Bi-objective optimization for multi-floor facility layout problem with fixed inner configuration and room adjacency constraints

The conventional facility layout problem (FLP) is concerned with arranging a number of interacting facilities, such as machines or departments, within a single-floor or multi-floor space to satisfy one or more objectives. In this paper, we devote ourselves to treating a novel bi-objective multi-floor FLP with fixed inner configuration and room adjacency constraints. In our problem, a given number of departments with required areas need to be arranged in a multi-floor building with fixed room configuration and the rooms of the same department should be adjacent to each other. In order to formulate the problem, a bi-objective mixed integer non-linear programming model is first proposed. The objective is to simultaneously minimize the total material handling cost among all the departments and the total occupied room area. The model is then linearized and further improved by determining the lower bound on the number of rooms occupied by each department. With the purpose of obtaining all Pareto optimal solutions, we employ an exact ε-constraint method to solve the model. Computational experiments on a real-life instance and randomly generated instances are conducted to validate the effectiveness of the proposed approach.