On the quadratic programming approach for hub location problems. (English) Zbl 1172.90340

He, Xiaozheng; Chen, Anthony; Chaovalitwongse, Wanpracha Art; Liu, Henry

Chaovalitwongse, Wanpracha (ed.) et al., Optimization and logistics challenges in the enterprise. New York, NY: Springer (ISBN 978-0-387-88616-9/hbk; 978-0-387-88617-6/ebook). Springer Optimization and Its Applications 30, 211-228 (2009).

Summary: Hub networks play an important role in many real-life network systems such as transportation and telecommunication networks. Hub location problem is concerned with identifying appropriate hub locations in a network and connecting an efficient hub-and-spoke network that minimizes the flow-weighted costs across the network. This chapter is focused on the uncapacitated single allocation \(p\)-hub median problem (USA\(p\)HMP), which arises in many real-world hub networks of logistics operations. There have been many approaches used to solve this problem. We herein focus on a quadratic programming approach, which has been proven very effective and efficient. This approach incorporates the use of the linearization for 0-1 quadratic program. In this chapter, we give a brief review of the linearization techniques for 0-1 quadratic programs and compare the performance of several existing linearization techniques for USA\(p\)HMP. Toward the end, we discuss some properties, comments and possible developments of these linearization techniques in the real-life USA\(p\)HMP.
For the entire collection see [Zbl 1173.90002].

MSC:

90B10	Deterministic network models in operations research
90C20	Quadratic programming
90B85	Continuous location
90C35	Programming involving graphs or networks