Singlefacility scheduling by logicbased Benders decomposition
 Elvin Coban,
 J. N. Hooker
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Logicbased Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve singlefacility nonpreemptive scheduling problems with time windows and long time horizons. The Benders master problem assigns jobs to predefined segments of the time horizon, where the subproblem schedules them. In one version of the problem, jobs may not overlap the segment boundaries (which represent shutdown times, such as weekends), and in another version, there is no such restriction. The objective is to find feasible solutions, minimize makespan, or minimize total tardiness.
Inside
Within this Article
 Introduction
 Previous work
 Logicbased Benders decomposition
 The problem
 Segmented feasibility problem
 Unsegmented feasibility problem
 Segmented makespan problem
 Unsegmented makespan problem
 Segmented tardiness problem
 Problem generation
 Computational results
 Conclusion
 References
 References
Other actions
 Aggoun, A., & Vazacopoulos, A. (2004). Solving sports scheduling and timetabling problems with constraint programming. In S. Butenko, J. GilLafuente, & P. M. Pardalos (Eds.), Economics, management and optimization in sports (pp. 243–264). New York: Springer. CrossRef
 Babonneau, F., Beltran, C., Haurie, A., Tadonki, C., & Vial, J. P. (2007). ProximalACCPM: A versatile oracle based optimization method. In E. J. Kontoghiorghes & C. Gatu (Eds.), Advances in computational management science: Vol. 9. Optimisation, econometric and financial analysis (pp. 69–92). New York: Springer.
 Baptiste, P., Le Pape, C., & Nuijten, W. (2001). Constraintbased scheduling: applying constraint programming to scheduling problems. Dordrecht: Kluwer. CrossRef
 Barlatta, A. Y., Cohn, A. M., & Gusikhinc, O. (2010). A hybridization of mathematical programming and dominancedriven enumeration for solving shiftselection and tasksequencing problems. Computers & Operations Research, 37, 1298–1307. CrossRef
 Benders, J. F. (1962). Partitioning procedures for solving mixedvariables programming problems. Numerische Mathematik, 4, 238–252. CrossRef
 Benini, L., Bertozzi, D., Guerri, A., & Milano, M. (2005). Allocation and scheduling for MPSoCs via decomposition and nogood generation. In Lecture notes in computer science: Vol. 3709. Principles and practice of constraint programming (CP 2005) (pp. 107–121). Berlin: Springer. CrossRef
 Bent, R., & Van Hentenryck, P. (2010). Spatial, temporal, and hybrid decompositions for largescale vehicle routing with time windows. In D. Cohen (Ed.), Lecture notes in computer science: Vol. 6308. Principles and practice of constraint programming (CP 2010) (pp. 99–113). Berlin: Springer. CrossRef
 Cambazard, H., Hladik, P.E., Déplanche, A.M., Jussien, N., & Trinquet, Y. (2004). Decomposition and learning for a hard real time task allocation problem. In M. Wallace (Ed.), Lecture notes in computer science: Vol. 3258. Principles and practice of constraint programming (CP 2004) (pp. 153–167). Berlin: Springer. CrossRef
 Chu, Y., & Xia, Q. (2004). Generating Benders cuts for a class of integer programming problems. In J. C. Régin & M. Rueher (Eds.), Lecture notes in computer science: Vol. 3011. Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR 2004) (pp. 127–141). Berlin: Springer. CrossRef
 Codato, G., & Fischetti, M. (2006). Combinatorial Benders’ cuts for mixedinteger linear programming. Operations Research, 54, 756–766. CrossRef
 Corréa, A. I., Langevin, A., & Rousseau, L. M. (2004). Dispatching and conflictfree routing of automated guided vehicles: a hybrid approach combining constraint programming and mixed integer programming. In J. C. Régin & M. Rueher (Eds.), Lecture notes in computer science: Vol. 3011. Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR 2004) (pp. 370–378). Berlin: Springer. CrossRef
 FazelZarandi, M. M., & Beck, J. C. (2009). Solving a locationallocation problem with logicbased Benders’ decomposition. In I. P. Gent (Ed.), Lecture notes in computer science: Vol. 5732. Principles and practice of constraint programming (CP 2009) (pp. 344–351). Berlin: Springer. CrossRef
 French, S. (1982). Sequencing and scheduling. New York: Wiley.
 Fulkerson, D. R. (1971). Blocking and antiblocking pairs of polyhedra. Mathematical Programming, 1, 168–194. CrossRef
 Geoffrion, A. M. (1972). Generalized Benders decomposition. Journal of Optimization Theory and Applications, 10, 237–260. CrossRef
 Harjunkoski, I., & Grossmann, I. E. (2001). A decomposition approach for the scheduling of a steel plant production. Computers & Chemical Engineering, 25, 1647–1660. CrossRef
 Harjunkoski, I., & Grossmann, I. E. (2002). Decomposition techniques for multistage scheduling problems using mixedinteger and constraint programming methods. Computers & Chemical Engineering, 26, 1533–1552. CrossRef
 Hooker, J. N. (1995). Logicbased Benders decomposition. In INFORMS national meeting (INFORMS 1995).
 Hooker, J. N. (1996). Inference duality as a basis for sensitivity analysis. In E. C. Freuder (Ed.), Lecture notes in computer science: Vol. 1118. Principles and practice of constraint programming (CP 1996) (pp. 224–236). Berlin: Springer. CrossRef
 Hooker, J. N. (2000). Logicbased methods for optimization: combining optimization and constraint satisfaction. New York: Wiley. CrossRef
 Hooker, J. N. (2004). A hybrid method for planning and scheduling. In M. Wallace (Ed.), Lecture notes in computer science: Vol. 3258. Principles and practice of constraint programming (CP 2004) (pp. 305–316). Berlin: Springer. CrossRef
 Hooker, J. N. (2005a). A hybrid method for planning and scheduling. Constraints, 10, 385–401. CrossRef
 Hooker, J. N. (2005b). Planning and scheduling to minimize tardiness. In Lecture notes in computer science: Vol. 3709. Principles and practice of constraint programming (CP 2005) (pp. 314–327). Berlin: Springer. CrossRef
 Hooker, J. N. (2006). An integrated method for planning and scheduling to minimize tardiness. Constraints, 11, 139–157. CrossRef
 Hooker, J. N. (2007a). Integrated methods for optimization. Berlin: Springer.
 Hooker, J. N. (2007b). Planning and scheduling by logicbased Benders decomposition. Operations Research, 55, 588–602. CrossRef
 Hooker, J. N., & Ottosson, G. (2003). Logicbased Benders decomposition. Mathematical Programming, 96, 33–60.
 Hooker, J. N., & Yan, H. (1995). Logic circuit verification by Benders decomposition. In V. Saraswat & P. Van Hentenryck (Eds.), Principles and practice of constraint programming: the newport papers (pp. 267–288). Cambridge: MIT Press.
 Jain, V., & Grossmann, I. E. (2001). Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS Journal on Computing, 13, 258–276. CrossRef
 Jeroslow, R. G. (1987). Representability in mixed integer programming, I: Characterization results. Discrete Applied Mathematics, 17, 223–243. CrossRef
 Keha, A. B., Khowala, K., & Fowler, J. W. (2009). Mixed integer programming formulations for single machine scheduling problems. Computers & Industrial Engineering, 56, 357–367. CrossRef
 Koulamas, C. (2010). The singlemachine total tardiness scheduling problem: review and extensions. European Journal of Operational Research, 202, 1–7. CrossRef
 Maravelias, C. T. (2006). A decomposition framework for the scheduling of single and multistage processes. Computers & Chemical Engineering, 30, 407–420. CrossRef
 Maravelias, C. T., & Grossmann, I. E. (2004a). A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants. Computers & Chemical Engineering, 28, 1921–1949. CrossRef
 Maravelias, C. T., & Grossmann, I. E. (2004b). Using MILP and CP for the scheduling of batch chemical processes. In J. C. Régin & M. Rueher (Eds.), Lecture notes in computer science: Vol. 3011. Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (CPAIOR 2004) (pp. 1–20). Berlin: Springer. CrossRef
 Padberg, M. (1973). On the facial structure of set packing polyhedra. Mathematical Programming, 5, 199–215. CrossRef
 Pinedo, M. (1995). Scheduling: theory, algorithms, and systems. New York: Prentice Hall.
 Rasmussen, R. (2008). Scheduling a triple round robin tournament for the best Danish soccer league. European Journal of Operational Research, 185, 795–810. CrossRef
 Rasmussen, R., & Trick, M. A. (2007). A Benders approach to the constrained minimum break problem. European Journal of Operational Research, 177, 198–213. CrossRef
 Sadykov, R., & Wolsey, L. A. (2006). Integer programming and constraint programming in solving a multimachine assignment scheduling problem with deadlines and release dates. INFORMS Journal on Computing, 18, 209–217. CrossRef
 Tarim, S. A., & Miguel, I. (2006). A hybrid Benders’ decomposition method for solving stochastic constraint programs with linear recourse. In B. Hnich, M. Carlsson, F. Fages, & F. Rossi (Eds.), Lecture notes in computer science: Vol. 3978. Recent advances in constraints (CSCLP 2005) (pp. 133–148). Berlin: Springer. CrossRef
 Terekhov, D., Beck, J. C., & Brown, K. N. (2005). Solving a stochastic queueing design and control problem with constraint programming. In Proceedings of the 22nd national conference on artificial intelligence (AAAI 2005) (pp. 261–266).
 Thorsteinsson, E. (2001). Branch and check: a hybrid framework integrating mixed integer programming and constraint logic programming. In T. Walsh (Ed.), Lecture notes in computer science: Vol. 2239. Principles and practice of constraint programming (CP 2001) (pp. 16–30). Berlin: Springer. CrossRef
 Timpe, C. (2002). Solving planning and scheduling problems with combined integer and constraint programming. ORSpektrum, 24, 431–448. CrossRef
 Title
 Singlefacility scheduling by logicbased Benders decomposition
 Journal

Annals of Operations Research
Volume 210, Issue 1 , pp 245272
 Cover Date
 20131101
 DOI
 10.1007/s104790111031z
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Logicbased Benders decomposition
 Constraint programming
 Mixed integer programming
 Singlefacility scheduling
 Makespan
 Tardiness
 Feasibility
 Industry Sectors
 Authors

 Elvin Coban ^{(1)}
 J. N. Hooker ^{(1)}
 Author Affiliations

 1. Tepper School of Business, Carnegie Mellon University, Pittsburgh, USA