Solving multi-agent scheduling problems on parallel machines with a global objective function
RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 2, pp. 255-269.

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 f 0, while maintaining the regular objective function of each agent, f k, 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.

DOI : 10.1051/ro/2014005
Classification : 90C39
Mots-clés : scheduling, multi-agent, complexity, dynamic programming 
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     author = {Sadi, F. and Soukhal, A. and Billaut, J.-C.},
     title = {Solving multi-agent scheduling problems on parallel machines with a global objective function},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {255--269},
     publisher = {EDP-Sciences},
     volume = {48},
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     mrnumber = {3264378},
     zbl = {1295.90012},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2014005/}
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Sadi, F.; Soukhal, A.; Billaut, J.-C. Solving multi-agent scheduling problems on parallel machines with a global objective function. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 2, pp. 255-269. doi : 10.1051/ro/2014005. http://archive.numdam.org/articles/10.1051/ro/2014005/

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