Development of a multi-objective optimization model for unequal area facility layout problem

Abstract

Facility layout problem is one of the most fundamental optimization problems encountered in today’s world since layout affects the overall operating efficiency of an organization. From the beginning of the facility layout literature, it has been a common trend to assume that the departments of a facility are of equal areas. But in reality departments are mostly unequal areas. Again, the earlier facility layout models considered only material transportation cost in designing optimal facility layout. Again, few recent works considered closeness preferences between the departments along with material handling cost in unequal-area facility layout model development. But one most important factor for customer satisfaction is makespan of the layout which was not taken in consideration. In this thesis work, three most important criteria in designing optimal facility layout has been considered which are material transportation cost, closeness rating score and makespan of the total layout. This multi-objective facility layout model has been developed for an unequal area facility layout problem. The goal of this thesis work is to determine the optimal arrangement as well as the optimal dimension of the departments by minimizing the material transportation cost, minimizing the makespan of the overall system and maximizing the total closeness rating score simultaneously. The constraint equations have been developed for non-overlapping of the departments, bounding the departments within the facility, department area constraints and aspect ratio constraints. Two suitable optimization algorithms: spatial branch and bound algorithm (sBB) and slicing tree structure embedded random weighted genetic algorithm (RWGA) are employed to optimize the constrained multi-objective mixed-integer nonlinear model. Two numerical examples and their solutions are then provided to have a better understanding about the demonstration of the proposed model. Finally sensitivity analysis is also carried out to have better insights about the model developed. It is found that, solutions found from both methods are pareto optimal and the proposed RWGA performs better in providing wide range of trade-off solutions. This model helps in developing an efficient layout for a facility by making a trade-off among material handling cost, closeness rating score and makespan.