Abstract: In this paper, we develop a bi-criteria approach to solving the competitive location and design problem with elastic demand. The problem involves a new company, its competitor, and its consumers. The competitor has already placed its enterprises. The new company can choose the locations and the design variants for its facilities within the budget. Consumers independently choose service points from the open facilities of the company or competitor based on their preferences. The goal of the new company is to capture the largest possible share of the total demand. This situation is described using a non-linear integer programming model. In real situations, demand data and other parameters may change. In this case, it is necessary to make a decision that would be stable regarding such changes. We consider one of the concepts of robustness and formulate a new bi-criteria statement of the problem under consideration. In addition to the criterion that maximizes the share of the total demand, it also contains a criterion that maximizes the robustness of the solutions obtained. To solve the bi-criteria problem, we propose an algorithm based on a variable neighborhood search and a modified version of the SEMO evolutionary algorithm. The features of the problem and the presence of two criteria are taken into account. Experimental studies have been carried out. The quality of the solutions obtained is analyzed, and a comparison with previous developments is discussed.

Cite: Levanova T.V. , Gnusarev A. , Rubtsova E. , Sigaev V.
Variable Neighborhood Search Approach for the Bi-Criteria Competitive Location and Design Problem with Elastic Demand
22nd International conference "Mathematical Optimization Theory and Operations Research" 02-08 Jul 2023