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A Hybrid Programming Framework for Resource-Constrained Scheduling Problems

  • Paweł SitekEmail author
  • Jarosław Wikarek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9375)

Abstract

Resource-constrained scheduling problems appear frequently at different levels of decisions in manufacturing, logistics, computer networks, software engineering etc. They are usually characterized by many types of constraints, which often make them unstructured and difficult to solve (NP-complete). Traditional mathematical programming (MP) approaches are deficient because their representation of allocation constraints is artificial (using 0–1 variables). Unlike traditional approaches, declarative constraint logic programming (CLP) provides for a natural representation of heterogeneous constraints. In CLP we state the problem requirements by constraints; we do not need to specify how to meet these requirements. CLP approach is very effective for binary constraints (binding at most two variables). If there are more variables in the constraints and the problem requires further optimization, the efficiency decreases dramatically. This paper presents a hybrid programming framework for constrained scheduling problems where two environments (mathematical programming and constraint logic programming) were integrated. This integration, hybridization as well as a transformation of the problem helped reduce the combinatorial problem substantially.

In order to compare the effectiveness of the proposed framework, also made implementation of illustrative example separately for the two environments MP and CLP.

Keywords

Constraint logic programming Mathematical programming Scheduling Decision support Hybrid approach 

References

  1. 1.
    Schrijver, A.: Theory of Linear and Integer Programming. Wiley, New York (1998)zbMATHGoogle Scholar
  2. 2.
    Rossi, F., Van Beek, P., Walsh, T.: Handbook of Constraint Programming (Foundations of Artificial Intelligence). Elsevier, New York (2006)zbMATHGoogle Scholar
  3. 3.
    Apt, K., Wallace, M.: Constraint Logic Programming using Eclipse. Cambridge University Press, Cambridge (2006)CrossRefGoogle Scholar
  4. 4.
    Bocewicz, G., Banaszak, Z.: Declarative approach to cyclic steady states space refinement: periodic processes scheduling. Int. J. Adv. Manuf. Technol. 67(1–4), 137–155 (2013)CrossRefGoogle Scholar
  5. 5.
    Sitek, P., Wikarek, J.: A hybrid approach to the optimization of multiechelon systems. Math. Probl. Eng. Article ID 925675 (2014). doi: 10.1155/2014/925675
  6. 6.
    Sitek, P., Nielsen, I.E., Wikarek, J.: A hybrid multi-agent approach to the solving supply chain problems. Procedia Comput. Sci. KES 35, 1557–1566 (2014)CrossRefGoogle Scholar
  7. 7.
    Milano, M., Wallace, M.: Integrating operations research in constraint programming. Ann. Oper. Res. 175(1), 37–76 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Achterberg, T., Berthold, T., Koch, T., Wolter, K.: Constraint integer programming: a new approach to integrate CP and MIP. In: Trick, M.A. (ed.) CPAIOR 2008. LNCS, vol. 5015, pp. 6–20. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Guyon, O., Lemaire, P., Pinson, Ă., Rivreau, D.: Solving an integrated job-shop problem with human resource constraints. Ann. Oper. Res. 213(1), 147–171 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Blazewicz, J., Lenstra, J.K., Rinnooy Kan, A.H.G.: Scheduling subject to resource constraints: classification and complexity. Discrete Appl. Math. 5, 11–24 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lawrence, S.R., Morton, T.E.: Resource-constrained multi-project scheduling with tardy costs: comparing myopic, bottleneck, and resource pricing heuristics. Eur. J. Oper. Res. 64(2), 168–187 (1993)CrossRefzbMATHGoogle Scholar
  12. 12.
    Sitek, P.: A hybrid CP/MP approach to supply chain modelling, optimization and analysis. In: Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, pp. 1345–1352 (2014). doi: 10.15439/2014F89
  13. 13.
    Lindo Systems INC: LINDO™ software for integer programming, linear programming, nonlinear programming, stochastic programming, global optimization. www.lindo.com. Accessed 4 May 2015
  14. 14.
    Eclipse: Eclipse - the eclipse foundation open source community website. www.eclipse.org. Accessed 4 May 2015
  15. 15.
    Relich, M.: Using ERP database for knowledge acquisition: a project management perspective. In: Proceedings of International Scientific Conference on Knowledge for Market Practice Use, Olomouc, Czech Republic, pp. 263–269 (2013)Google Scholar
  16. 16.
    Toth, P., Vigo, D.: Models, relaxations and exact approaches for the capacitated vehicle routing problem. Discrete Appl. Math. 123(1–3), 487–512 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Coelho, J., Vanhoucke, M.: Multi-mode resource-constrained project scheduling using RCPSP and SAT solvers. Eur. J. Oper. Res. 213, 73–82 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Krenczyk, D., Skolud, B.: Transient states of cyclic production planning and control. Appl. Mech. Mater. 657, 961–965 (2014). doi: 10.4028/www.scientific.net/AMM.657.961 CrossRefGoogle Scholar
  19. 19.
    Gola, A., Świeć, A.: Computer-aided machine tool selection for focused flexibility manufacturing systems using economical criteria. Actual Probl. Econ. 10(124), 383–389 (2011)Google Scholar
  20. 20.
    Sitek, P., Wikarek, J.: A hybrid framework for the modelling and optimisation of decision problems in sustainable supply chain management. Int. J. Prod. Res. 1–18, 2015 (2015). doi: 10.1080/00207543.2015.1005762 Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Control and Management Systems SectionTechnical University of KielceKielcePoland

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