Two Agents Competing for a Shared Machine

Abstract

In this paper we address a deterministic scheduling problem in which two agents compete for the usage of a single machine. The agents submit their tasks in successive steps to an external coordinator, who sequences them according to a known priority rule. We introduce the problem for three different shop configurations, namely when the agents’ parts are transferred to the machine through two distinct linear conveyor belts, when they are transferred through circular conveyor belts, and when parts can be freely picked from the two agents’ buffer. We consider the problem from different perspectives. First, we look at the problem from a centralized point of view as a bicriteria optimization problem and characterize the set of Pareto optimal solutions from the computational complexity perspective. Then, we address the problem from one agent’s point of view. In particular, we propose algorithms suggesting to an agent how to sequence its own tasks in order to optimize its own objective function, regardless of the other agents objectives.