Abstract
This chapter reports on a new solution approach for the multi-mode resource-constrained project scheduling problem (MRCPSP, MPS | prec | C max ). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and nonrenewable) resource-feasible project schedule with a minimal makespan. The problem type is known to be \(\mathcal{N}\mathcal{P}\)-hard and has been solved using various exact as well as (meta-)heuristic procedures. The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean nonrenewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.
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Notes
- 1.
In general, a constraint \(y_{1} + y_{2} +\ldots +y_{n} = 1\) can be represented in the CNF as \((y_{1} \vee y_{2} \vee \ldots \vee y_{n}) \wedge (\overline{y_{1}} \vee \overline{y_{2}}) \wedge \ldots \wedge (\overline{y_{1}} \vee \overline{y_{n}}) \wedge (\overline{y_{2}} \vee \overline{y_{3}}) \wedge \ldots \wedge (\overline{y_{n-1}} \vee \overline{y_{n}})\).
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Coelho, J., Vanhoucke, M. (2015). The Multi-Mode Resource-Constrained Project Scheduling Problem. In: Schwindt, C., Zimmermann, J. (eds) Handbook on Project Management and Scheduling Vol.1. International Handbooks on Information Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-05443-8_22
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