Abstract
We propose a hybrid MIP/CP approach for solving multi-activity shift scheduling problems, based on regular languages that partially describe the set of feasible shifts. We use an aggregated MIP relaxation to capture the optimization part of the problem and to get rid of symmetry. Whenever the MIP solver generates a integer solution, we use a CP solver to check whether it can be turned into a feasible solution of the original problem. A MIP-based heuristic is also developed. Computational results are reported, showing that the proposed method is a promising alternative compared to the state-of-the-art.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Beldiceanu, N., Carlsson, M., Petit, T.: Deriving Filtering Algorithms from Constraint Checkers. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 107–122. Springer, Heidelberg (2004)
Côté, M.-C., Gendron, B., Rousseau, L.-M.: Modeling the Regular Constraint with Integer Programming. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 29–43. Springer, Heidelberg (2007)
Côté, M.C., Gendron, B., Quimper, C.G., Rousseau, L.M.: Formal languages for integer programming modeling of shift scheduling problems. Constraints 16(1), 54–76 (2011)
Côté, M.C., Gendron, B., Rousseau, L.M.: Grammar-based integer programming models for multiactivity shift scheduling. Management Science 57(1), 151–163 (2011)
Demassey, S., Pesant, G., Rousseau, L.M.: A cost-regular based hybrid column generation approach. Constraints 11(4), 315–333 (2006)
Fischetti, M., Liberti, L.: Orbital Shrinking. In: Mahjoub, A.R., Markakis, V., Milis, I., Paschos, V.T. (eds.) ISCO 2012. LNCS, vol. 7422, pp. 48–58. Springer, Heidelberg (2012)
Gecode Team: Gecode: Generic constraint development environment (2012), http://www.gecode.org
Hooker, J.N.: Integrated Methods for Optimization. Springer (2006)
Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Mathematical Programming 96(1), 33–60 (2003)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison Wesley (1979)
IBM ILOG: CPLEX 12.2 User’s Manual (2011)
Milano, M.: Constraint and Integer Programming: Toward a Unified Methodology. Kluwer Academic Publishers (2003)
Pesant, G.: A Regular Language Membership Constraint for Finite Sequences of Variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004)
Pesant, G., Quimper, C.-G., Rousseau, L.-M., Sellmann, M.: The Polytope of Context-Free Grammar Constraints. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 223–232. Springer, Heidelberg (2009)
Quimper, C.-G., Walsh, T.: Global Grammar Constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 751–755. Springer, Heidelberg (2006)
Quimper, C.-G., Walsh, T.: Decomposing Global Grammar Constraints. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 590–604. Springer, Heidelberg (2007)
Quimper, C.G., Rousseau, L.M.: A large neighbourhood search approach to the multi-activity shift scheduling problem. Journal of Heuristics 16, 373–392 (2010)
Sellmann, M.: The Theory of Grammar Constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 530–544. Springer, Heidelberg (2006)
Sellmann, M.: Theoretical Foundations of CP-Based Lagrangian Relaxation. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 634–647. Springer, Heidelberg (2004)
Van Hentenryck, P., Milano, M.: Hybrid Optimization: The Ten Years of CPAIOR. Springer Optimization and Its Applications. Springer (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Salvagnin, D., Walsh, T. (2012). A Hybrid MIP/CP Approach for Multi-activity Shift Scheduling. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_46
Download citation
DOI: https://doi.org/10.1007/978-3-642-33558-7_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33557-0
Online ISBN: 978-3-642-33558-7
eBook Packages: Computer ScienceComputer Science (R0)