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P-facility capacitated location problem with customer-equilibrium decisions: a recreational case study in Mazandaran province

Mehdi Zaferanieh (Department of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran)
Mahmood Sadra (Department of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran)
Toktam Basirat (Department of Mathematics and Computer Science, Hakim Sabzevari University, Sabzevar, Iran)

Journal of Modelling in Management

ISSN: 1746-5664

Article publication date: 27 May 2024

Issue publication date: 26 November 2024

33

Abstract

Purpose

This paper aims to propose a bi-level mixed integer linear location-allocation problem. The upper-level objective function is dedicated to minimizing the total distances covered by customers to meet the p-selected facilities and the fixed cost values for establishing these facilities. While in the lower level, a customer preference function evaluates the priority of customers in selecting facilities.

Design/methodology/approach

The solution approach to the proposed model uses the Karush–Kuhn–Tucker (KKT) optimality conditions to the lower-level problem where a set of p-selected facilities are introduced as the selection of the upper-level decision maker. The bi-level model reduces to a single-level model with some added binary variables.

Findings

Sensitivity analysis of the proposed bi-level model concerning variations of such different parameters as customers’ preferences and the number of selected facilities have been provided, using some numerical examples. Also, locating a recreational facility in Mazandaran province, Iran, has been provided to evaluate the reliability of the proposed model and efficiency of the solution approach, as well.

Originality/value

To the best of the authors’ knowledge, this paper is original and its findings are not available elsewhere.

Keywords

Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their invaluable comments that contributed to the enhancement of this research.

Citation

Zaferanieh, M., Sadra, M. and Basirat, T. (2024), "P-facility capacitated location problem with customer-equilibrium decisions: a recreational case study in Mazandaran province", Journal of Modelling in Management, Vol. 19 No. 6, pp. 1883-1906. https://doi.org/10.1108/JM2-08-2023-0194

Publisher

:

Emerald Publishing Limited

Copyright © 2024, Emerald Publishing Limited

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