Mathematical modeling and multi-start search simulated annealing for unequal-area facility layout problem

In this paper, a mixed integer nonlinear programming model (MINLP) is formulated to allocate the position of a number of unequal-area rectangular facilities within the continuum of a planar plant site with a predetermined fixed area. Facilities have predetermined dimensions and are not orientation-free. A continuous approach to the problem is taken. Constraints are developed to eliminate the possible overlap between the different facilities. The model accommodates for aisles, whether vertical or horizontal, as well as blocks and preference locations, where no facilities are allowed to be placed. The problem seeks to minimize total material handling the cost. Four test cases including one from the local industry is used to justify the developed model. The problem at hand is computationally intractable; hence, a novel Simulated Annealing (SA) algorithm is developed to solve large instances of the problem. A unique heuristic algorithm is used for initialization. A multi-start search mechanism is implemented to increase the diversity and mitigate the chances of getting entrapped in local optima. For validation, a group of benchmark problems is being used.