Open Access
Translator Disclaimer
2013 A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach
Jian-Lin Jiang, Saeed Assani, Kun Cheng, Xiao-Xing Zhu
Abstr. Appl. Anal. 2013(SI54): 1-15 (2013). DOI: 10.1155/2013/624398

Abstract

This paper considers the locations of multiple facilities in the space R p , with the aim of minimizing the sum of weighted distances between facilities and regional customers, where the proximity between a facility and a regional customer is evaluated by the closest distance. Due to the fact that facilities are usually allowed to be sited in certain restricted areas, some locational constraints are imposed to the facilities of our problem. In addition, since the symmetry of distances is sometimes violated in practical situations, the gauge is employed in this paper instead of the frequently used norms for measuring both the symmetric and asymmetric distances. In the spirit of the Cooper algorithm (Cooper, 1964), a new location-allocation heuristic algorithm is proposed to solve this problem. In the location phase, the single-source subproblem with regional demands is reformulated into an equivalent linear variational inequality (LVI), and then, a projection-contraction (PC) method is adopted to find the optimal locations of facilities, whereas in the allocation phase, the regional customers are allocated to facilities according to the nearest center reclassification (NCR). The convergence of the proposed algorithm is proved under mild assumptions. Some preliminary numerical results are reported to show the effectiveness of the new algorithm.

Citation

Download Citation

Jian-Lin Jiang. Saeed Assani. Kun Cheng. Xiao-Xing Zhu. "A Heuristic Algorithm for Constrained Multi-Source Location Problem with Closest Distance under Gauge: The Variational Inequality Approach." Abstr. Appl. Anal. 2013 (SI54) 1 - 15, 2013. https://doi.org/10.1155/2013/624398

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095181
MathSciNet: MR3121507
Digital Object Identifier: 10.1155/2013/624398

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.2013 • No. SI54 • 2013
Back to Top