Abstract
This paper presents an approach, based on propositional satisfiability (SAT), for the resource constrained project scheduling problem with general precedence relations. This approach combines propositional satisfiability formulations with a bisection method, in order to achieve an optimal solution. The empirical results suggest that when the optimal schedule is significantly affected by the availability of resources, this strategy outperforms the typical integer linear programming approach.
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References
Brucker, P., Drexl, A., Möhring, R., Neumann, K.: Resource-constrained project scheduling: Notation, classification, models, and methods. European Journal of Operational Research 112(1), 3–41 (1999)
Tavares, L.V.: Advanced Models for Project Management. Kluwer Academic Publishers (1998)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP Completeness. W.H. Freeman and Company (1979)
Hammer, P.L., Rudeanu, S.: Boolean Methods in Operations Research and Related Areas. Springer (1968)
Talbot, B.: Resource-Constrained Project Scheduling with Time-Resource Tradeoffs: The Nonpreemptive Case. Management Science 28(10), 1197–1210 (1982)
Reyck, B., Herroelen, W.: A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations. Operations Research 45(2) (March-April 1997)
Wiest, J.D.: A heuristic model for scheduling large projects with limited resources. Management Science 13(6), 359–377 (1967)
Liess, O., Michelon, P.: A constraint programming approach for the resource-constrained project scheduling problem. Annals of Operation Research 157(1), 25–36 (2008)
Cho, J.H., Kim, Y.D.: A simulated annealing algorithm for resource constrained project scheduling problems. Journal of the Operational Research Society 48(7), 736–744 (1997)
Fu, N., Lau, H.C., Varakantham, P., Xiao, F.: Robust Local Search for Solving RCPSP/max with Durational Uncertainty. Journal of Artificial Intelligence Research 43, 43–86 (2012)
Hartmann, S.: A competitive genetic algorithm for resource constrained project scheduling. Naval Research Logistics 45(7), 733–750 (1998)
Colak, S., Agarwal, A., Erenguc, S.: Resource Constrained Scheduling Problem: A Hybrid Neural Approach. Perspectives in Modern Project Scheduling 112(1983), 3–41 (1999)
Huang, R., Chen, Y., Zhang, W.: SAS+ Planning as Satisfiability. Journal of Artificial Intelligence Research 43(1), 293–328 (2012)
Coelho, J., Vanhoucke, M.: Multi-mode resource-constrained project scheduling using RCPSP and SAT solvers. Journal of Operational Research 213(1), 73–82 (2011) ISSN 0377-2217
Horbach, A.: A Boolean satisfiability approach to the resource-constrained project scheduling problem. Annals of Operations Research 181(1), 89–107, doi:10.1007/s10479-010-0693-2
Davis, M., Putnam, H.: A Computing Procedure for Quantification Theory. Journal of the Association of Computing Machinery (1960)
Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem Proving. Communications of the ACM 5, 394–397 (1962)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Annual ACM IEEE Design Automation Conference (2001)
Ryan, L.: Efficient Algorithms for Clause-Learning SAT Solvers, M.S. Thesis, Simon Fraser (2004)
Goldberg, E., Novikov, Y.: BerkMin: A fast and robust Sat-solver. Discrete Applied Mathematics 155(12) (June 2007)
Biere, A.: Adaptive Restart Strategies for Conflict Driven SAT Solvers. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 28–33. Springer, Heidelberg (2008)
Marques, J.P., Karem, S., Sakallah, A.: Conflict analysis in search algorithms for propositional satisfiability. In: Proc. of the IEEE Intl. Conf. on Tools with Artificial Intelligence (1996)
Chakradhar, S.T., Agrawal, V.D., Tothweiller, S.G.: A Transitive Closure Algorithm for Test Generation. IEEE Trans. Computer-Aided Design 12(7), 1015–1028 (1993)
Larrabee, T.: Efficient Generation of Test Patterns Using Boolean Satisfiability. PhD Dissertation, Dept. of Computer Science, Stanford Univ., STAN-CS-90-1302 (February 1990)
Kautz, H., Selman, B.: Planning as Satisfiability. In: Proceedings of the 10th European Conference on Artificial Intelligence, ECAI 1992 (August 1992)
Lynce, I., Marques-Silva, J.: Efficient Haplotype Inference with Boolean Satisfiability. In: AAAI 2006 (2006)
Ivancic, F., Yang, Z., Ganai, M.K., Gupta, A., Ashar, P.: Efficient SAT-based bounded model checking for software verification. Journal of Theoretical Computer Science 404(3) (September 2008)
Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Kolisch, R., Sprecher, A.: PSPLIB – A project scheduling problem library. European Journal of Operational Research, 205–216 (1996)
IBM CPLEX, http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/ (January 10, 2013)
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Alves, R., Alvelos, F., Sousa, S.D. (2013). Resource Constrained Project Scheduling with General Precedence Relations Optimized with SAT. In: Correia, L., Reis, L.P., Cascalho, J. (eds) Progress in Artificial Intelligence. EPIA 2013. Lecture Notes in Computer Science(), vol 8154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40669-0_18
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DOI: https://doi.org/10.1007/978-3-642-40669-0_18
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