Keywords: resource-constrained project scheduling, fuzzy project scheduling, robust scheduling, metaheuristics, hybrid methods, spatial development, water management.

The paper presents a hybrid metaheuristic for the resource-constrained project scheduling problem with fuzzy activity durations that can be applied to the Os-Dráva spatial development program. Spatial developmental programs in Hungary are important to support economically lagging regions. As a result of their nature they can be considered as big projects, with long timescales, high levels of capital, causing significant impact on the targeted fields. For an effective performance, an accurate planning phase is essential. In this paper we concentrate on the project scheduling element of planning, to reduce risk and gain knowledge on the possible, net present value and makespans.

The Os-Dráva program is a water-management based spatial development program. There have been no reference projects like this in Hungary that can support the scheduling of the problem with applicable information. This means that a highly uncertain case is considered with resource constraints implied as well. Our goal is to support the program with an appropriate project scheduling method, resulting in a reliable makespan. For this we present a stochastic programming model and a hybrid metaheuristic for resource constrained project scheduling problems.

The stochastic programming model was presented by Goel and Grossman [1], considering the net present value of subprojects. It is able to build logical predecessor relations based of the returns of subprojects to extend the overall budget of the whole programme. The hybrid metaheuristic was presented by Danka [2] which is a modification of the model developed by Csébfalvi [3]. In the approach presented, it is assumed that each activity duration is considered as a fuzzy variable which, can be described with an appropriate membership function. The heuristic algorithm produces "robust" resource-feasible schedules which are totally immune against uncertainties in the activity durations. The presented hybrid algorithm is based on the "Sounds of Silence" harmony search metaheuristic developed by Csébfalvi et al. [4].

1

V. Goel, I.E. Grossmann, "A Stochastic Programming Approach to Planning of Offshore Gas Field Developments under Uncertainty in Reserves", Computers and Chemical Engineering, 28, 1409-1429, 2004. doi:10.1016/j.compchemeng.2003.10.005

2

S. Danka, "A Hybrid Metaheuristic for the Resource-Constrained Project Scheduling Problem with Fuzzy Activity Durations", in Y. Tsompanakis and B.H.V. Topping, (Editors), "Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 19, 2011. doi:10.4203/ccp.97.19

3

G. Csébfalvi, "Robust Resource-Constrained Project Scheduling with Uncertain Activity Durations", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Seventh International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 94, 2010. doi:10.4203/ccp.94.94

4

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), Proc. on Project Management and Scheduling, Istanbul, Turkey, 56-59, 28-30 April 2008.

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