Finding Pure Nash Equilibrium for the Resource-Constrained Project Scheduling Problem

Guillermo De Ita Luna, Fernando Zacarias-Flores and L. Carlos Altamirano-Robles

Computer Science Department, Autonomous University of Puebla (BUAP), México. deita@cs.buap.mx, altamirano@cs.buap.mx, fzflores@yahoo.com.mx

Corresponding author is Fernando Zacarias-Flores.

Abstract

The paper focuses on solving the Resource-Constrained Project Scheduling (RCPS) problem with a method based on intelligent agents. Parallelism for performing the tasks is allowed. Common and limited resources are available to all agents. The agents are non-cooperative and compete with each other for the use of common resources, thereby forming instances of RCPS problem. We analyze the global joint interaction of scheduling via a congestion network and seek to arrive at stable assignments of scheduling. For this class of network, stable assignments of scheduling correspond to a pure Nash equilibrium, and we show that in this case there is a guarantee of obtaining a pure Nash equilibrium in polynomial time complexity. The pure Nash equilibrium point for this congestion network will be a local optimum in the neighborhood structure of the projects, where no project can improve its completion time without negatively affecting the completion time of the total system. In our case, each state of the neighborhood represents an instance of the RCPS problem, and for solving such problem, we apply a novel greedy heuristic. It has a polynomial time complexity and works similar to the well-knowing heuristic NEH.

Keywords: Intelligent agents, congestion network, pure Nash equilibrium, RCPS problem, multi-scheduling, greedy heuristic NEH.

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