A simple and effective exact method for the medianoid problem with multipurpose trips
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Springer
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We study the medianoid problem with multipurpose trips, a discrete facility location problem set in a static competitive environment where a new firm enters the market. Unlike traditional competitive facility location problems, we consider customers’ multipurpose trips to various facilities for different products, integrating location and routing decisions. To model the problem, we propose a bilevel formulation involving one leader and multiple followers. In this framework, the entering firm acts as the leader, seeking to maximize its benefit, while customers are positioned as followers, aiming to minimize the distance of their multipurpose purchasing tours to fulfill demands for several products at different locations. By leveraging the structure of the model, we demonstrate that the bilevel formulation can be efficiently solved through an equivalent reformulation based on the maximal covering location problem. To validate our approach, we created new datasets and conducted an extensive computational study. From the results, we highlight the number of stops made by customers to demonstrate the significance of our study. Additionally, we parallelized the follower’s problem to assess its effectiveness in reducing computational time. The results show that instances of practical size, previously addressed with metaheuristics, can now be solved to proven optimality within reasonable computing times while allowing multiple stops along their routes. © 2025 Elsevier B.V., All rights reserved.
Palabras clave
Bilevel optimization, Competitive facility location, Maximal covering location problem, Medianoid problem, Traveling purchaser problem, Facilities, Sales, Bi-level optimization, Bilevel, Competitive facility location, Covering location problems, Exact methods, Facility location problem, Maximal covering location problem, Medianoid problem, Simple++, Traveling purchaser problem, Location