Computational Optimization and Applications

, Volume 51, Issue 3, pp 1275–1295 | Cite as

A Barzilai-Borwein-based heuristic algorithm for locating multiple facilities with regional demand

  • Jianlin Jiang
  • Xiaoming YuanEmail author


We are interested in locations of multiple facilities in the plane with the aim of minimizing the sum of weighted distance between these facilities and regional customers, where the distance between a facility and a regional customer is evaluated by the farthest distance from this facility to the demand region. By applying the well-known location-allocation heuristic, the main task for solving such a problem turns out to solve a number of constrained Weber problems (CWPs). This paper focuses on the computational contribution in this topic by developing a variant of the classical Barzilai-Borwein (BB) gradient method to solve the reduced CWPs. Consequently, a hybrid Cooper type method is developed to solve the problem under consideration. Preliminary numerical results are reported to verify the evident effectiveness of the new method.


Facility location Barzilai-Borwein gradient method Weiszfeld procedure Regional demand Farthest distance 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityHong KongChina

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