The Cooperative Maximal Covering Location Problem with ordered partial attractions Articles uri icon

authors

  • Domínguez, Concepción
  • GAZQUEZ TORRES, RICARDO
  • Morales, Juan Miguel
  • Pineda, Salvador

publication date

  • October 2024

start page

  • 106782

volume

  • 170

International Standard Serial Number (ISSN)

  • 0305-0548

Electronic International Standard Serial Number (EISSN)

  • 1873-765X

abstract

  • The Maximal Covering Location Problem (MCLP) is a classical location problem where a company maximizes the demand covered by placing a given number of facilities, and each demand node is covered if the closest facility is within a predetermined radius. In the cooperative version of the problem (CMCLP), it is assumed that the facilities of the decision maker act cooperatively to increase the customers' attraction towards the company. In this sense, a demand node is covered if the aggregated partial attractions (or partial coverings) of open facilities exceed a threshold. In this work, we generalize the CMCLP introducing an Ordered Median function (OMf), a function that assigns importance weights to the sorted partial attractions of each customer and then aggregates the weighted attractions to provide the total level of attraction. We name this problem the Ordered Cooperative Maximum Covering Location Problem (OCMCLP). The OMf serves as a means to compute the total attraction of each customer to the company as an aggregation of ordered partial attractions and constitutes a unifying framework for CMCLP models. We introduce a multiperiod stochastic non-linear formulation for the CMCLP with an embedded assignment problem characterizing the ordered cooperative covering. For this model, two exact solution approaches are presented: a MILP reformulation with valid inequalities and an effective approach based on Generalized Benders' cuts. Extensive computational experiments are provided to test our results with randomly generated data and the problem is illustrated with a case study of locating charging stations for electric vehicles in the city of Trois-Rivières, Québec (Canada).

subjects

  • Mathematics
  • Statistics

keywords

  • maximal covering; cooperative cover; facility location; ordered median function; mixed-integer optimization; benders decomposition