Journal Article10.1134/S1990478914020045
The branch-and-bound algorithm for a competitive facility location problem with the prescribed choice of suppliers
V. L. Beresnev,A. A. Melnikov +1 more
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TL;DR: In this paper, a branch-and-bound algorithm was proposed to find approximate and optimal solutions to the bilevel integer programming problem, which can be applied to solve the individual problems of low and medium dimension.
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Abstract: In the mathematical model under study, the two competing sides consecutively place their facilities aiming to capture consumers and maximize profits. The model amounts to a bilevel integer programming problem. We take the optimal noncooperative solutions as optimal to this problem. To find approximate and optimal solutions, we propose a branch-and-bound algorithm. Simulations show that the algorithm can be applied to solve the individual problems of low and medium dimension.
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Citations
Exact method for the capacitated competitive facility location problem
V. L. Beresnev,A. A. Melnikov +1 more
TL;DR: A branch-and-bound algorithm where an estimating problem in a form of mixed-integer programming is utilized to calculate an upper bound for values of the objective function is suggested and the quality of the upper bound and the performance of the method on randomly generated inputs is studied.
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An Effective Branch-and-cut algorithm in Order to Solve the Mixed Integer Bi-level Programming
Arsalan Rahmani,Majid Yousefikhoshbakht +1 more
- 31 Jan 2017
TL;DR: In this article, a branch and cut algorithm for mixed integer bi-level programming is proposed, which uses a preference function to determine the choice of branching and specialized cuts in a branch-and-cut tree.
9
Exact algorithms for solving a bi-level location–allocation problem considering customer preferences
TL;DR: A clustering-based algorithm has been presented that can provide a good approximation to the mentioned binary problem and is introduced in this paper which include three types of full enumeration procedures and a developed branch-and-bound procedure.
8
Location of competitive facilities: a comprehensive review and future research agenda
TL;DR: A comprehensive review of competitive facility location (CFL) modeling efforts from 1981 to 2021 is presented in this paper , which provides a depth study of the research evolution in this area and highlights the popular problem areas and dedicated research in the respective domain.
6
References
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Foundations of Bilevel Programming
Stephan Dempe
- 31 May 2002
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and expensive process of solving linear and Discrete Bilevel Problems.
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The simple plant location problem: Survey and synthesis
Jakob Krarup,Peter Pruzan +1 more
TL;DR: In this paper, the authors consider a family of discrete, deterministic, single-criterion, NP-hard problems, including set packing, set covering, and set partitioning.
591
Branch-and-bound algorithm for a competitive facility location problem
TL;DR: A branch-and-bound algorithm for finding the optimal noncooperative solution for maximizing a pseudo-Boolean function is proposed and the results of a simulation demonstrating the computational capabilities of the proposed algorithm are presented.
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