Sequencing on two-stage hybrid flowshops with uniform machines to minimize makespan

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.

The hybrid flow shop scheduling problem

“…The 2-stage case with any number of uniform parallel machines is studied in [181] and later revisited by [108]. [30] considers a problem with a set of initial batches, and jobs have a predefined sequence inside each batch.…”

A two-stage hybrid flowshop scheduling problem with a function constraint and unrelated alternative machines

“…The second category of this problem involves parallel machines at the first center and a common machine at the second center (m1 > 1, m2 = 1), such as those reported by Arthanary and Ramaswamy [2], Mittal and Nagga [13], Gupta [14], Chen [15], Hoogeveen et al [11], Vignier et al [16], Gupta et al [17], Oguz et al [18], and Zhang et al [19]. The third category of the problem involves parallel machines at both centers (m1 > 1, m2 > 1), such as those reported by Paul [5], Narasimhan and Mangiamell [20], Sriskandarajah and Sethi [8], Rajendran and Chaudhuri [21], Guinet et al [22], Haouari and M'Hallah [23], Suresh [24], Soewandi and Elmaghraby [25], and Oguz et al [26]. Within the aforementioned research done on FS m1,m2 scheduling problems, most studies have concentrated on identical parallel processor problems.…”

“…Within the aforementioned research done on FS m1,m2 scheduling problems, most studies have concentrated on identical parallel processor problems. Only Huang and Li [3] and Soewandi and Elmaghraby [25] consider uniform parallel machines at one machine center or both centers, and Suresh [24] considers multiple unrelated parallel machines at both centers.…”

No-wait flexible flowshop with uniform parallel machines and sequence-dependent setup time: a hybrid meta-heuristic approach

“…Huang and Li (1998) contemplated the twostage problem with uniform machines in the second stage, whereas Dessouky et al (1998), Soewandi and Elmaghraby (2003), Kyparisis and Koulamas (2006a) considered uniform machines in both stages. The three stages problem has been investigated in Bertel and Billaut (2004).…”