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Minimizing the completion time of a project under resource constraints and feeding precedence relations: a Lagrangian relaxation based lower bound

Content Provider	Springer Nature Link
Author	Bianco, Lucio Caramia, Massimilia
Copyright Year	2011
Abstract	In this paper we study the Resource Constrained Project Scheduling Problem (RCPSP) with “Feeding Precedence” (FP) constraints and minimum makespan objective. This problem typically arises in production planning environment, like make-to-order manufacturing, where the effort associated with the execution of an activity is not univocally related to its duration percentage and the traditional finish-to-start precedence constraints or the generalized precedence relations cannot completely represent the overlapping among activities. In this context, we need to introduce in the RCPSP the FP constraints. For this problem we propose a new mathematical formulation and define a lower bound based on the Lagrangian relaxation of the resource constraints. A computational experimentation on randomly generated instances of sizes of up to 100 activities shows a better performance of this lower bound when compared to other lower bounds. Moreover, for the optimally solved instances, its value is very close to the optimal one. Furthermore, in order to show the effectiveness of the proposed lower bound on large instances for which the optimal solution is known, we adapted our approach to solve the benchmarks of the basic RCPSP from the PSLIB with 120 activities.
Starting Page	371
Ending Page	389
Page Count	19
File Format	PDF
ISSN	16194500
Journal	4OR
Volume Number	9
Issue Number	4
e-ISSN	16142411
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-04-20
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	RCPSP Feeding precedence relations Lower bound Lagrangian relaxation Operations Research/Decision Theory Industrial and Production Engineering Optimization
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Management Science and Operations Research Management Information Systems Computational Theory and Mathematics

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