A review of exact solution methods for the non-preemptive multiprocessor flowshop problem

Abstract The hybrid or flexible flowshop problem is a generalization of the flowshop in such a way that every job can be processed by one among several machines on each machine stage. In recent years a number of effective exact methods have been developed. A major reason for this progress is the development of new job and machine based lower bounds as well as the rapidly increasing importance of constraint programming. In this paper we provide the first comprehensive and uniform overview on exact solution methods for flexible flowshops with branching, bounding and propagation of constraints under two different objective functions: minimizing the makespan of a schedule and the mean flow time.

[1]  Jatinder N. D. Gupta,et al.  Two-Stage, Hybrid Flowshop Scheduling Problem , 1988 .

[2]  Linus Schrage,et al.  Letter to the Editor - A Proof of the Optimality of the Shortest Remaining Processing Time Discipline , 1968, Oper. Res..

[3]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[4]  Chelliah Sriskandarajah,et al.  Scheduling algorithms for flexible flowshops: Worst and average case performance , 1988 .

[5]  Suna Kondakci Köksalan,et al.  A flexible flowshop problem with total flow time minimization , 2001, Eur. J. Oper. Res..

[6]  Klaus H. Ecker,et al.  Scheduling Computer and Manufacturing Processes , 2001 .

[7]  D. Chaudhuri,et al.  A multi-stage parallel-processor flowshop problem with minimum flowtime , 1992 .

[8]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[9]  Jacek Blazewicz,et al.  The job shop scheduling problem: Conventional and new solution techniques , 1996 .

[10]  Jan Karel Lenstra,et al.  PREEMPTIVE SCHEDULING IN A TWO-STAGE MULTIPROCESSOR FLOW SHOP IS NP-HARD , 1996 .

[11]  George L. Vairaktarakis,et al.  Minimizing makespan in hybrid flowshops , 1994, Oper. Res. Lett..

[12]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[13]  Marie-Claude Portmann,et al.  Branch and bound crossed with GA to solve hybrid flowshops , 1998, Eur. J. Oper. Res..

[14]  Jean-Charles Billaut,et al.  Les problèmes d'ordonnancement de type flow-shop hybride : état de l'art , 1999, RAIRO Oper. Res..

[15]  Eric Pinson,et al.  Jackson's Pseudo Preemptive Schedule for the Pm/ri, qi/Cmax scheduling problem , 1998, Ann. Oper. Res..

[16]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[17]  Jacques Carlier,et al.  Scheduling jobs with release dates and tails on identical machines to minimize the makespan , 1987 .

[18]  David S. Johnson,et al.  Two-Processor Scheduling with Start-Times and Deadlines , 1977, SIAM J. Comput..

[19]  J. Hunsucker,et al.  BRANCH AND BOUND ALGORITHM FOR THE FLOW SHOP WITH MULTIPLE PROCESSORS , 1991 .

[20]  Marius M. Solomon,et al.  A computational study of heuristics for two-stage flexible flowshops , 1996 .

[21]  D. Santos,et al.  Global lower bounds for flow shops with multiple processors , 1995 .

[22]  Jacques Carlier,et al.  An Exact Method for Solving the Multi-Processor Flow-Shop , 2000, RAIRO Oper. Res..

[23]  Jon Rigelsford,et al.  Scheduling Computer and Manufacturing Processes 2nd Edition , 2002 .

[24]  A. Vignier,et al.  Contribution à la résolution des problèmes d'ordonnancement de type monogamme, multimachine (Flow-Shop Hybride) , 1997 .

[25]  J. Gupta,et al.  Schedules for a two-stage hybrid flowshop with parallel machines at the second stage , 1991 .