Journal of Combinatorial Optimization

, Volume 33, Issue 3, pp 977–1010 | Cite as

The no-wait job shop with regular objective: a method based on optimal job insertion

  • Reinhard Bürgy
  • Heinz Gröflin


The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.


No-wait job shop General regular objective Fixed time lags Optimal job insertion Local search 



We gratefully acknowledge the constructive remarks of an anonymous referee which led to several improvements in the presentation. The first author also gratefully acknowledges the support of the Swiss National Science Foundation Grant P2FRP2_161720.


  1. Brucker P, Knust S (2011) Complex scheduling, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  2. Bürgy R, Gröflin H (2013) Optimal job insertion in the no-wait job shop. J. Comb. Optim. 26(2):345–371. doi: 10.1007/s10878-012-9466-y MathSciNetCrossRefzbMATHGoogle Scholar
  3. Condotta A (2011) Scheduling with due dates and time-lags: new theoretical results and applications. PhD thesis, University of LeedsGoogle Scholar
  4. Condotta A, Shakhlevich N (2012) Scheduling coupled-operation jobs with exact time-lags. Discret Appl Math 160(16–17):2370–2388. doi: 10.1016/j.dam.2012.05.026 MathSciNetCrossRefzbMATHGoogle Scholar
  5. Eilon S, Hodgson R (1967) Job shops scheduling with due dates. Int J Prod Res 6(1):1–13CrossRefGoogle Scholar
  6. Lawrence S (1984) Supplement to resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques. GSIA, Carnegie Mellon University, PittsburghGoogle Scholar
  7. Leung JYT, Li H, Zhao H (2007) Scheduling two-machine flow shops with exact delays. Int J Found Comput Sci 18(2):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  8. Mati Y, Dauzère-Pérès S, Lahlou C (2011) A general approach for optimizing regular criteria in the job-shop scheduling problem. Eur J Oper Res 212(1):33–42. doi: 10.1016/j.ejor.2011.01.046 MathSciNetCrossRefzbMATHGoogle Scholar
  9. McGeoch C (1992) Analyzing algorithms by simulation: variance reduction techniques and simulation speedups. ACM Comput Surv 24(2):195–212CrossRefGoogle Scholar
  10. Pinedo ML (2012) Scheduling: theory, algorithms, and systems, 4th edn. Springer, New YorkCrossRefzbMATHGoogle Scholar
  11. Schrijver A (2003) Combinatorial optimization, polyhedra and efficiency. Springer, BerlinzbMATHGoogle Scholar
  12. Schuster C (2006) No-wait job shop scheduling: Tabu search and complexity of subproblems. Math Methods Oper Res 63(3):473–491. doi: 10.1007/s00186-006-0056-6 MathSciNetCrossRefzbMATHGoogle Scholar
  13. Storer RH, Wu SD, Vaccari R (1992) New search spaces for sequencing problems with application to job shop scheduling. Manag Sci 38(10):1495–1509. doi: 10.1287/mnsc.38.10.1495 CrossRefzbMATHGoogle Scholar
  14. Yamada T, Nakano R (1992) A genetic algorithm applicable to large-scale job-shop problems. Parallel Problem Solving Nat 2:281–290Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.GERAD & Department of Mathematics and Industrial EngineeringPolytechnique MontréalMontréalCanada
  2. 2.Department of InformaticsUniversity of FribourgFribourgSwitzerland

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