Resource-Constrained Project Scheduling:Computing Lower Bounds by Solving Minimum Cut Problems
We present a novel approach to compute Lagrangian lower bounds on the objective function value of a wide class of resource-constrained project scheduling problems. The basis is a polynomial-time algorithm to solve the following scheduling problem: Given a set of activities with start-time dependent costs and temporal constraints in the form of time windows, find a feasible schedule of minimum total cost. In fact, we show that any instance of this problem can be solved by a minimum cut computation in a certain directed graph.
We then discuss the performance of the proposed Lagrangian approach when applied to various types of resource-constrained project scheduling problems. An extensive computational study based on different established test beds in project scheduling shows that it can significantly improve upon the quality of other comparably fast computable lower bounds.
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- 3.P. Brucker and S. Knust. A linear programming and constraint propagation-based lower bound for the RCPSP. Technical Report 204, Osnabrücker Schriften zur Mathematik, 1998.Google Scholar
- 4.C. C. B. Cavalcante, C. C. De Souza, M. W. P. Savelsbergh, Y. Wang, and L. A. Wolsey. Scheduling projects with labor constraints. CORE Discussion Paper 9859, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, 1998.Google Scholar
- 6.B. Cherkassky and A. V. Goldberg. On implementing push-relabel method for the maximum flow problem. In Proceedings of the 4th Conference on Integer Programming and Combinatorial Optimization, pages 157–171, 1995.Google Scholar
- 8.A. Drexl and A. Kimms. Optimization guided lower and upper bounds for the Resource Investment Problem. Technical Report 481, Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel, 1998.Google Scholar
- 12.J. Kallrath and J. M. Wilson. Business Optimisation using Mathematical Programming. Macmillan Business, London, U.K., 1997.Google Scholar
- 16.R. H. Möhring. Algorithmic aspects of comparability graphs and interval graphs. In I. Rival, editor, Graphs and Order, pages 41–101. D. Reidel Publishing Company, Dordrecht, 1985.Google Scholar
- 17.R. H. Möhring, A. S. Schulz, F. Sork, and M. Uetz. In preparation, 1999.Google Scholar
- 19.M. W. P. Savelsbergh, R. N. Uma, and J. Wein. An experimental study of LP-based approximation algorithms for scheduling problems. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 453–462, 1998.Google Scholar
- 21.C. Schwindt. Generation of resource constrained project scheduling problems with minimal and maximal time lags. Technical Report 489, WIOR, University of Karlsruhe, Germany, 1996.Google Scholar