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Solving multi-agent scheduling problems on parallel machines with a global objective function

Published online by Cambridge University Press:  07 March 2014

F. Sadi ,
A. Soukhal  and
J.-C. Billaut
F. Sadi
Affiliation:
UniversitéFrançois-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 avenue Jean Portalis, 37200 Tours, France.. faiza.sadi@univ-tours.fr, ameur.soukhal@univ-tours.fr, jean-charles.billaut@univ-tours.fr
A. Soukhal
Affiliation:
UniversitéFrançois-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 avenue Jean Portalis, 37200 Tours, France.. faiza.sadi@univ-tours.fr, ameur.soukhal@univ-tours.fr, jean-charles.billaut@univ-tours.fr
J.-C. Billaut
Affiliation:
UniversitéFrançois-Rabelais de Tours, CNRS, LI EA 6300, OC ERL CNRS 6305, 64 avenue Jean Portalis, 37200 Tours, France.. faiza.sadi@univ-tours.fr, ameur.soukhal@univ-tours.fr, jean-charles.billaut@univ-tours.fr
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Abstract

In this study, we consider a scheduling environment with m(m ≥ 1) parallel machines. The set of jobs to schedule is divided into K disjoint subsets. Each subset of jobs is associated with one agent. The K agents compete to perform their jobs on common resources. The objective is to find a schedule that minimizes a global objective function f0, while maintaining the regular objective function of each agent, fk, at a level no greater than a fixed value, εk (fk ∈ {fkmax, ∑fk}, k = 0, ..., K). This problem is a multi-agent scheduling problem with a global objective function. In this study, we consider the case with preemption and the case without preemption. If preemption is allowed, we propose a polynomial time algorithm based on a network flow approach for the unrelated parallel machine case. If preemption is not allowed, we propose some general complexity results and develop dynamic programming algorithms.

Keywords

Schedulingmulti-agentcomplexitydynamic programming
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 2: Isco 2012, guest editors Nelson Maculan, A. Ridha Mahjoub, Eduardo Uchoa , April 2014 , pp. 255 - 269
Copyright
© EDP Sciences, ROADEF, SMAI, 2014

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