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

This paper presents a hybrid method for the resource-constrained project scheduling problem with hammock activities and strip packing like resource constraints. Hammock activities are used to fill the time span between other "normal" activities since their duration cannot be calculated or estimated at the initial stage of project planning. In the proposed model, a resource-constrained project is characterized by its "best" schedule, where best means a makespan minimal resource-constrained schedule with dedicated resource demand servicing for which the total hammock cost is minimal and the resource profiles approach the ideal rectangular shape as much as possible. The algorithm is an improved conflict repairing version of the "Sounds of Silence" harmony search metaheuristic developed by Csébfalvi et al. [1,2,3] and Eliezer and Csébfalvi [4]. In the improved algorithm the harmony search is combined with a resource leveling-assigning procedure based on a mixed integer linear programming (MILP) formulation developed by Csébfalvi and Konstantinidis [3]. 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 hammock members from the popular PSPLIB [5] benchmark set.

1

G. Csébfalvi, A. Csébfalvi, "Hammock Activities in Project Scheduling", in S. Panwalkar, J. Li, (Editors), "Proceedings of the Sixteenth Annual Conference of POMS", POMS, USA, 2005. URL

2

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.

3

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.

4

O. Eliezer, G. Csébfalvi, "A Hybrid Method for the Resource-Constrained Project Scheduling Problem with Hammock Activities", 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 1, 2009. doi:10.4203/ccp.92.1

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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