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

Abstract

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.