Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard

Hoogeveen, J.A.; Lenstra, JK Jan Karel; Veltman, Bart

doi:10.1016/s0377-2217(96)90070-3

Cited by 164 publications

(50 citation statements)

References 6 publications

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“…))||non-regular MPF, heuristics, photographic film production [45] F Hm, ((P M (k) ) m k=1 ))|pmtn, prec|Cmax polynomial algorithm for special case of prec ( [78]) [64] F Hm, ((P M (k) ) m k=1 ))||Ē u +T v +C w +d z heuristic, assignable due dates, controllable processing times [73] F H2, ((1 (1) , P m (2) ))|assembly (2) |Cmax MPF, heuristics [87] F H3, ((P M (k) ) 3 k=1 ))||Cmax GA, printed circuit boards [157] F H2, ((1 (1) , Q2 (2) ))||Cmax MPF, DP, heuristics, NP-complete proof…”

Section: Research Opportunities and Conclusionmentioning

confidence: 99%

“…For instance, HFS restricted to two processing stages, even in the case when one stage contains two machines and the other one a single machine, is N P-hard, after the results of [62]. Similarly, the HFS when machines are allowed to stop processing operations before their completion and to resume them on different time slots (something referred to as preemption) results also in strongly N P-hard problems even with m = 2, according to [78]. Moreover, the special case where there is a single machine per stage, known as the flow shop, and the case where there is a single stage with several machines, known as the parallel machines environment, are also N P-hard, [51].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The hybrid flow shop scheduling problem

Ruíz

Vázquez-Rodríguez

2010

European Journal of Operational Research

681

236

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The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the Hybrid Flow Shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution.The paper discusses several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.

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Section: Research Opportunities and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The hybrid flow shop scheduling problem

Ruíz

Vázquez-Rodríguez

2010

European Journal of Operational Research

681

236

View full text Add to dashboard Cite

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“…We begin by the following two small theorems which establish complexity of some special cases of the problem. is unary NP-complete (Hoogeveen et al, 1996). □ …”

Section: Complexty and Special Casesmentioning

confidence: 99%

“…For other cases where either of the two stages has more than one machine, Hoogeveen et al (1996) show that the hybrid flow shop scheduling problems with the objective of minimizing makespan are unary NP-complete both in the preemptive and the non-preemptive case. Regarding the solution procedures, researchers have developed several branch and bound algorithms and heuristic methods for the problems under various conditions (Brah and Hunsucker, 1991;Rajendran and Chaudihari, 1992;Deal and Hunsucker, 1991;Gupta, 1988;Gupta and Tunc, 1991;Gupta, et al, 1997;Hunsucker, 1992).…”

Section: Introductionmentioning

confidence: 99%

Hybrid Flow Shop with Parallel Machines at the First Stage and Dedicated Machines at the Second Stage

Yang¹

2015

Industrial Engineering and Management Systems

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In this paper, a two-stage hybrid flow shop problem is considered. Specifically, there exist identical parallel machines at stage 1 and two dedicated machines at stage 2, and the objective of the problem is to minimize makespan. After being processed by any machine at stage 1, a job must be processed by a specific machine at stage 2 depending on the job type, and one type of jobs can have different processing times on each machine. First, we introduce the problem and establish complexity of several variations of the problem. For some special cases, we develop optimal polynomial time solution procedures. Then, we establish some simple lower bounds for the problem. In order to solve this NPhard problem, three heuristics based on simple rules such as the Johnson's rule and the LPT (Longest Processing Time first) rule are developed. For each of the heuristics, we provide some theoretical analysis and find some worst case bound on relative error. Finally, we empirically evaluate the heuristics.

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“…FFSP has a various applications in the practical scenarios, however, it is proven to be NP-hard (Hoogeveen et al, 1996). There is extensive research focusing on FFSP (Sriskandarajah and Sethi, 1989;Engin et al, 2011;Singh and Mahapatra, 2012;Xu et al, 2013;Rabiee et al, 2014), nevertheless, among most of them, setup times are either ignored or considered as a part of the processing time.…”

Section: Introductionmentioning

confidence: 99%

Multiple rules with game theoretic analysis for flexible flow shop scheduling problem with component altering times

Han

Zhu

et al. 2016

IJMIC

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This paper studies the flexible flow shop scheduling problem with component altering times (FFSP-CAT), which is a specific form of the flexible flow shop scheduling problem with sequence dependent setup times in the practical scenario. Dealing with FFSP-CAT includes the jobs' machine assignment determination and the globe optimisation. We develop six rules for jobs' machine assignment, and since these rules will easily conflict with one another if they are used with the same priorities, we construct a repeated cooperative model and provide a game theoretical analysis, then derive a Nash equilibrium machine assignment scheme (NEMAS) to effectively manage these rules for jobs' machines assignment at each stage. Furthermore, to achieve the global optimum, we design an advanced compact genetic algorithm (ACGA). By combining NEMAS and ACGA, an approach named advanced compact genetic algorithm with Nash equilibrium machine assignment scheme (ACGA-NEMAS) is used for minimising the makespan of FFSP-CAT. Through extensive comparison experiments with different scales of instances, we show that the algorithm with NEMAS acquires 56.85% improvement over the algorithm without NEMAS, and ACGA-NEMAS performs 80.28% better than genetic algorithm.

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Preemptive scheduling in a two-stage multiprocessor flow shop is NP-hard

Cited by 164 publications

References 6 publications

The hybrid flow shop scheduling problem

The hybrid flow shop scheduling problem

Hybrid Flow Shop with Parallel Machines at the First Stage and Dedicated Machines at the Second Stage

Multiple rules with game theoretic analysis for flexible flow shop scheduling problem with component altering times

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