Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

A simultaneous and iterative approach for parallel machine scheduling with sequence-dependent family setups

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

In this paper, we address a parallel machine scheduling problem to minimize the total weighted completion time, where product families are involved. Major setups occur when processing jobs of different families, and sequence dependencies are also taken into account. Considering its high practical relevance, we focus on the special case where all jobs of the same family have identical processing times. In order to avoid redundant setups, batching jobs of the same family can be performed. We first develop a variable neighborhood search algorithm (VNS) to solve the interrelated subproblems in a simultaneous manner. To further reduce computing time, we also propose an iterative scheme which alternates between a specific heuristic to form batches and a VNS scheme to schedule entire batches. Computational experiments are conducted which confirm the benefits of batching. Test results also show that both simultaneous and iterative approach outperform heuristics based on a fixed batch size and list scheduling. Furthermore, the iterative procedure succeeds in balancing solution quality and computing time.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Albers, S., & Brucker, P. (1993). The complexity of one-machine batching problems. Discrete Applied Mathematics, 47, 87–107.

    Article  Google Scholar 

  • Aldowaisan, T., & Allahverdi, A. (1998). Total flowtime in no-wait flowshops with separated setup times. Computers and Operations Research, 25(9), 757–765.

    Article  Google Scholar 

  • Allahverdi, A. (2000). Minimizing mean flowtime in a two machine flowshop with sequence independent setup times separated. Computers and Operations Research, 27, 111–127.

    Article  Google Scholar 

  • Allahverdi, A., & Aldowaisan, T. (1998). Job lateness in flowshops with setup and removal times separated. Journal of the Operational Research Society, 49(9), 1001–1006.

    Article  Google Scholar 

  • Allahverdi, A., Gupta, J. N. D., & Aldowaisan, T. (1999). A review of scheduling research involving setup considerations. Omega International Journal of Management Science, 27, 219–239.

    Article  Google Scholar 

  • Allahverdi, A., Ng, C. T., Cheng, T. C. E., & Kovalyov, Y. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187, 985–1032.

    Article  Google Scholar 

  • Almeder, C., & Mönch, L. (2011). Scheduling jobs with incompatible families on parallel batch machines. Journal of the Operational Resarch Society, 62, 2083–2096.

    Article  Google Scholar 

  • Barnes, J. W., & Vanston, L. K. (1981). Scheduling jobs with linear delay penalties and sequence dependent setup costs. Operations Research, 29, 146.

    Article  Google Scholar 

  • Cheng, T. C. E., Chen, Y. L., & Oguz, C. (1994). One-machine batching and sequencing of multiple-type items. Computers and Operations Research, 21, 717–721.

    Article  Google Scholar 

  • Cheng, T. C. E., Gupta, J. N. D., & Wang, G. (2000). A review of flowshop scheduling research with setup times. Production and Operations Management, 9, 262–282.

    Article  Google Scholar 

  • Coffman, E. G., Yannakakis, M., Magazine, M. J., & Santos, C. A. (1990). Batch sizing and job sequencing on a single machine. Annals of Operations Research, 26, 135–147.

    Article  Google Scholar 

  • Driessel, R., & Mönch, L. (2011). Variable neighborhood search approaches for scheduling jobs on parallel machines with sequence-dependent setup times, precedence constraints, and ready times. Computers and Industrial Engineering, 61(2), 336–345.

    Article  Google Scholar 

  • Franca, P. M., Gupta, J. N. D., Mendes, A. S., Moscato, P., & Veltink, K. J. (2005). Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups. Computers and Industrial Engineering, 48, 491–506.

    Article  Google Scholar 

  • Graham, R. L., Lawler, E. L., Lenstra, J. K., & Kan, A. H. G. Rinnooy. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5, 287–326.

    Article  Google Scholar 

  • Gupta, J. N. D., & Tunc, E. A. (1994). Scheduling a two-stage hybrid flowshop with separable setup and removal times. European Journal of Operational Research, 77(3), 415–428.

    Article  Google Scholar 

  • Han, W., & Dejax, P. (1994). An efficient heuristic based on machine workload for the flow shop scheduling problem with setup and removal times. Annals of Operations Research, 50, 263–279.

    Article  Google Scholar 

  • Hansen, P., & Mladenovic, N. (2001). Variable neighborhood search: principles and applications. European Journal of Operational Research, 130, 449–467.

    Article  Google Scholar 

  • Hendizadeh, S. H., Faramarzi, H., Mansouri, S. A., Gupta, J. N. D., & Elmekkawy, T. Y. (2008). Meta-heuristics for scheduling a flowline manufacturing cell with sequence dependent family setup times. International Journal of Production Economics, 111, 593–605.

    Article  Google Scholar 

  • Hurink, J. (1998). A tabu search approach for a single-machine batching problem using an efficient method to calculate a best neighbor. Journal of Scheduling, 1, 127–148.

    Google Scholar 

  • Laguna, M. (1999). A heuristic for production scheduling and inventory control in the presence of sequence-dependent setup times. IIE Transactions, 31, 125–134.

    Google Scholar 

  • Logendran, R., de Szoeke, P., & Barnard, F. (2006). Sequence-dependent group scheduling problems in flexible flow shops. International Journal of Production Economics, 102, 66–86.

    Google Scholar 

  • Mehta, S. V., & Uzsoy, R. (1998). Minimizing total tardiness on a batch processing machine with incompatible job families. IIE Transactions, 30, 165–178.

    Google Scholar 

  • Mladenovic, N., & Hansen, P. (1997). Variable neighborhood search. Computers and Operations Research, 24, 1097–1100.

    Article  Google Scholar 

  • Monma, C. L., & Potts, C. N. (1989). On the complexity of scheduling with batch setups. Operations Research, 37, 798–804.

    Article  Google Scholar 

  • Mosheiov, G., Oron, D., & Ritov, Y. (2004). Flow-shop batching scheduling with identical processing-time jobs. Naval Research Logistics, 51, 783–799.

    Article  Google Scholar 

  • Potts, C. N., & Kovalyov, M. Y. (2000). Scheduling with batching: A review. European Journal of Operational Research, 120, 228–249.

    Article  Google Scholar 

  • Rajendran, C., & Ziegler, H. (1997). Heuristics for scheduling in a flowshop with setup, processing and removal times separated. Production Planning and Control, 8, 568–576.

    Article  Google Scholar 

  • Reddy, V., & Narendran, T. T. (2003). Heuristics for scheduling sequence-dependent set-up jobs in flow line cells. International Journal of Production Research, 41, 193–206.

    Article  Google Scholar 

  • Rocha, M. L., Ravetti, M. G., Mateus, G. R., & Pardalos, P. M. (2007). Solving parallel machines scheduling problems with sequence-dependent setup times using variable neighbourhood search. IMA Journal of Management Mathematics, 18, 101–115.

    Article  Google Scholar 

  • Shen, L., Mönch, L., & Buscher, U. (2011). An iterative scheme for parallel machine scheduling with sequence dependent family setups. In Proceedings MISTA, 2011, 519–522.

  • Shen, L., Mönch, L., & Buscher, U. (2012). An iterative approach for the serial batching problem with parallel machines and job families. Working paper, Nr. 164/12, Technische Universitaet Dresden (in press).

  • Srikar, B. N., & Ghosh, S. (1986). A MILP model for the \(n\)-job, \(m\)-stage flowshop with sequence dependent set-up times. International Journal of Production Research, 24, 1459–1474.

    Article  Google Scholar 

  • Tahar, D. N., Yalaoui, F., Chu, C., & Amodeo, L. (2006). A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times. International Journal of Production Economics, 99, 63–73.

    Article  Google Scholar 

  • van Hoesel, S., Wagelmans, A., & Moerman, B. (1994). Using geometric techniques to improve dynamic programming algorithms for the economic lot-sizing problems and extensions. European Journal of Operational Research, 75, 312–331.

    Article  Google Scholar 

  • Wang, X., & Tang, L. (2009). A population-based variable neighborhood search for the single machine total weighted tardiness problem. Computers and Operations Research, 68, 2105–2110.

    Article  Google Scholar 

  • White, C. H., & Wilson, R. C. (1977). Sequence dependent set-up times and job sequencing. International Journal of Production Research, 16, 191.

    Article  Google Scholar 

  • Yalaoui, F., & Chu, C. (2003). An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times. IIE Transactions, 35, 183–190.

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous referees for their constructive comments and valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Business and Economics, Technische Universitaet Dresden, 01069 , Dresden, Germany

    Liji Shen & Udo Buscher

  2. Department of Mathematics and Computer Science, University of Hagen, 58097 , Hagen, Germany

    Lars Mönch

Authors
  1. Liji Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lars Mönch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Udo Buscher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liji Shen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shen, L., Mönch, L. & Buscher, U. A simultaneous and iterative approach for parallel machine scheduling with sequence-dependent family setups. J Sched 17, 471–487 (2014). https://doi.org/10.1007/s10951-013-0315-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-013-0315-3

Keywords

Search

Navigation