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Developing equilibrium optimization methods for hub location problems. (English) Zbl 1362.90113

Summary: This paper develops three new equilibrium optimization models for \(p\)-hub center problem, in which the travel times are characterized by fuzzy random variables. The proposed equilibrium optimization methods are to find the locations of hub facilities and demand nodes so as to maximize equilibrium service levels of uncertain travel times. Under mild assumptions, we first handle equilibrium service levels and reduce them to their equivalent probability constraints. According to structural characteristics of equivalent stochastic programming models, we design a new parametric decomposition-based hybrid tabu search (PD-HTS) algorithm that incorporates parametric decomposition (PD), sample average approximation and tabu search algorithm. To demonstrate the effectiveness of designed solution method, we conduct some numerical experiments by using Australian Post data set and randomly generated data set. The comparison study shows that the PD-HTS algorithm exhibits better performance than the parametric decomposition-based hybrid genetic algorithm.

MSC:

90B06 Transportation, logistics and supply chain management
90C59 Approximation methods and heuristics in mathematical programming
90B80 Discrete location and assignment
90C15 Stochastic programming
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