Keywords: resource-constrained project scheduling, cash flow models, heuristic and metaheuristic techniques, harmony search optimization, hybrid methods, strip packing.

This paper presents an improved hybrid method for the resource-constrained project scheduling problem with discounted cash flows and strip packing like resource constraints. In the proposed approach, a resource-constrained project is characterized by its "best" schedule, where best means a makespan minimal resource-constrained schedule for which the net present value (NPV) measure is maximal and the resource profiles approach the ideal rectangular shape as much as possible. In the model the positive (negative) cash flow events are represented by dummy activities with zero duration which are connected to the finishing (starting) milestone and succeed (precede) a particular subset of "normal" activities. The algorithm is an improved conflict repairing version of the "Sounds of Silence" harmony search metaheuristic developed by Csébfalvi et al. [1,2] and Láng [3]. In the improved algorithm presented, harmony search is combined with a resource leveling-assigning procedure based on a mixed integer linear programming (MILP) formulation developed by Csébfalvi and Konstantinidis [4]. To generate the improvements a state-of-the-art callable MILP solver (CPLEX) was used. In order to illustrate the essence and viability of the proposed approach, we present detailed computational results for the first J30 instance with randomly generated cash flow events from the popular PSPLIB [5] benchmark set.

1

G. Csébfalvi, A. Csébfalvi, E. Szendroi, "A harmony search metaheuristic for the resource-constrained project scheduling problem and its multi-mode version", in F.S. Serifoglu, Ü. Bilge, (Editors), "Project Management and Scheduling 2008", Istanbul, Turkey, 56-59, 2008.

2

G. Csébfalvi, O. Eliezer, B. Láng, R. Levi, "A conflict repairing harmony search metaheuristic and its application for bi-objective resource-constrained project scheduling problems", in F.S. Serifoglu, Ü. Bilge, (Editors), "Project Management and Scheduling 2008", Istanbul, Turkey, 60-63, 2008.

3

B. Láng, "A Hybrid Method for the Resource-Constrained Project Scheduling Problem with Discounted Cash Flows", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the First International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, United Kingdom, paper 2, 2009. doi:10.4203/ccp.92.2

4

G. Csébfalvi, P. Konstantinidis, "A new exact resource balancing procedure for the multiple resource-constrained project scheduling problem", in "Proceedings of APMOD '98", Limasol, Cyprus, 11-13 March, 1998.

5

R. Kolisch, A. Sprecher, "PSPLIB - a project scheduling library", European Journal of Operational Research, 96, 205-216, 1996. doi:10.1016/S0377-2217(96)00170-1

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