Zoning Constrained Machine Layout Problem with Mutual Clearances

Abstract

In this paper, a single row machine layout problem is considered with zoning constraints and mutual clearances under an enhanced objective of minimizing material flow cost and machine installation cost. The problem is restricted by positive and negative zoning constraints to represent real life problems. Moreover, clearances needed between machine pairs are divided into two types, which are must and extra clearances, and extra clearances are reduced by mutual use between adjacent machines to decrease material flow costs. Objective function also considers fixed costs of locating machines which usually neglected in machine layout problems in literature but a necessity in real life problems. Two mathematical models are formulated, which are nonlinear and linear mixed integer programs, to solve the problem optimally and to compare the effect of linearity/nonlinearity in mathematical programming formulations in terms of solution quality and time. The mathematical models are not effective in terms of time for large problem instances; therefore, a genetic algorithm is proposed generating high quality solutions in reasonable time. It is shown that the genetic algorithm outperforms both the nonlinear and linear mathematical models with lower cost and shorter time.