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

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.