Abstract
In this paper we introduce Xpress-CP—a Constraint Programming tool-and demonstrate its modeling and solving capabilities. We consider the multi-machine assignment and scheduling problem (Hooker et al. (1999)), where jobs, with release dates and deadlines, have to be processed on parallel unrelated machines (where processing times depend on machine assignment). Given a job/machine assignment cost matrix, the objective is to minimize the total cost while keeping all machine schedules feasible. We show that by deriving the benefits of MIP and CP techniques simultaneously this problem can be modeled and solved efficiently in a hybrid fashion using Xpress Optimization suite.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggoun, A. and Vazacopoulos, A. 2004. Solving Sports Scheduling and Time tabling Problems with Constraint Programming, in Economics, Management and Optimization in Sports, Edited by S. Butenko, J. Gil-Lafuente and P.M. Pardalos, Springer.
Baptiste, P., Le Pape, C. and Nuijten, W. 2001. Constraint Based Scheduling. Kluwer.
Bockmayr, A. and Kasper, T. 2003. Branch-and-infer: A framework for combining CP and IP. In Constraint and Integer Programming (Ed. M. Milano), Chapter 3, 59–87, Kluwer.
Bockmayr, A. and Hooker, J.N. 2003. Constraint programming. In Handbooks in Operations Research and Management Science: Discrete Optimization (Eds. K. Aardal, G. Nemhauser, and R. Weismantel), Elsevier, To appear.
Bockmayr, A. and Pisaruk, N. 2003. Detecting Infeasibility and Generating Cuts for MIP using CP. 5th International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR’03, Montreal, May 2003.
Brucker, P. 2001. Scheduling Algorithms. Third Edition, Springer.
Carlier, J. and Pinson., E. 1990. A Practical Use of Jackson’s Preemptive Schedule for Solving the Job-Shop Problem. Annals of Operations Research 26, 269–287.
Colombani, Y and Heipcke, S. 2002. Mosel: An Overview. May 2002, available at http://www.dashoptimization.com/home/downloads/pdf/mosel.pdf.
Easton, K., Nemhauser, G. and Trick, M. 2003. CP Based Branch-and-Price. In Constraint and Integer Programming (Ed. M. Milano), Chapter 7, 207–231, Kluwer.
Hooker, J.N., Ottosson, G., Thorsteinsson, E.S. and Kim, H.J. 1999. On integrating constraint propagation and linear programming for combinatorial optimization. Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI-99), AAAI, The AAAI Press/MIT Press, Cambridge, MA. 136–141.
Jain, V. and Grossmann, I.E. 2001. Algorithms for hybrid MIP/CP models for a class of optimization problems. INFORMS J. Computing, 13(4), 258–276, 2001.
Peter, B. 2001. Scheduling Algorithms. Springer Lehrbuch.
Pritsker, A., Watters, L. and Wolfe, P. 1969. Multi-project scheduling with limited resources: a zero-one programming approach. Management Science, 16:93–108.
Pinedo, M. 1995. Scheduling: Theory, Algorithms and Systems. Prentice-Hall, NJ.
Pinedo, M. and Chao, X. 1998. Operations Scheduling with Applications in Manufacturing and services. McGraw-Hill/Irwin.
Sadykov, R. and Wolsey, L. 2003. Integer programming and constraint programming in solving a multi-machine assignment scheduling problem with deadlines and release dates. CORE discussion paper, Nov 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Vazacopoulos, A., Verma, N. (2005). Hybrid MIP-CP Techniques to Solve a Multi-Machine Assignment and Scheduling Problem in Xpress-CP. In: Geunes, J., Pardalos, P.M. (eds) Supply Chain Optimization. Applied Optimization, vol 98. Springer, Boston, MA. https://doi.org/10.1007/0-387-26281-4_12
Download citation
DOI: https://doi.org/10.1007/0-387-26281-4_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-26280-2
Online ISBN: 978-0-387-26281-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)