Abstract
We consider a two-machine flow shop problem with a common due date where the objective is to minimize the sum of functions which penalize early as well as tardy completion of jobs. Since the problem is NP-hard in the strong sense, we investigate some general properties of optimal schedules for the problem, we develop lower and upper bounds, derive dominance criteria, and propose an enumerative algorithm for finding an optimal schedule. The performance of the proposed algorithm together with the influence of the individual components is thoroughly discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Achuthan, N. R., Grabowski, J. and Sidney, J.: Optimal flow-shop scheduling with earliness and tardiness penalties, Opsearch 18 (1981), 117–138.
Baker, K. R. and Scudder, G. D.: Sequencing with earliness and tardiness penalties, Oper. Res. 38 (1989), 22–36.
Brandimarte, P. and Maiocco, M.: Job shop scheduling with a non-regular objective: A comparison of neighbourhood structures based on a sequencing/timing decomposition, Internat. J. Prod. Res. 37(8) (1999), 1697–1715.
Della Croce, F., Narayan, V. and Tadei, R.: The two-machine total completion time flow shop problem, Eur. J. Oper. Res. 90 (1996), 227–237.
Garey, M. R., Johnson, D. S. and Sethi, R.: The complexity of flowshop and jobshop scheduling, Math. Oper. Res. 1 (1976), 117–129.
Graham, R. L., Lawler, E. L., Lenstra, J. K. and Rinnooy Kan, A. H. G.: Optimization and approximation in deterministic sequencing and scheduling, Ann. Discr. Math. 5 (1979), 287–326.
Gowrishankar, K., Rajendran, C. and Srinivasan, G.: Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date, Eur. J. Oper. Res. 132 (2001), 643–665.
Gupta, J. N. D., Lauff, V. and Werner, F.: A branch and bound algorithm for two-machine flow shop problems with earliness and tardiness penalties, Preprint 33/99, FMA, Otto-von-Guericke-Universität Magdeburg, FMA, 1999.
Hall, N., Kubiak, W. and Sethi, S.: Earliness-tardiness scheduling problems, ii: Deviation of completion times about a common due date, Oper. Res. 5 (1991), 847–856.
Hall, N. and Posner, M.: Earliness-tardiness scheduling problems, i: Weighted deviation of completion times about a common due date, Oper. Res. 5 (1991), 836–846.
Ignall, E. and Schrage, L.: Application of the branch and bound technique to some flow-shop scheduling problems, Oper. Res. 13(3) (1965), 400–412.
Johnson, S. M.: Optimal two and three stage production schedules with setup times included, Naval Res. Logist. Quart. 1(1) (1954), 61–68.
Jozefowska, J., Jurisch, B. and Kubiak, W.: Scheduling shops to minimize the weighted number of late jobs, Oper. Res. Lett. 16(5) (1994), 277–283.
Kanet, J. J.: Minimizing the average deviations of job completion times about a common due date, Naval Res. Logist. Quart. 28 (1981), 643–651.
Lauff, V.: Multi-stage scheduling problems with non-regular optimization criteria, PhD Thesis, Otto-von-Guericke-University Magdeburg, Germany, 2001.
Lauff, V. and Werner, F.: Heuristics for two-machine flow shop problems with earliness and tardiness penalties, Preprint 01/01, Otto-von-Guericke-Universität Magdeburg, FMA, 2001 (to appear in International Journal of Operations and Quantitative Management).
Lauff, V. and Werner, F.: On the complexity of some properties of multi-stage scheduling problems with earliness and tardiness penalties, Comput. Oper. Res. 31 (2004), 317–345.
Majaj, S. A.: Just-in-time production for the two machine common due date scheduling problem, Master's Thesis, Univ. of Southern Colorado, Pueblo, CO, 1991.
Sarper, H.: Minimizing the sum of absolute deviations about a common due date for the twomachine flow shop problem, Appl. Math. Modelling 19 (1995), 153–161.
Schrage, L.: Linear, Interactive and Discrete Optimization (LINDO), 1989.
Sotskov, Y. N., Tautenhahn, T. and Werner, F.: On the application of insertion techniques for job-shop problems with setup times, RAIRO Rech. Oper. 33 (1999), 209–245.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gupta, J.N.D., Lauff, V. & Werner, F. Two-Machine Flow Shop Scheduling with Nonregular Criteria. Journal of Mathematical Modelling and Algorithms 3, 123–151 (2004). https://doi.org/10.1023/B:JMMA.0000036573.01968.1b
Issue Date:
DOI: https://doi.org/10.1023/B:JMMA.0000036573.01968.1b