A three criteria scheduling problem with two competing agents

Abstract

In this paper we consider the problem of scheduling independent jobs when two customers compete to perform their jobs on a common machine (the workshop). Given that the cost function of the workshop is minimized first, we aim to minimize the cost function of one agent as well, while guaranteeing that the cost function of the other will be kept below or at a threshold. By doing so, both the goal of the workshop and the goals of two competing agents are jointly considered in our model for multiagent scheduling. The cost function of the workshop we are considering includes the total completion time and maximum lateness, whereas for that of the customers we consider a number of cost functions such as the total (weighted) completion time, the number of tardy jobs and total tardiness. For efficient implementation of these problems, polynomial and/or pseudo-polynomial time algorithms are presented with a detailed complexity analysis.