Journal of Scheduling

, Volume 20, Issue 4, pp 391–422 | Cite as

A neighborhood for complex job shop scheduling problems with regular objectives

  • Reinhard Bürgy


Due to the limited applicability in practice of the classical job shop scheduling problem, many researchers have addressed more complex versions of this problem by including additional process features, such as time lags, setup times, and buffer limitations, and have pursued objectives that are more practically relevant than the makespan, such as total flow time and total weighted tardiness. However, most proposed solution approaches are tailored to the specific scheduling problem studied and are not applicable to more general settings. This article proposes a neighborhood that can be applied for a large class of job shop scheduling problems with regular objectives. Feasible neighbor solutions are generated by extracting a job from a given solution and reinserting it into a neighbor position. This neighbor generation in a sense extends the simple swapping of critical arcs, a mechanism that is widely used in the classical job shop but that is not applicable in more complex job shop problems. The neighborhood is embedded in a tabu search, and its performance is evaluated with an extensive experimental study using three standard job shop scheduling problems: the (classical) job shop, the job shop with sequence-dependent setup times, and the blocking job shop, combined with the following five regular objectives: makespan, total flow time, total squared flow time, total tardiness, and total weighted tardiness. The obtained results support the validity of the approach.


Job shop scheduling General regular objective Sequence-dependent setup times Blocking job shop Job insertion Neighborhood Tabu search 



The author gratefully acknowledges the constructive remarks of three anonymous referees which led to several improvements in the presentation. This research is partially funded by the Swiss National Science Foundation Grant P2FRP2 161720.


  1. Applegate, D., & Cook, W. (1991). A computational study of the job-shop scheduling problem. ORSA Journal on Computing, 3(2), 149–156.CrossRefGoogle Scholar
  2. Balas, E., Simonetti, N., & Vazacopoulos, A. (2008). Job shop scheduling with setup times, deadlines and precedence constraints. Journal of Scheduling, 11(4), 253–262.CrossRefGoogle Scholar
  3. Blazewicz, J., Domschke, W., & Pesch, E. (1996). The job shop scheduling problem: Conventional and new solution techniques. European Journal of Operational Research, 93(1), 1–33.CrossRefGoogle Scholar
  4. Brucker, P., & Knust, S. (2011). Complex scheduling (2nd ed.). Berlin: Springer.Google Scholar
  5. Brucker, P., & Thiele, O. (1996). A branch and bound method for the general-shop problem with sequence dependent setup-times. OR Spectrum, 18(3), 145–161.CrossRefGoogle Scholar
  6. Brucker, P., Jurisch, B., & Sievers, B. (1994). A branch and bound algorithm for the job-shop scheduling problem. Discrete Applied Mathematics, 49(1), 107–127.CrossRefGoogle Scholar
  7. Bülbül, K., & Kaminsky, P. (2013). A linear programming-based method for job shop scheduling. Journal of Scheduling, 16(2), 161–183.CrossRefGoogle Scholar
  8. Bürgy, R. (2014). Complex Job Shop Scheduling: A General Model and Method. PhD thesis, Department of Informatics, University of Fribourg.Google Scholar
  9. Bürgy, R., & Gröflin, H. (2016). The blocking job shop with rail-bound transportation. Journal of Combinatorial Optimization, 31(1), 151–181.CrossRefGoogle Scholar
  10. Eilon, S., & Hodgson, R. (1967). Job shops scheduling with due dates. International Journal of Production Research, 6(1), 1–13.CrossRefGoogle Scholar
  11. Glover, F. W., & Laguna, M. (1997). Tabu search. Norwell: Kluwer.CrossRefGoogle Scholar
  12. Gonçalves, J. F., & Resende, M. G. C. (2014). An extended Akers graphical method with a biased random-key genetic algorithm for job-shop scheduling. International Transactions in Operational Research, 21(2), 215–246.CrossRefGoogle Scholar
  13. González, M. A., Vela, C. R., Sierra, M., Varela, R. (2010). Tabu search and genetic algorithm for scheduling with total flow time minimization. In COPLAS 2010: ICAPS Workshop on constraint satisfaction techniques for planning and scheduling problems (pp. 33–41).Google Scholar
  14. González, M. Á., González-Rodríguez, I., Vela, C. R., & Varela, R. (2012a). An efficient hybrid evolutionary algorithm for scheduling with setup times and weighted tardiness minimization. Soft Computing, 16(12), 2097–2113.CrossRefGoogle Scholar
  15. González, M. A., Vela, C. R., & Varela, R. (2012b). A competent memetic algorithm for complex scheduling. Natural Computing, 11(1), 151–160.CrossRefGoogle Scholar
  16. Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5, 287–326.CrossRefGoogle Scholar
  17. Grimes, D., & Hebrard, E. (2015). Solving variants of the job shop scheduling problem through conflict-directed search. INFORMS Journal on Computing, 27(2), 268–284.CrossRefGoogle Scholar
  18. Gröflin, H., & Klinkert, A. (2007). Feasible insertions in job shop scheduling, short cycles and stable sets. European Journal of Operational Research, 177(2), 763–785.CrossRefGoogle Scholar
  19. Gröflin, H., & Klinkert, A. (2009). A new neighborhood and tabu search for the blocking job shop. Discrete Applied Mathematics, 157(17), 3643–3655.CrossRefGoogle Scholar
  20. Gröflin, H., Pham, D. N., & Bürgy, R. (2011). The flexible blocking job shop with transfer and set-up times. Journal of Combinatorial Optimization, 22(2), 121–144.CrossRefGoogle Scholar
  21. Hooker, J. N. (1995). Testing heuristics: We have it all wrong. Journal of Heuristics, 1(1), 33–42.Google Scholar
  22. Lawrence, S. (1984). Supplement to resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques. Pittsburgh, PA: GSIA: Carnegie Mellon University.Google Scholar
  23. Mascis, A., & Pacciarelli, D. (2002). Job-shop scheduling with blocking and no-wait constraints. European Journal of Operational Research, 143(3), 498–517.CrossRefGoogle Scholar
  24. Mati, Y., Dauzère-Pérès, S., & Lahlou, C. (2011). A general approach for optimizing regular criteria in the job-shop scheduling problem. European Journal of Operational Research, 212(1), 33–42.CrossRefGoogle Scholar
  25. Nowicki, E., & Smutnicki, C. (1996). A fast taboo search algorithm for the job shop problem. Management Science, 42(6), 797–813.CrossRefGoogle Scholar
  26. Nowicki, E., & Smutnicki, C. (2005). An advanced tabu search algorithm for the job shop problem. Journal of Scheduling, 8(2), 145–159.CrossRefGoogle Scholar
  27. Oddi, A., Rasconi, R., Cesta, A., Smith, S. F. (2012). Iterative improvement algorithms for the blocking job shop. In Twenty-second international conference on automated planning and scheduling.Google Scholar
  28. Peng, B., Lü, Z., & Cheng, T. C. E. (2015). A tabu search/path relinking algorithm to solve the job shop scheduling problem. Computers and Operations Research, 53, 154–164.CrossRefGoogle Scholar
  29. Perregaard, M., & Clausen, J. (1998). Parallel branch-and-bound methods for the job-shop scheduling problem. Annals of Operations Research, 83, 137–160.CrossRefGoogle Scholar
  30. Pinedo, M. L. (2012). Scheduling: Theory, algorithms, and systems (4th ed.). Berlin: Springer.CrossRefGoogle Scholar
  31. Potts, C. N., & Strusevich, V. A. (2009). Fifty years of scheduling: A survey of milestones. Journal of the Operational Research Society, 60, S41–S68.CrossRefGoogle Scholar
  32. Pranzo, M., Pacciarelli, D. (2015). An iterated greedy metaheuristic for the blocking job shop scheduling problem. Journal of Heuristics, 22(4), 587–611.Google Scholar
  33. Taillard, E. (1994). Parallel taboo search techniques for the job shop scheduling problem. ORSA Journal on Computing, 6, 108–108.CrossRefGoogle Scholar
  34. Tufte, E. R. (2001). The visual display of quantitative information (2nd ed.). Norwich: Bertrams.Google Scholar
  35. Vela, C., Varela, R., & González, M. (2010). Local search and genetic algorithm for the job shop scheduling problem with sequence dependent setup times. Journal of Heuristics, 16, 139–165.CrossRefGoogle Scholar
  36. Zhang, C. Y., Li, P., Rao, Y., & Guan, Z. (2008). A very fast TS/SA algorithm for the job shop scheduling problem. Computers and Operations Research, 35(1), 282–294.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.GERAD & Department of Mathematics and Industrial EngineeringPolytechnique MontréalMontréalCanada

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