A Multi-Agent system to solve a new formulation of machine layout problem

Abstract

This paper focuses on the machine arrangement problem on common loop network. The machines are arranged in a cycle and materials transported in only one direction around the cycle using a conveyor belt. The goal of this problem is to minimize the maximum number of loops required for the manufacture of any of the products. The problem is known to be NP-hard. Thus, the right way to proceed is through the use of heuristics techniques. However, the industrial managers complain about an issue which is the mishandling of large variables and constraints that led to a lack of realism. In this work, we introduce a new formulation for the machine layout problem by adding new constraints which are the machine dimensions and the proximity constraints between the machines. This new formulation led us to propose two-stage approach to solve this problem. The first step consists on positioning the machines on a grid while respecting the proximity constraints and machines dimensions. The second step aim to optimize the path between these machines already positioned in order to minimize number of the loops traveled by parts. In this paper, we are interested in the first step by using multi-agent system. This choice can be explained by the well-known cooperation of the multi-agent system. The effectiveness of our approaches is demonstrated through numerical examples.