Goal Programming Approach to the Bi-Objective Competitive Flow-Capturing Location-Allocation Problem

Majority of models in location literature are based on assumptions such as point demand, absence of competitors, as well as monopoly in location, products, and services. However in real-world applications, these assumptions are not well-matched with reality. In this study, a new mixed integer nonlinear programming model based on weighted goal programming approach is proposed to maximize the captured demand while minimizing the fixed costs of locating new facilities. To make the proposed model optimization simple, the proposed model is linearized using proper modeling techniques. Although goal programming method does not ensure obtaining Pareto-optimal solutions, solving a numerical example demonstrates the possibility of obtaining Pareto-optimal solutions for the research problem besides higher speed of the classical branch & bound method in obtaining the optimal solution in comparison to the conventional single objective model.