The Multi-Mode Resource-Constrained Project Scheduling Problem

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 non-renewable) resource-feasible project schedule with a minimal makespan. The problem type is known to be N 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 resourceconstrained 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 non-renewable 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.

Mathematical models and decomposition algorithms for cutting and packing problems

“…Based on the idea proposed by Coelho and Vanhoucke [70], we decompose the MM-RCPSP into two phases: first, we solve a b-DTCTP (with one constraint (8.32) for each non-renewable resource) that fixes the modes selected for the tasks and gives a lower bound ES(n + 1) for the project makespan. At a second stage, we solve a RCPSP with a fixed deadline LS(n + 1) = ES(n + 1) and the modes selected at the first stage.…”

“…We mention in addition the work by Coelho and Vanhoucke [70] that solves heuristically the MMRCPSP by decomposing it into successions of two phases: a mode selection step (b-DTCTP) and a task scheduling step (RCPSP).…”

Bi-objective optimization of a multi-mode, multi-site resource-constrained project scheduling problem

“…The rise in the study of the MRCPSP leads to many variants on the topic with different problem features resulting from various assumptions on activities, resources, dependencies, objective functions, time management and solution methods. Many research studies carried out studies on the standard MRCPSP, such as Słowiński (1980), Elloumi and Fortemps (2010), Coelho and Vanhoucke (2011, 2015), Van Peteghem and Vanhoucke (2011, 2014) and Chakrabortty et al (2020).…”

Optimizing Shipbuilding Production Project Scheduling Under Resource Constraints Using Genetic Algorithms and Fuzzy Sets

“…developed a hybrid GA with a fuzzy logic controller Hindi et al (2002). incorporated a crossover strategy related to the maintenance of order Coelho & Tavares (2003). introduced a new crossover operator and activity representation Valls et al (2004).…”