A branch-and-bound algorithm for the resource-constrained project scheduling problem

Dorndorf, Ulrich; Pesch, Erwin; Phan‐Huy, Toàn

doi:10.1007/s001860000091

Cited by 68 publications

(32 citation statements)

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“…Our implementation of SSTS is inspired by one described in [Godard et al, 2005]. It can be seen as a serial scheduling schema [Kolisch, 1996], which branches the search on the possible earliest start times [Dorndorf et al, 2000]. A recursive and non deterministic version of the solver is shown in Fig.…”

Section: Sst Search (Ssts)mentioning

confidence: 99%

Iterative flattening search for resource constrained scheduling

et al. 2008

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Iterative Flattening Search (IFS) is a meta-heuristic strategy for solving multi-capacity scheduling problems. Given an initial solution, IFS iteratively applies: (1) a relaxationstep, in which a subset of scheduling decisions are randomly retracted from the current solution; and (2) a flattening-step, in which a new solution is incrementally recomputed from this partial schedule. Whenever a better solution is found, it is retained, and, upon termination, the best solution found during the search is returned. Prior research has shown IFS to be an effective and scalable heuristic procedure for minimizing schedule makespan in multi-capacity resource settings.In this paper we experimentally investigate the impact on IFS performance of algorithmic variants of the flattening step. The variants considered are distinguished by different computational requirements and correspondingly vary in the type and depth of search performed. The analysis is centered around the idea that given a time bound to the overall optimization procedure, the IFS optimization process is driven by two different and contrasting mechanisms: the random sampling performed by iteratively applying the "relaxation/flattening" cycle and the search conducted within the Stephen F. Smith The Robotics Institute, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA E-mail: sfs@cs.cmu.edu constituent flattening procedure. On one hand, one might expect that efficiency of the flattening process is key: the faster the flattening procedure, the greater the number of iterations (and number of sampled solutions) for a given time bound; and hence the greater the probability of finding better quality solutions. On the other hand, the use of more accurate (and more costly) flattening procedures can increase the probability of obtaining better quality solutions even if their greater computational cost reduces the number of IFS iterations. Comparative results on well-studied benchmark problems are presented that clarify this tradeoff with respect to previously proposed flattening strategies, identify qualitative guidelines for the design of effective IFS procedures, and suggest some new directions for future work in this area.

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Section: Sst Search (Ssts)mentioning

confidence: 99%

Iterative flattening search for resource constrained scheduling

et al. 2008

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“…Being strongly NP hard, the exact resolution of this problem has most often been tackled by branch-andbound procedures; see, e.g., Baptiste and Le Pape (2000), Brucker et al (1998), Demeulemeester and Herroelen (1997), Dorndorf et al (2000), Mingozzi et al (1998), andSprecher (2000). Consequently, some research focuses on the computation of good lower bounds.…”

Section: Introductionmentioning

confidence: 99%

“…In a second category, we can group together constraint-programming-based lower bounds like the ones proposed by Klein and Scholl (1999), Caseau and Laburthe (1996), Baptiste and Le Pape (2000), or Dorndorf et al (2000). In fact, among all these authors, Klein and Scholl are the only ones actually to compute a lower bound of the optimal makespan.…”

Section: Introductionmentioning

confidence: 99%

Constraint-Propagation-Based Cutting Planes: An Application to the Resource-Constrained Project Scheduling Problem

Demassey

Artigues

Michelon

2005

INFORMS Journal on Computing

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W e propose a cooperation method between constraint programming and integer programming to compute lower bounds for the resource-constrained project scheduling problem (RCPSP). The lower bounds are evaluated through linear-programming (LP) relaxations of two different integer linear formulations. Efficient resource-constraint propagation algorithms serve as a preprocessing technique for these relaxations. The originality of our approach is to use additionally some deductions performed by constraint propagation, and particularly by the shaving technique, to derive new cutting planes that strengthen the linear programs. Such new valid linear inequalities are given in this paper, as well as a computational analysis of our approach. Through this analysis, we also compare the two considered linear formulations for the RCPSP and confirm the efficiency of lower bounds computed in a destructive way.

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“…Other MILP models were proposed later on by AlvarezValdes and Tamarit [8], Mingozzi et al [217], Artigues et al [15], and Koné et al [178], but they appear to have mainly theoretical interests as the results they exhibit when solved through MILP solvers tend to be worse than those obtained by DT and DDT (see Koné et al [178]). Among the exact approaches that were tried to solve the RCPSP, we cite branch-and-bound algorithms (see, e.g., Demeulemeester and Herroelen [102,103], Brucker et al [47], Klein and Scholl [175], and Sprecher [265]), and constraint programming (CP) approaches (see, e.g., Dorndorf et al [105], Laborie [183], Liess and Michelon [189], and Schutt et al [253]). …”

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confidence: 99%

Mathematical models and decomposition algorithms for cutting and packing problems

Delorme¹

2017

4OR-Q J Oper Res

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A branch-and-bound algorithm for the resource-constrained project scheduling problem

Cited by 68 publications

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Iterative flattening search for resource constrained scheduling

Iterative flattening search for resource constrained scheduling

Constraint-Propagation-Based Cutting Planes: An Application to the Resource-Constrained Project Scheduling Problem

Mathematical models and decomposition algorithms for cutting and packing problems

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