Abstract
Many optimisation problems contain substructures involving constraints on sequences of decision variables. Such constraints can be very complex to express with mixed integer programming (MIP), while in constraint programming (CP), the global constraint regular easily represents this kind of substructure with deterministic finite automata (DFA). In this paper, we use DFAs and the associated layered graph structure built for the regular constraint consistency algorithm to develop a MIP version of the constraint. We present computational results on an employee timetabling problem, showing that this new modeling approach can significantly decrease computational times in comparison with a classical MIP formulation.
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.
References
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)
Ernst, A.T., Jiang, H., Krishnamoorthy, M., Sier, D.: Staff scheduling and rostering: A review of applications, methods and models. European Journal of Operational Research 153, 3–27 (2004)
Ernst, A.T., Jiang, H., Krishnamoorthy, M., Owens, B., Sier, D.: An annotated bibliography of personnel scheduling and rostering. Annals of Operations Research 127, 21–144 (2004)
Dantzig, G.: A comment on Edie’s traffic delay at toll booths. Operations Research 2, 339–341 (1954)
Segal, M.: The operator-scheduling problem: A network-flow approach. Operations Research 22, 808–823 (1974)
Moondra, B.: An LP model for work force scheduling for banks. Journal of Bank Research 7, 299–301 (1976)
Bechtolds, S., Jacobs, L.: Implicit optimal modeling of flexible break assigments. Management Science 36, 1339–1351 (1990)
Bechtolds, S., Jacobs, L.: The equivalence of general set-covering and implicit integer programming formulations for shift scheduling. Naval Research Logistics 43, 223–249 (1996)
Thompson, G.: Improved implicit modeling of the labor shift scheduling problem. Management Science 41, 595–607 (1995)
Aykin, T.: Optimal shift scheduling with multiple break windows. Management Science 42, 591–602 (1996)
Brusco, M., Jacobs, L.: Personnel tour scheduling when starting-time restrictions are present. Management Science 44, 534–547 (1998)
Laporte, G., Nobert, Y., Biron, J.: Rotating schedules. European Journal of Operational Research 4(1), 24–30 (1980)
Balakrishan, A., Wong, R.: Model for the rotating workforce scheduling problem. Networks 20, 25–42 (1990)
Isken, M.: An implicit tour scheduling model with applications in healthcare. Annals of Operations Research (Special Issue on Staff Scheduling and Rostering) 128, 91–109 (2004)
Çezik, T., Günlük, O., Luss, H.: An integer programming model for the weekly tour scheduling problem. Naval Research Logistic 48(7) (1999)
Millar, H., Kiragu, M.: Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming. European Journal of Operational Research 104(3), 582–592 (1998)
Ernst, A., Hourigan, P., Krishnamoorthy, M., Mills, G., Nott, h., Sier, D.: Rostering ambulance officers. In: Proceedings of the 15th National Conference of the Australian Society for Operations Research, Gold Coast, pp. 470–481 (1999)
Sodhi, M.S.: A flexible, fast, and optimal modeling approach applied to crew rostering at London Underground. Annals of Operations Research 127, 259–281 (2003)
Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages and computation. Addison-Wesley, Reading (1979)
van Hoeve, W.J., Pesant, G., Rousseau, L.M.: On global warming: Flow-based soft global constraints. Journal of Heuristics 12(4-5), 347–373 (2006)
Demassey, S., Pesant, G., Rousseau, L.-M.: A cost-regular based hybrid column generation approach. Constraints 11(4), 315–333 (2006)
Quimper, C.-G., Walsh, T.: Global grammar constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 751–755. Springer, Heidelberg (2006)
Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)
Demassey, S., Pesant, G., Rousseau, L.-M.: Constraint programming based column generation for employee timetabling. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 140–154. Springer, Heidelberg (2005)
Achterberg, T.: SCIP - a framework to integrate constraint and mixed integer programming. Technical Report 04-19, Zuse Institute Berlin (2004), http://www.zib.de/Publications/abstracts/ZR-04-19/
Sellmann, M.: The theory of grammar constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 530–544. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Côté, MC., Gendron, B., Rousseau, LM. (2007). Modeling the Regular Constraint with Integer Programming. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-72397-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72396-7
Online ISBN: 978-3-540-72397-4
eBook Packages: Computer ScienceComputer Science (R0)