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

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  • Mehdi Zaferanieh

    (Hakim Sabzevari University)

  • Maryam Abareshi

    (Hakim Sabzevari University)

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.

Suggested Citation

  • Mehdi Zaferanieh & Maryam Abareshi, 2025. "A Tri-level minimum information demand estimation model to the inverse p-median problem," OPSEARCH, Springer;Operational Research Society of India, vol. 62(2), pages 877-904, June.
    • Handle: RePEc:spr:opsear:v:62:y:2025:i:2:d:10.1007_s12597-024-00815-8
    DOI: 10.1007/s12597-024-00815-8
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