Max-Min Probabilistic Algorithms for Parallel Machines

Abstract

This paper treats the maximization of the minimum completion time regarding the identical parallel machines problem. This problem is well known as follows. Our work concerns with industry field, when we have several identical and parallel machines and we have faced to many different jobs. The problem is how to find an appropriate solution that gives us a method to schedule the different jobs on the given machines. The objective function is the maximization of machine completion time which has the minimum time comparing with all other machines. This problem is shown as NP-hard. We propose some algorithms that give approximate solutions to the studied problem. Several instances were tested in this paper to show the performance of the proposed approximate solutions.