Skip to main content
SpringerLink
Log in

A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures

  • Published:
International Journal of Flexible Manufacturing Systems Aims and scope Submit manuscript

Abstract

Many real world situations exist where job scheduling is required. This is the case of some entities, machines, or workers who have to execute certain jobs as soon as possible. Frequently what happens is that several workers or machines are not available to perform their activities during some time periods, due to different circumstances. This paper deals with these situations, and considers stochastic scheduling models to study these problems. When scheduling models are used in practice, they have to take into account that some machines may not be working. That temporal lack of machine availability is known as breakdowns, which happen randomly at any time. The times required to repair those machines are also random variables. The jobs have operations with stochastic processing times, their own release times, and there is no precedence between them. Each job is divided into operations and each operation is performed on the corresponding specialized machine. In addition, in the problems considered, the order in which the operations of each job are done is irrelevant. We develop a heuristic approach to solve these stochastic open-shop scheduling problems where random machine breakdowns can happen. The proposed approach is general and it does not depend on the distribution types of the considered random input data. It provides solutions to minimize the expected makespan. Computational experiences are also reported. The results show that the proposed approach gives a solid performance, finding suitable solutions with short CPU times.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alcaide D, Rodriguez-Gonzalez A, Sicilia J (2002) An approach to solve the minimum expected makespan flow-shop problem subject to breakdowns. Europ J Oper Res 140(2):384–398

    Article  MathSciNet  MATH  Google Scholar 

  • Alcaide D, Sicilia J, Vigo D (1997) A tabu search algorithm for the open shop problem. Top 5(2):283–296

    MathSciNet  MATH  Google Scholar 

  • Allahverdi A (1994) Optimal policies for a deterministic two-machine semi-ordered flowshop with maximum lateness objective. Int Trans Oper Res 6:47–54

    MathSciNet  Google Scholar 

  • Allahverdi A (1995) Two-stage production scheduling with separate setup times and stochastic breakdowns. J Oper Res Soc 46:896–904

    Article  MATH  Google Scholar 

  • Allahverdi A (1996) Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness. Comp Oper Res 23:909–916

    Article  MATH  Google Scholar 

  • Allahverdi A (1997) Scheduling in stochastic flowshops with independent setup, processing, and removal times. Comp Oper Res 24:955–960

    Google Scholar 

  • Allahverdi A (1999) Stochastically minimizing total flowtime in flowshops with no waiting space. Europ J Oper Res 113:101–112

    Article  MATH  Google Scholar 

  • Allahverdi A, Mittenthal J (1994a) Two-machine ordered flowshop scheduling under random breakdowns. Math Comp Model 20:9–17

    Article  MATH  Google Scholar 

  • Allahverdi A, Mittenthal J (1994b) Scheduling on m parallel machines subject to random breakdowns to minimize expected mean flowtime. Naval Res Logist 41:677–682

    MATH  Google Scholar 

  • Allahverdi A, Mittenthal J (1995) Scheduling on a two-machine flowshop subject to random breakdowns with a makespan objective function. Europ J Oper Res 81:376–387

    Article  MATH  Google Scholar 

  • Allahverdi A, Mittenthal J (1998) Dual criteria scheduling on a two-machine flowshop subject to random breakdowns. Int Trans Oper Res 5:317–324

    Article  Google Scholar 

  • Allahverdi A, Savsar M (2001) Stochastic proportionate flowshop scheduling with setups. Comp Ind Eng 39:357–369

    Article  Google Scholar 

  • Allahverdi A, Tatari MF (1997) Stochastic machine dominance in flowshops. Comp Ind Eng 32:735–741

    Article  Google Scholar 

  • Anderson EJ, Glass CA, Potts CN (1997) Machine scheduling. In: Aarts E, Lenstra JK (eds) Local search in combinatorial optimization, Ch. 11. Wiley, New York

  • Baker KR (1974) Introduction to sequencing and scheduling. Wiley, New York

    Google Scholar 

  • Blazewicz J, Ecker K, Pesch E, Schmidt G, Weglarz J (2001) Scheduling computer and manufacturing processes. Springer-Verlag, New York

  • Brucker P (2001) Scheduling algorithms. Springer, Berlin

    MATH  Google Scholar 

  • Cai X, Zhou S (1999) Stochastic scheduling on parallel machines subject to random breakdowns to minimize expected costs for earliness and tardy jobs. Oper Res 47(3):422–437

    MathSciNet  MATH  Google Scholar 

  • Fabrycky WJ, Ghare PM, Torgersen PE (1972) Indus oper res. Prentice-Hall, New Jersey

    Google Scholar 

  • French S (1982) Sequencing and scheduling. An Introduction to the mathematics of the job shop, Wiley, New York

    MATH  Google Scholar 

  • Gonzalez T, Sahni S (1976) Open shop scheduling to minimize finish time. J Assoc Comp Mach 23:665– 679

    MathSciNet  MATH  Google Scholar 

  • Gonzalez T, Sahni S (1978) Flowshop and jobshop schedules: Complexity and approximation. Oper Res 26(1):665–679

    Article  MathSciNet  Google Scholar 

  • Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discr Math 5:287–326

    Article  MathSciNet  MATH  Google Scholar 

  • Grant EL, Leavenworth RS (1996) Statistical quality control. McGraw-Hill, New York

    Google Scholar 

  • Lawler EL, Lenstra JK, Rinnooy-Kan AHG (1981) Minimizing maximum lateness in a two machine open shop. Math of Oper res 6:153–158. Erratum. Math Oper Res 7:635

    Google Scholar 

  • Lawler EL, Lenstra JK, Rinnooy-Kan AHG (1982) Recent developments in deterministic sequencing and scheduling: A survey. In: Dempster MAH, Lenstra JK, Rinnooy Kan AHG (eds) Deterministic and stochastic scheduling, NATO Advanced Study Institute Series. Serie C. Reidel Publishing Company, Dordrecht, Holland

    Google Scholar 

  • Lawler EL, Lenstra JK, Rinnooy Kan AHG, Shmoys DB (1993) Sequencing and scheduling: Algorithms and complexity, In: Graves SC, Rinnooy Kan AHG, Zipkin PH (eds) Handbooks in operations research and management science, vol. 4, Logistics of Production and Inventory, Ch. 9. North Holland, Amsterdam, The Netherlands

  • Li W, Cao J (1995) Stochastic scheduling on a single machine subject to multiple breakdowns according to different probabilities. Oper Res Lett 18:81–91

    Article  MathSciNet  MATH  Google Scholar 

  • Pinedo ML (1981) A note on the two-machine job shop with exponential processing time. Nav Res Logist Quart 28:693–696

    Google Scholar 

  • Pinedo M (2002) Scheduling: Theory, algorithms and systems. Prentice Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  • Pinedo ML, Rammouz E (1988) A note on stochastic scheduling on a single machine subject to breakdowns and repair. Probab Eng Inform Sci 2:41–49

    Article  MATH  Google Scholar 

  • Pinedo ML, Ross SM (1982) Minimizing expected makespan in stochastic open shops. Adv Appl Probab 14:898–911

    Article  MathSciNet  MATH  Google Scholar 

  • Pinedo ML, Schrage L (1982) Stochastic shop scheduling: A survey. In: Dempster MAH, Lenstra JK, Rinnooy Kan AHG (eds) Deterministic and stochastic scheduling, NATO Advanced Study Institute Series. Serie C, Reidel Publishing Company, Dordrecht, Holland

    Google Scholar 

  • Pinedo ML, Wie SH (1986) Inequalities for stochastic flow shops and job shops. Appl Stoch Mod Data Anal 2:61–69

    MATH  Google Scholar 

  • Weiss G (1982) Multiserver stochastic scheduling. In: Dempster MAH, Lenstra JK Rinnooy Kan AHG, (eds), Deterministic and stochastic scheduling, NATO Advanced Study Institute Series. Serie C, Reidel Publishing Company, Dordrecht, Holland

    Google Scholar 

  • Weiss G (1995) A tutorial in stochastic scheduling. In: P. Chretienne, E.G. Coffman, J.K. Lenstra, Z. Liu (eds) Scheduling theory and its applications. Wiley, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística, Investigación Operativa y Computación, Universidad de La Laguna, Tenerife, Canary Islands, Spain

    David Alcaide, Andrés Rodriguez-Gonzalez & Joaquín Sicilia

Authors
  1. David Alcaide
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrés Rodriguez-Gonzalez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joaquín Sicilia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Alcaide.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alcaide, D., Rodriguez-Gonzalez, A. & Sicilia, J. A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures. Int J Flex Manuf Syst 17, 201–226 (2005). https://doi.org/10.1007/s10696-006-8819-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10696-006-8819-1

Keywords

Search

Navigation