Abstract
We consider m machines in parallel with each machine capable of producing one specific product type. There are n orders with each one requesting specific quantities of the various different product types. Order j may have a release date r j and a due date d j . The different product types for order j can be produced at the same time. We consider the class of objectives ∑ f j (C j ) that includes objectives such as the total weighted completion time ∑ w j C j and the total weighted tardiness ∑ w j T j of the n orders. We present structural properties of the various problems and a complexity result. In particular, we show that minimizing ∑ C j when m ≥ 3 is strongly NP-hard. We introduce two new heuristics for the ∑ C j objective. An empirical analysis shows that our heuristics outperform all heuristics that have been proposed for this problem in the literature.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Barnes, J., M. Laguna, and F. Glover, “An overview of Tabu Search approaches to production scheduling problems,” in D. Brown and W. Scherer (eds.), Intelligent Scheduling Systems, Kluwer Academic Publishers, 1995, pp. 101–127.
Du, J. and J. Y.-T. Leung, “Minimizing total tardiness on one machine is NP-hard,” Mathematics of Operations Research, 15, 483–495 (1990).
Emmons, H., “One-machine sequencing to minimize certain functions of job tardiness,” Operations Research, 17, 701–715 (1969).
Garey, M. R. and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
Glover, F. and M. Laguna, Tabu Search, Kluwer Academic Publishers, Boston, USA, 1997.
Graham, R. L., E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan, “Optimization and approximation in deterministic sequencing and scheduling: A survey,” Annals of Discrete Mathematics, 5, 287–326 (1979).
Julien, F. M. and M. J. Magazine, “Scheduling customer orders—An alternative production scheduling approach,” Journal of Manufacturing and Operations Management, 3, 177–199 (1990).
Laguna, M., “Implementing and testing the Tabu Cycle and conditional probability methods, Working paper, 2004.
Lenstra, J. K., “Sequencing by enumerative methods,” Mathematical Centre Tracts 69, Mathematisch Centrum, Amsterdam, The Netherlands, 1977.
Leung, J. Y-T., H. Li, M. Pinedo, and S. Sriskandarajah, “Open shops with jobs overlap—revisited,” European Journal of Operational Research, 163(2), 569–571 (2005).
Li, H., “Order scheduling in dedicated and flexible machine environment,” PhD Thesis, Department of Computer Science, New Jersey Institute of Technology, Newark, New Jersey, 2005.
Smith, W. E., “Various optimizers for single stage production,” Naval Research Logistics Quarterly, 3, 59–66 (1956).
Sung, C. S. and S. H. Yoon, “Minimizing total weighted completion time at a pre-assembly stage composed of two feeding machines,” International Journal of Production Economics, 54, 247–255 (1998).
Wagneur, E. and C. Sriskandarajah, “Open shops with jobs overlap,” European Journal of Operational Research, 71, 366–378 (1993).
Wang, G. and T. C. E. Cheng, “Customer order scheduling to minimize total weighted completion time,” in Proceedings of the 1st Multidisciplinary Conference on Scheduling Theory and Applications, 2003, pp. 409–416.
Yang, J., “Scheduling with batch objectives. PhD Thesis, Industrial and Systems Engineering Graduate Program, The Ohio State University, Columbus, Ohio, 1998.
Zweben, M. and M. Fox (eds.), Intelligent Scheduling, Morgan Kaufmann Publishers, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leung, J.Y.T., Li, H. & Pinedo, M. Order Scheduling in an Environment with Dedicated Resources in Parallel. J Sched 8, 355–386 (2005). https://doi.org/10.1007/s10951-005-2860-x
Issue Date:
DOI: https://doi.org/10.1007/s10951-005-2860-x