Maximization of Profit for a Problem of Location and Routing, with Price-sensitive Demands

This article seeks to study and solve a problem of profit maximization of a company by defining the location of an optimal number of facilities, allocation and routing of vehicles, and costs for home delivery to meet the demand of its customers. This study is based on an article in which, for the first time, a problem of location and routing and maximization of utilities with price-sensitive demands is integrated. This problem, unlike other studies that only minimize other metrics such as waiting times, route distances, and transportation costs, seeks a greater benefit by increasing profits by discriminating prices depending on the customer's location or adding an additional cost to retail sales. This paper presents a model for small instances based on the model proposed in the aforementioned article. Next, a two-phase heuristic is proposed that solves larger instances with a result close to that obtained in the previous article where a branch-and-price heuristic was used.