Development of an Optimization Model for Unequal-Area Facility Layout Problems

Optimisation of unequal-area facility layout problems (UA-FLPs) aims to find the optimal arrangement of a given number of non-overlapping departments having unequal area requirements within the facility premises. This paper studies a multi-objective UA-FLP that considers minimising the material transportation cost, maximising the closeness rating score and minimising makespan of the overall facility in developing the layout. We develop a mixed-integer nonlinear programming (MINLP) facility layout model and optimise using a reformulation-based spatial branch-and-bound algorithm. Constraints are developed to ensure non-overlapping of the departments, bounding the departments within the facility, nonlinear expression of required area, and aspect ratio. We reformulate the non-smooth functions of the original model by the smooth ones. The solution of our model provides optimal arrangements as well optimal dimensions of the departments within the facility. Additionally, our model provides a set of Pareto-optimal layouts that enable decision makers in selecting a layout depending on different real-world scenarios.