Hybrid Flow Shop Scheduling with Availability Constraints

The success of a product depends on the costs incurred through its entire processing. Indeed, an efficient schedule can significantly reduce the total costs. Most of the literature on scheduling assumes that machines are always available. However, due to maintenance activities machines cannot operate continuously without some unavailability periods. This chapter deals with scheduling a hybrid flow shop with availability constraints to minimize makespan. We investigate exact methods to solve two special cases of this problem to optimality. We formulate a dynamic programming to solve two-machine flow shop and a branch and bound algorithm to solve the two-stage hybrid flow shop.

[1]  Mohamed Ben-Daya,et al.  A maintenance inspection model: optimal and heuristic solutions , 1998 .

[2]  Wieslaw Kubiak,et al.  Heuristic algorithms for the two-machine flowshop with limited machine availability ☆ , 2001 .

[3]  Abdelhakim Artiba,et al.  Scheduling two-stage hybrid flow shop with availability constraints , 2006, Comput. Oper. Res..

[4]  Ali Allahverdi,et al.  Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness , 1996, Comput. Oper. Res..

[5]  Chung-Yee Lee,et al.  Minimizing the makespan in the two-machine flowshop scheduling problem with an availability constraint , 1997, Oper. Res. Lett..

[6]  Han Hoogeveen,et al.  Short Shop Schedules , 1997, Oper. Res..

[7]  Michael A. Langston,et al.  Interstage Transportation Planning in the Deterministic Flow-Shop Environment , 1987, Oper. Res..

[8]  Robert J. Wittrock,et al.  Scheduling Algorithms for Flexible Flow Lines , 1985, IBM J. Res. Dev..

[9]  Chris N. Potts,et al.  Scheduling a two-stage hybrid flow shop with parallel machines at the first stage , 1997, Ann. Oper. Res..

[10]  James R. Wilson,et al.  Integrated Variance Reduction Strategies for Simulation , 1996, Oper. Res..

[11]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[12]  Seetharama L. Narasimhan,et al.  A COMPARISON OF SEQUENCING RULES FOR A TWO‐STATE HYBRID FLOW SHOP , 1987 .

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

[14]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

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

[16]  Abdelhakim Artiba,et al.  Introduction to Intelligent Simulation: The Rao Language , 1998 .

[17]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[18]  Chung-Yee Lee,et al.  Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem , 1993 .

[19]  Michael Pinedo,et al.  Current trends in deterministic scheduling , 1997, Ann. Oper. Res..

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

[21]  Chung-Yee Lee,et al.  Machine scheduling with an availability constraint , 1996, J. Glob. Optim..

[22]  Chung-Yee Lee Two-machine flowshop scheduling with availability constraints , 1999, Eur. J. Oper. Res..

[23]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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

[25]  Abdelhakim Artiba,et al.  A hybrid three-stage flowshop problem: Efficient heuristics to minimize makespan , 1998, Eur. J. Oper. Res..

[26]  Wieslaw Kubiak,et al.  Two-machine flow shops with limited machine availability , 2002, Eur. J. Oper. Res..

[27]  Huang Dao,et al.  Optimization production scheduling of multi-stage interrelated discrete system via synthetic knowledge , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[28]  M Ben-Daya,et al.  Integrated production and quality model under various preventive maintenance policies , 1998, J. Oper. Res. Soc..

[29]  Seetuarma L. Narastmhan,et al.  Scheduling in a two-stage manufacturing process , 1984 .

[30]  T. C. Edwin Cheng,et al.  An improved heuristic for two-machine flowshop scheduling with an availability constraint , 2000, Oper. Res. Lett..

[31]  Oliver Braun,et al.  Stability of Johnson's schedule with respect to limited machine availability , 2002 .

[32]  Salah E. Elmaghraby,et al.  SCHEDULING HYBRID FLOWSHOPS IN PRINTED CIRCUIT BOARD ASSEMBLY LINES , 2009 .

[33]  Gerhard J. Woeginger,et al.  A polynomial time approximation scheme for the two-stage multiprocessor flow shop problem , 2000, Theor. Comput. Sci..

[34]  Ali Allahverdi,et al.  Dual criteria scheduling on a two-machine flowshop subject to random breakdowns , 1998 .

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

[36]  Michael Pinedo,et al.  BPSS: A Scheduling Support System for the Packaging Industry , 1993, Oper. Res..

[37]  Robert J. Wittrock,et al.  An Adaptable Scheduling Algorithm for Flexible Flow Lines , 1988, Oper. Res..

[38]  Abdelhakim Artiba,et al.  Scheduling of a two-machine flowshop with availability constraints on the first machine , 2006 .

[39]  George L. Vairaktarakis,et al.  Performance Comparison of Some Classes of Flexible Flow Shops and Job Shops , 1998 .

[40]  Chandrasekharan Rajendran,et al.  Scheduling in n-job, m-stage flowshop with parallel processors to minimize makespan , 1992 .

[41]  Abdelhakim Artiba,et al.  Integrating simulation and optimization to schedule a hybrid flow shop with maintenance constraints , 2004, Comput. Ind. Eng..

[42]  Gerd Finke,et al.  New trends in machine scheduling , 1988 .

[43]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

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

[45]  M. Held,et al.  A dynamic programming approach to sequencing problems , 1962, ACM National Meeting.

[46]  Tibor Illés,et al.  The finite criss-cross method for hyperbolic programming , 1996, Eur. J. Oper. Res..

[47]  Günter Schmidt,et al.  Scheduling with limited machine availability , 2000, Eur. J. Oper. Res..

[48]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[49]  Gerhard J. Woeginger,et al.  A Review of Machine Scheduling: Complexity, Algorithms and Approximability , 1998 .

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

[51]  Richard J. Linn,et al.  Hybrid flow shop scheduling: a survey , 1999 .

[52]  Leslie A. Hall,et al.  Approximability of flow shop scheduling , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[53]  Michael S. Salvador,et al.  A Solution to a Special Class of Flow Shop Scheduling Problems , 1973 .

[54]  Chung-Yee Lee,et al.  Parallel machines scheduling with nonsimultaneous machine available time , 1991, Discret. Appl. Math..

[55]  R. J. Paul A Production Scheduling Problem in the Glass-Container Industry , 1979, Oper. Res..

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

[57]  M. Ben-Daya Integrated production maintenance and quality model for imperfect processes , 1999 .

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