Multiple objective programming for the quadratic assignment problem

Abstract

In this paper, we formulate the quadratic assignment problem through multiple objective programming in which we can have several objectives. In the facility layout problem, the objectives can be materials handling cost, production rate, and flexibility. We define efficiency and describe how efficient alternatives can be generated. A heuristic procedure based on pairwise exchange of subfacilities is developed to generate the efficient solution associated with a given set of objective weights. Our approach could just as easily implement the graph theoretic or other approaches to solve the quadratic assignment problem and generate efficient points associated with given weights. A paired comparison method based on the strength of preference among alternatives is developed. The paired comparison method generates the decision maker's weights of an assumed unknown utility function. The method asks simple questions and uses linear programming to solve the problem. An experiment with the developed computer package is discussed. Some examples are provided for solving the facility layout problem.