Balancing the Average Weighted Completion Times in Large-Scale Two-Agent Scheduling Problems: An Evolutionary-Type Computational Study

Abstract

The problem of balancing the average weighted completion times of two classes of jobs is an NP-hard scheduling problem that was very recently introduced in the literature. Interpreted as a cooperative-type two-agent single-machine problem, its applications are in various practical contexts such as in logistics for balancing the delivery times, in manufacturing for balancing the assembly lines and in services for balancing the waiting times of groups of people. The only solution technique currently existing in the literature is a Lagrangian heuristic, based on solving a finite number of successive linear assignment problems, whose dimension depends on the total number of jobs. Since the Lagrangian approach has not appeared to be particularly suitable for solving large-scale problems, to overcome this drawback, we propose to face the problem by means of a genetic algorithm. Differently from the Lagrangian heuristic, our approach is found to be effective also for large instances (up to 2000 jobs), as confirmed by numerical experiments.