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Abstract

The Resource-constrained Project Scheduling Problem (Rcpsp), in which a schedule must obey the resource constraints and the precedence constraints between pairs of activities, is one of the most studied scheduling problems. An important variation of the problem (RcpspDc) is to find a schedule which maximises the net present value (discounted cash flow), when every activity has a given cash flow associated with it. Given the success of lazy clause generation (Lcg) approaches to solve Rcpsp with and without generalised precedence relations it seems worthwhile investigating Lcg’s use on Rcpspdc. To do so, we must construct propagators for the net-present-value constraint that explain their propagation to the Lcg solver. In this paper we construct three different propagators for net-present-value constraints, and show how they can be used to rapidly solve RcpspDc.

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References

  1. Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling 17(7), 57–73 (1993)

    Article  MathSciNet  Google Scholar 

  2. Beringer, H., De Backer, B.: Satisfiability of boolean formulas over linear constraints. In: IJCAI, pp. 296–304 (1993)

    Google Scholar 

  3. Brucker, P., Drexl, A., Möhring, R., Neumann, K., Pesch, E.: Resource-constrained project scheduling: Notation, classification, models, and methods. European Journal of Operational Research 112(1), 3–41 (1999)

    Article  MATH  Google Scholar 

  4. Demeulemeester, E.L., Herroelen, W.S.: A branch-and-bound procedure for the multiple resource-constrained project scheduling problem. Management Science 38(12), 1803–1818 (1992)

    Article  MATH  Google Scholar 

  5. Demeulemeester, E.L., Herroelen, W.S.: New benchmark results for the resource-constrained project scheduling problem. Management Science 43(11), 1485–1492 (1997)

    Article  MATH  Google Scholar 

  6. Demeulemeester, E.L., Herroelen, W.S., Van Dommelen, P.: An optimal recursive search procedure for the deterministic unconstrained max-npv project scheduling problem. Tech. rep., Katholieke Universiteit Leuven (1996), Research Report 9603

    Google Scholar 

  7. Grinold, R.C.: The payment scheduling problem. Naval Research Logistics Quarterly 19(1), 123–136 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hartmann, S., Briskorn, D.: A survey of variants and extensions of the resource-constrained project scheduling problem. European Journal of Operational Research 207(1), 1–14 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Harvey, W., Stuckey, P.J.: Improving linear constraint propagation by changing constraint representation. Constraints 8(2), 173–207 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Herroelen, W.S., Demeulemeester, E.L., De Reyck, B.: A classification scheme for project scheduling. In: Weglarz, J. (ed.) Project Scheduling. International Series in Operations Research and Management Science, vol. 14, pp. 1–26. Kluwer Academic Publishers (1999)

    Google Scholar 

  11. Icmeli, O., Erengüç, S.S.: A branch and bound procedure for the resource constrained project scheduling problem with discounted cash flows. Management Science 42(10), 1395–1408 (1996)

    Article  MATH  Google Scholar 

  12. Liu, S.-S., Wang, C.-J.: Resource-constrained construction project scheduling model for profit maximization considering cash flow. Automation in Construction 17(8), 966–974 (2008)

    Article  Google Scholar 

  13. Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Inf. Proc. Let. 47(4), 173 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Procs. of DAC 2001, pp. 530–535 (2001)

    Google Scholar 

  15. Neumann, K., Zimmermann, J.: Exact and truncated branch-and-bound procedures for resource-constrained project scheduling with discounted cash flows and general temporal constraints. Central European Journal of Operations Research 10(4), 357–380 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Ohrimenko, O., Stuckey, P.J., Codish, M.: Propagation via lazy clause generation. Constraints 14(3), 357–391 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Russell, A.H.: Cash flows in networks. Management Science 16(5), 357–373 (1970)

    Article  MATH  Google Scholar 

  18. Schulte, C., Stuckey, P.J.: Efficient constraint propagation engines. ACM Transactions on Programming Languages and Systems 31(1), Article No. 2 (2008)

    Google Scholar 

  19. Schulte, C., Tack, G.: Views and Iterators for Generic Constraint Implementations. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 817–821. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Solving the resource constrained project scheduling problem with generalized precedences by lazy clause generation (September 2010), http://arxiv.org/abs/1009.0347

  21. Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Explaining the cumulative propagator. Constraints 16(3), 250–282 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Schwindt, C., Zimmermann, J.: A steepest ascent approach to maximizing the net present value of projects. Mathematical Methods of Operations Research 53, 435–450 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Selle, T., Zimmermann, J.: A bidirectional heuristic for maximizing the net present value of large-scale projects subject to limited resources. Naval Research Logistics (NRL) 50(2), 130–148 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. Shaw, P.: Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems. In: Maher, M., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998), http://dx.doi.org/10.1007/3-540-49481-2_30

    Chapter  Google Scholar 

  25. Vanhoucke, M., Demeulemeester, E.L., Herroelen, W.S.: On maximizing the net present value of a project under renewable resource constraints. Management Science 47, 1113–1121 (2001)

    Article  MATH  Google Scholar 

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Schutt, A., Chu, G., Stuckey, P.J., Wallace, M.G. (2012). Maximising the Net Present Value for Resource-Constrained Project Scheduling. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds) Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol 7298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29828-8_24

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  • DOI: https://doi.org/10.1007/978-3-642-29828-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

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