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A selfish allocation heuristic in scheduling: Equilibrium and inefficiency bound analysis

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Article
Author/s: 
Jac Braat, Herbert Hamers, Flip Klijn, Marco Slikker
European Journal of Operational Research
Issue number: 
Volume 273, Issue 2, 1 March 2019
Publisher: 
Elsevier
Year: 
2019
Journal pages: 
634-645
For single decision maker optimization problems that lack time efficient algorithms to determine the optimum, there is a need for heuristics. In the context of coordinated production planning, the seminal paper of Graham (1969) provided a performance analysis of heuristics and obtained a bound in relation to the centralized optimum. This paper introduces a framework that includes a performance analysis of a so-called equilibrium heuristic in the setting of multiple decision maker problems. The framework consists of three steps: a heuristic for each player that leads to a strategy profile, the verification that this strategy profile is a Nash equilibrium, and finally a worst case cost analysis to obtain a bound on the performance of the heuristic in terms of the aggregate cost in the obtained Nash equilibrium in relation to the centralized optimum. We implement our general framework in a setting of sequencing situations with selfish agents, multiple identical machines, and the sum of completion times as cost criterion. We provide a tight upper bound for the performance of our equilibrium heuristic. Simulations show that the equilibrium heuristic generally performs much better than the derived tight upper bound. Finally, the relation with the price of anarchy is discussed.
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