A Tri-level minimum information demand estimation model to the inverse p-median problem

Mehdi Zaferanieh () and Maryam Abareshi ()
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Mehdi Zaferanieh: Hakim Sabzevari University
Maryam Abareshi: Hakim Sabzevari University

OPSEARCH, 2025, vol. 62, issue 2, No 16, 877-904

Abstract: Abstract In this paper, a novel inverse approach to the p-median problem is introduced in which the locations of p facilities and their supplies are known, while the demands of client nodes and the fraction allocated to each facility need to be estimated. To achieve this purpose, a tri-level programming problem is proposed. The primary objective of the first-level model is to minimize the sum of the squared differences between the estimated demand values and the observed target values. The second and third level problems together form a bi-level p-median model that incorporates the minimum information approach into the allocation phase. By substituting the optimality conditions of the third-level problem into the second one, a nonlinear bi-level mixed-integer model is obtained, which is addressed by using a particle swarm optimization algorithm. The added value of the tri-level model and the proposed method is verified by some small and large-sized examples.

Keywords: Tri-level programming; Location-allocation; Inverse p-median problem; Minimum information (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12597-024-00815-8

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