Abstract
Order scheduling models can be described as follows: A machine environment with a number of non-identical machines in parallel can produce a fixed variety of different products. Any one machine can process a given set of the different product types. If it can process only one type of product it is referred to as a dedicated machine, otherwise it is referred to as a flexible machine. A flexible machine may be subject to a setup when it switches from one product type to another product type. Each product type has certain specific processing requirements on the various machines. There are n customers, each one sending in one order. An order requests specific quantities of the various different products and has a release date as well as a due date (committed shipping date). After the processing of all the different products for an order has been completed, the order can be shipped to the customer. This paper is organised as follows. We first introduce a notation for this class of models. We then focus on various different conditions on the machine environment as well as on several objective functions, including the total weighted completion time, the maximum lateness, the number of orders shipped late, and so on. We present polynomial time algorithms for the easier problems, complexity proofs for NP-hard problems and worst case performance analyses as well as empirical analyses of heuristics.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Blocher, J. and Chhajed, D. (1996) The customer order lead-time problem on parallel machines. Naval Research Logistics, 43:629–654.
Brucker, P. (1995) Scheduling Algorithms. Springer, Berlin.
Cheng, T. and Wang, G. (1999) Customer order scheduling on multiple facilities. Technical Report 11/98-9, Faculty of Business and Information Systems, The Hong Kong Polytechnic University.
Du, J. and Leung, J. Y.-T. (1990) Minimizing total tardiness on one machine is NP-hard. Mathematics of Operations Research, 15:483–495.
Duenyas, I. (1994) Estimating the throughput of a cyclic assembly system. International Journal of Production Research, 32:403–1410.
Fréville, A. (2004) The multidimensional 0–1 knapsack problem: An overview. European Journal of Operational Research, 155:1–21.
Gerodimos, A., Potts, C., and Tautenhahn, T. (1999) Scheduling multi-operation jobs on a single machine. Annals of Operations Research, 92:87–105.
Graham, R., Lawler, E., Lenstra, J., and Rinnooy Kan, A. (1979) Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5:287–326.
Hochbaum, D. (1996) Approximating covering and packing problems: set cover, vertex cover, independent set, and related problems. In Approximation Algorithms for NP-Hard Problems, D. Hochbaum (Ed.), PWS Publishing Company, Boston, MA, pp. 94–143.
Julien, F. and Magazine, M. (1990) Scheduling customer orders—an alternative production scheduling approach. Journal of Manufacturing and Operations Management, 3:177–199.
Lawler, E. (1973) Optimal sequencing of a single machine subject to precedence constraints. Management Science, 19:544–546.
Lee, C., Cheng, T., and Lin, B. (1993) Minimizing the makespan in the 3-machine assembly-type flowshop scheduling problem. Management Science, 39:616–625.
Leung, J. Y.-T., Li, H. and Pinedo, M. (2002a) Order scheduling in an environment with dedicated resources in parallel. Journal of Scheduling, accepted for publication.
Leung, J. Y.-T., Li, H., and Pinedo, M. (2002b) Scheduling orders for multiple product types with due date related objectives. European Journal of Operational Research. Accepted for publication.
Leung, J. Y.-T., Lee, C. Y., Young, G. H. and Ng, C. W. (2002c) Minimizing total flow time in generalized task systems. Submitted.
Leung, J. Y.-T., Li, H., Pinedo, M. and Sriskandarajah, C. (2005) Open shops with jobs overlap—revisited. European Journal of Operational Research. Accepted for publication.
Leung, J. Y.-T., Li, H., and Pinedo, M. (2003b) Order scheduling in a flexible environment with parallel resources. Working Paper.
Leung, J. Y.-T., Li, H., and Pinedo, M. (2003c) Scheduling multiple product types with weighted objectives. Working Paper.
Leung, J. Y.-T., Li, H., and Pinedo, M. (2003a) Scheduling orders for multiple product types to minimize total weighted completion time. Working Paper.
Moore, J. (1968) An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15:102–109.
Ng, C., Cheng, T., and Yuan, J. (2002) Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem. Information Processing Letters, 82:187–191.
Ng, C., Cheng, T., and Yuan, J. (2003) Concurrent open shop scheduling to minimize the weighted number of tardy jobs. Journal of Scheduling, 6:405–412.
Pinedo, M. (2002) Scheduling: Theory, Algorithms, and Systems. Prentice-Hall, Englewood Cliffs, NJ.
Potts, C., Sevast'janov, S., Strusevich, V., Wassenhove, L., and Zwaneveld, C. (1995) The two-stage assembly scheduling problem: complexity and approximation. Operations Research, 43:346–355.
Rajagopalan, S. and Vazirani, V. (1998) Primal-dual rnc approximation algorithms for set cover and covering integer programs. SIAM Journal on Computing, 28(2):525–540.
Sung, C. and Yoon, S. (1998) Minimizing total weighted completion time at a pre-assembly stage composed of two feeding machines. International Journal of Production Economics, 54:247–255.
Wagneur, E. and Sriskandarajah, C. (1993) Open shops with jobs overlap. European Journal of Operational Research, 71:366–378.
Wang, G. and Cheng, T. (2003) Customer order scheduling to minimize total weighted completion time. In Proceedings of the 1st Multidisciplinary Conference on Scheduling Theory and Applications, pp. 409–416.
Yang, J. (1998) Scheduling with batch objectives. Ph.D. Thesis, Industrial and Systems Engineering Graduate Program, The Ohio State University, Columbus, OH.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this paper
Cite this paper
Leung, J.YT., Li, H., Pinedo, M. (2005). Order Scheduling Models: An Overview. In: Kendall, G., Burke, E.K., Petrovic, S., Gendreau, M. (eds) Multidisciplinary Scheduling: Theory and Applications. Springer, Boston, MA. https://doi.org/10.1007/0-387-27744-7_3
Download citation
DOI: https://doi.org/10.1007/0-387-27744-7_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25266-7
Online ISBN: 978-0-387-27744-8
eBook Packages: Business and EconomicsBusiness and Management (R0)