Location-routing in competition environment using game theory

Competitive advantage in features, number of branches, or location of any company enables it to provide better services to cus- tomers than competitors. In this article, the issue of location in a situation where competitors can decide based on competitor conditions to maximize their profits is examined. First, based on the conditions and characteristics of each competitor, including the number of branches and budget limit, the performance range of each competitor is determined as the radius of effect. Two mathematical formulas are presented for the player and using the concepts of game theory, each player's market share in the competitive environment is determined to earn maximum profit. To solve the problem, first, the initial answers were obtained through the ant colony algorithm, then these answers were entered as input to the Simulated Annealing algorithm, which has a high speed to obtain the answer. The models developed for the two supermarkets have been evaluated and the results have been approved by experts.