An automated negotiation approach to solve single machine scheduling problems with interfering job sets

Abstract

In this paper, we propose a decentralized approach to solve multiple-criteria single machine scheduling problems. We consider a single machine that is utilized by two agents where each of them has its own jobs and a private objective. The objective function of the first agent is the total completion time or the total weighted completion time of its jobs, respectively, whereas the objective function of the second agent is the maximum lateness or the total weighted completion time of its jobs. The problem is motivated by scheduling problems found in semiconductor manufacturing. An automated negotiation mechanism is presented to solve the scheduling problems. The basic ingredient of the mechanism is a mediator that proposes contracts using a variable neighborhood search (VNS) technique. We study the behavior of both greedy and cooperative agents. In addition, a hybrid strategy is developed where the mediator accepts deteriorations of the objective values with a certain probability. The performance of the negotiation schemes is assessed using randomly generated problem instances. It turns out that the solutions determined by the negotiation mechanism are close to the Pareto frontier from a centralized approach with full information. We use a problem-specific Non-Dominated Sorting Genetic Algorithm (NSGA)-II scheme to determine the solutions on the Pareto frontier. It is shown that the degree of cooperation of the two agents depends on the objective function used.