

Abstract

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.

A taxonomy of flexible flow line scheduling procedures

“…The procedure is (with an increasing number of jobs) asymptotically optimal for makespan minimization. A three-stage flexible flow line under the same criterion is also considered by Soewandi and Elmaghraby (2001). They develop four variants of standard flow line adaptations.…”

The hybrid flow shop scheduling problem

“…The authors presented both exact as well as heuristic algorithms. In a related and later work, the same problem, this time with any number of identical parallel machines per stage, is studied by [180]. Later, [100] studied the same problem and proposed improved heuristics with best known performances.…”

An approximation algorithm for proportionate scheduling in the two-stage hybrid flow shop

“…Schuurman and Woeginger [15] revisited the two-stage case and obtained a polynomial time approximation scheme (PTAS) that has worst case ratio arbitrarily close to 1. Soewandi and Elmaghraby [16] extended the problem to the three-stage case, where an approximation algorithm with worst-case ratio no more than 10 3 is provided. A PTAS for the hybrid flow shop with any constant number of stages is finally proposed by Jansen and Sviridenko [17].…”