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

Brucker, Peter; Knust, Sigrid; Schoo, Arno; Thiele, Olaf

doi:10.1016/s0377-2217(97)00335-4

Cited by 248 publications

(130 citation statements)

References 17 publications

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“…Since some project scheduling problems are highly disjunctive, we consider the generation of redundant disjunctive resource constraints as a means to strengthen constraint propagation (see also (Brucker et al, 1997)). The basic idea is simple: if a set S of activities is such that no two activities in S can execute in parallel, a new (artificial) resource of capacity 1 can be created, and all the activities in S can be constrained to require the new resource.…”

Section: Redundant Disjunctive Resource Constraintsmentioning

confidence: 99%

Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems

Baptiste

Papel

1997

Principles and Practice of Constraint Programming-Cp97

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Abstract. In recent years, constraint satisfaction techniques have been successfully applied to "disjunctive" scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in the area of "cumulative" scheduling. Multiple constraint propagation algorithms have been developed for cumulative resources but they tend to be less uniformly effective than their disjunctive counterparts. Different problems in the cumulative scheduling class seem to have different characteristics that make them either easy or hard to solve with a given technique. The aim of this paper is to investigate one particular dimension along which problems differ. Within the cumulative scheduling class, we distinguish between "highly disjunctive" and "highly cumulative" problems: a problem is highly disjunctive when many pairs of activities cannot execute in parallel, e.g., because many activities require more than half of the capacity of a resource; on the contrary, a problem is highly cumulative if many activities can effectively execute in parallel. New constraint propagation and problem decomposition techniques are introduced with this distinction in mind. This includes an O(n 2 ) "edge-finding" algorithm for cumulative resources (where n is the number of activities requiring the same resource) and a problem decomposition scheme which applies well to highly disjunctive project scheduling problems. Experimental results confirm that the impact of these techniques varies from highly disjunctive to highly cumulative problems. In the end, we also propose a refined version of the "edge-finding" algorithm for cumulative resources which, despite its worst case complexity in O(n 3 ), performs very well on highly cumulative instances.

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Section: Redundant Disjunctive Resource Constraintsmentioning

confidence: 99%

Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems

Baptiste

Papel

1997

Principles and Practice of Constraint Programming-Cp97

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“…But note that in practice, they are applied only a couple of times. We refer to Brucker et al (1998) for more details about the four local techniques enumerated below:…”

Section: Local Constraint Propagationmentioning

confidence: 99%

“…Other relations are deduced considering an additional activity l related to such a symmetric triple i j k . We have implemented the O m 2 n 4 algorithm proposed by Brucker et al (1998).…”

Section: Local Constraint Propagationmentioning

confidence: 99%

“…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%

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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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“…A solution to RCSP can be sought through a number of possible methodologies. A very common approach is to utilize implicit enumeration and backtracking (the methods used by most commercially available exact solvers) such as branch and bound methods, as proposed in Brucker and Knust [2], *Address correspondence to this author at the Department of Civil and Environmental Engineering, University of Cyprus, Nicosia 1678, Cyprus; Tel: +357-22892270; Fax: +357-22892295; E-mails: SCHRISTO@UCY.AC.CY or SC163@HOTMAIL.COM Demeulemeester and Herroelen [3], Mingozzi et al [4], Crawford [5], and Garey et al [6]. Other methods utilize intelligent branching and evaluation techniques such as mathematical programming [7], dynamic programming [8], zero-one programming [9], or artificial agent techniques such as genetic algorithms [10] and ant colony optimization [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Activity Prioritization Under Resource Constraints Using a Utility Index Method

Aslani¹,

Christodoulou²,

Griffis³

et al. 2009

TOBCTJ

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Abstract:Resource availability constraints are a typical real-life construction scheduling problem; a problem that limits a constructor's ability to execute and deliver a project as originally planned. It is, thus, imperative that developed project schedules should have not only well-thought project logic networks (successor/predecessor information and activity durations) but also resource assignments (including cost) for each activity in the network so that the effects of resource constraints can effectively be accounted for. The paper presents a new approach to resource-constrained scheduling that allows for activity prioritization when a project is subject to limited resources. The methodology proposed is based on a utility index, hereby defined as the ratio of the number of required resources for a specific activity to the total number of required resources among competing activities. A dynamic programming technique is adopted to maximize the utility value for each activity so that the resource allocation among competing activities, as suggested by the method, results in the minimum overall project duration.

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

Cited by 248 publications

References 17 publications

Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems

Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems

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

Activity Prioritization Under Resource Constraints Using a Utility Index Method

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