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Median location problem with two probabilistic line barriers: Extending the hook and jeeves algorithm

Shiripour, S ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.3934/jimo.2021128
  3. Publisher: American Institute of Mathematical Sciences , 2022
  4. Abstract:
  5. We consider a median location problem in the presence of two probabilistic line barriers on the plane under rectilinear distance. It is assumed that the two line barriers move on their corresponding horizontal routes uniformly. We first investigate different scenarios for the position of the line barriers on the plane and their corresponding routes, and then define the visibility and invisibility conditions along with their corresponding expected barrier distance functions. The proposed problem is formulated as a mixed-integer nonlinear programming model. Our aim is to locate a new facility on the plane so that the total weighted expected rectilinear barrier distance is minimized. We present efficient lower and upper bounds using the forbidden location problem for the proposed problem. To solve the proposed model, the Hooke and Jeeves algorithm (HJA) is extended. We investigate various sample problems to test the performance of the proposed algorithm and appropriateness of the bounds. Also, an empirical study in Kingston-upon-Thames, England, is conducted to illustrate the behavior and applicability of the proposed model. © 2022. Journal of Industrial and Management Optimization. All Rights Reserved
  6. Keywords:
  7. Extended hooke and jeeves algorithm ; Median location problem ; Probabilistic line barriers ; Rectilinear barrier distance ; Integer programming ; Nonlinear programming ; Condition ; Extended hooke and jeeves algorithm ; Hooke and Jeeves algorithm ; Location problems ; Median location problem ; Probabilistic line barrier ; Probabilistics ; Rectilinear barrier distance ; Two-line ; Visibility and invisibilities ; Location
  8. Source: Journal of Industrial and Management Optimization ; Volume 18, Issue 5 , 2022 , Pages 3613-3639 ; 15475816 (ISSN)
  9. URL: https://www.aimsciences.org/article/doi/10.3934/jimo.2021128