Non-disjoint Multi-agent Scheduling Problem on Identical Parallel Processors

  • F. Sadi
  • T. Van Ut
  • N. Huynh Tuong
  • A. SoukhalEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10018)


Scheduling problems in which agents (users, customers, application masters, resource manager, etc.) have to share the same set(s) of resources are at the frontier of combinatorial optimization and cooperative game theory. This paper deals with scheduling problems arising when two agents, each with a set of nonpreemptive jobs, compete to perform their respective jobs on two common identical parallel machines. Each agent aims at minimizing a certain objective function that depends on the completion times of its jobs only. The objective functions we consider in our study are makespan and number of tardy jobs. The agents may share some jobs and this problem is called non-disjoint multi-agent scheduling problem [3]. Finding the optimal solution for one agent with a constraint on the other agent’s cost function is known to be \(\mathcal {NP}\)-hard. To obtain best compromise solutions for each agent, we propose polynomial and pseudo-polynomial heuristics. Two mixed integer linear programming models are developed to calculate exact non-dominated solutions. Experimental results are conducted to measure the solutions quality given by heuristics.


Multicriteria optimization Multiagent scheduling Parallel processors Heuristics Dynamic programming Linear mathematical programming 



This research was partially funded by the European Union through the Erasmus STA program.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • F. Sadi
    • 1
    • 2
  • T. Van Ut
    • 1
    • 3
  • N. Huynh Tuong
    • 4
  • A. Soukhal
    • 1
    Email author
  1. 1.Laboratory of Computer Science (EA 6300), Team Recherche Opérationnelle, Ordonnacement et Transport ROOT ERL-CNRS 6305)Université François Rabelais ToursFrance
  2. 2.INSA Centre Val de LoireBloisFrance
  3. 3.Can Tho University of Technology (CTUT)Can Tho CityVietnam
  4. 4.Faculty of Computer Science and EngineeringHo Chi Minh City University of TechnologyHo Chi Minh CityVietnam

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