Nash equilibria for the multi-agent project scheduling problem with controllable processing times

Alessandro Agnetis (1) , Cyril Briand (2) , Jean-Charles Billaut (3) , Přemysl Sůcha (4)

1 UNISI - Università degli Studi di Siena = University of Siena
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
3 LIFAT - Laboratoire d'Informatique Fondamentale et Appliquée de Tours
4 CAK - Centre for Applied Cybernetics

This paper considers a project scheduling environment in which the activities of the project network are partitioned among a set of agents. Activity durations are controllable, i.e., every agent is allowed to shorten the duration of its activities, incurring a crashing cost. If the project makespan is reduced with respect to its normal value, a reward is offered to the agents and each agent receives a given ratio of the total reward. Agents want to maximize their profit. Assuming a complete knowledge of the agents' parameters and of the activity network, this problem is modeled as a non-cooperative game and Nash equilibria are analyzed. We characterize Nash equilibria in terms of the existence of certain types of cuts on the project network. We show that finding one Nash equilibrium is easy, while finding a Nash strategy that minimizes the project makespan is NP-hard in the strong sense. The particular case where each activity belongs to a different agent 1 is also studied and some polynomial-time algorithms are proposed for this case.

Mots clés: multi-agent project scheduling; Nash equilibria; flow networks

Domaines: Recherche opérationnelle [math.OC]

Alessandro Agnetis, Cyril Briand, Jean-Charles Billaut, Přemysl Sůcha. Nash equilibria for the multi-agent project scheduling problem with controllable processing times. Journal of Scheduling, 2015, 18 (1), pp.15-27. ⟨10.1007/s10951-014-0393-x⟩. ⟨hal-01231028⟩