Lower Bounds for Resource Constrained Project Scheduling Problem

Néron, Emmanuel; Artigues, Christian; Baptiste, Philippe; Carlier, Jacques; Damay, Jean; Demassey, Sophie; Laborie, Philippe

doi:10.1007/978-0-387-33768-5_7

Cited by 13 publications

(16 citation statements)

References 34 publications

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“…There is a large number of publications devoted to the discussion on lower bounds for RCPSP. Recent comprehensive reviews can be found in Neron et al (2006) and Knust (2015) . The analysis of the computational complexity of some algorithms and the quality of the obtained bounds are discussed in Gafarov, Lazarev, and Werner (2010) .…”

Section: Previous Researchmentioning

confidence: 99%

“…In the literature, a number of algorithms to calculate lower bounds on the makespan were proposed. Their overview is presented in Section 2 , more details can be found in the following comprehensive surveys ( Neron et al, 2006 ) and ( Knust, 2015 ). In this paper, a novel pseudo-polynomial algorithm is developed which extends the relaxation of RCPSP to a Cumulative Scheduling Problem by considering pairs of resources.…”

Section: Introductionmentioning

confidence: 99%

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An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

Arkhipov

Battaïa

Lazarev

2019

European Journal of Operational Research

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Several algorithms for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem (RCPSP) were proposed in the literature. However, fast computable lower bounds usually do not provide the best estimations and the methods that obtain better bounds are mainly based on the cooperation between linear and constraint programming and therefore are time-consuming. In this paper, a new pseudo-polynomial algorithm is proposed to find a makespan lower bound for RCPSP with time-dependent resource capacities. Its idea is based on a consecutive evaluation of pairs of resources and their cumulated workload. Using the proposed algorithm, several bounds for the PSPLIB benchmark were improved. The results for industrial applications are also presented where the algorithm could provide good bounds even for very large problem instances.

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Section: Previous Researchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

Arkhipov

Battaïa

Lazarev

2019

European Journal of Operational Research

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“…Event-based formulations are presented in Koné et al [124] where also a computational comparison of different formulations can be found. Linear programming based lower bounds are also surveyed in Néron et al [150] and computationally tested in Demassey et al [53]. Project scheduling problems with labor constraints are, for example, studied in Drezet and Billaut [71] and Brucker et al [39].…”

Section: Reference Notesmentioning

confidence: 99%

Complex Scheduling

Brucker

Knust

2012

118

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In this revised edition some errors were corrected, some parts were explained in more detail, and new material has been added. In particular, further generalizations of the RCPSP, additional practical applications and some more algorithms were integrated.Since in recent years commercial and non-commercial solvers for mixed integer linear programs or satisfiability problems became much more efficient, they may be a good alternative for calculating exact (or heuristic) solutions. Hence, we provided new sections on MIP formulations and a SAT formulation for the RCPSP. Furthermore, a description of ant colony optimization was added to the section on heuristic methods for solving the RCPSP. The section on lower bounds was augmented by bounds based on Lagrangian relaxation. In connection with the new methods for solving the RCPSP, basic concepts for SAT solvers, Lagrangian relaxation, and ant colony optimization have been added to Chapter 2. We also wrote a new basic section on constraint programming.Since in the first edition in the section on constraint propagation for the RCPSP the input-or-output test was incorrect, we corrected it in this edition.A list of errata according to the book can be found at the website Preface Scheduling problems have been investigated since the late fifties. Two types of applications have mainly motivated research in this area: project planning and machine scheduling. While in machine scheduling a large number of specific scheduling situations depending on the machine environment and the job characteristics have been considered, the early work in project planning investigated scheduling situations with precedence constraints between activities assuming that sufficient resources are available to perform the activities. More recently, in project scheduling scarce resources have been taken into account leading to so-called resource-constrained project scheduling problems. On the other hand, also in machine scheduling more general and complex problems have been investigated. Due to these developments today both areas are much closer to each other. Furthermore, applications like timetabling, rostering or industrial scheduling are connected to both areas.This book deals with such complex scheduling problems and methods to solve them. It consists of three parts: The first part (Chapters 1 and 2) contains a description of basic scheduling models with applications and an introduction into discrete optimization (covering complexity, shortest path algorithms, linear programming, network flow algorithms and general optimization methods). In the second part (Chapter 3) resource-constrained project scheduling problems are considered. Especially, methods like constraint propagation, branch-andbound algorithms and heuristic procedures are described. Furthermore, lower bounds and general objective functions are discussed. In the last part (Chapter 4) generalizations of the job-shop problem are covered leading to applications like job-shop problems with flexible machines, transport robots or with limited...

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“…Reviews of different methods can be found in [2], [5]. For example, mixed integer linear programming [8], as well as branch and bound algorithms [9], have been applied. Some of these algorithms have been extended to the multi-mode case [11].…”

Section: Related Workmentioning

confidence: 99%

Multi-robot task scheduling

Zhang

Parker

2013

2013 IEEE International Conference on Robotics and Automation

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Abstract-The scheduling problem has been studied extensively in the literature. Many algorithms have been developed to operate with different types of processors and tasks. In the robotics domain, when considering each robot as a processor, some of these algorithms can be directly adapted. However, most of the existing algorithms can only handle single-robot tasks, or multi-robot tasks that can be divided into singlerobot tasks. As the task requirements may only be partially known, and the available (heterogeneous) robots can dynamically change, robots may be required to cooperate tightly to share different capabilities (i.e., sensors and motors). In such cases, considering scheduling for individual robots is no longer sufficient, since the robots need to work at the coalition level. Although there exist a few algorithms that also support these more complex cases, they do not represent efficient solutions that can be adapted by various multi-robot systems in a convenient manner. In this paper, we propose heuristics to address the multi-robot task scheduling problem at the coalition level, which hides the details of robot specifications, thus allowing these heuristics to be incorporated straightforwardly. These heuristics are easy to implement and efficient enough to run in real time. We provide formal analyses and simulation results to demonstrate and compare their performances.

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Lower Bounds for Resource Constrained Project Scheduling Problem

Cited by 13 publications

References 34 publications

An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

Complex Scheduling

Multi-robot task scheduling

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