Hub Network Design Problem with Capacity, Congestion, and Stochastic Demand Considerations

Abstract

Our study introduces the hub network design problem with congestion, capacity, and stochastic demand considerations (HNDC), which generalizes the classical hub location problem in several directions. In particular, we extend state-of-the-art by integrating capacity acquisition decisions and congestion cost effect into the problem and allowing dynamic routing for origin-destination (OD) pairs. Connecting strategic and operational level decisions, HNDC jointly decides hub locations and capacity acquisitions by considering the expected routing and congestion costs. A path-based mixed-integer second-order cone programming (SOCP) formulation of the HNDC is proposed. We exploit SOCP duality results and propose an exact algorithm based on Benders decomposition and column generation to solve this challenging problem. We use a specific characterization of the capacity-feasible solutions to speed up the solution procedure and develop an efficient branch-and-cut algorithm to solve the master problem. We conduct extensive computational experiments to test the proposed approach’s performance and derive managerial insights based on realistic problem instances adapted from the literature. In particular, we found that including hub congestion costs, accounting for the uncertainty in demand, and whether the underlying network is complete or incomplete have a significant impact on hub network design and the resulting performance of the system. Funding: This work was supported by Türkiye Bilimsel ve Teknolojik Araştırma Kurumu [Grant 218M520]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.0112 .

An exact second order cone programming approach for traffic assignment problems

“…Advances in interior point methodologies have allowed to solve second order cone programming problems almost as efficiently as solving linear programming problems [18]. Due to that, SOCP has been successfully applied to a wide range of convex optimization problems such as portfolio optimization [20], machine-job assignment [2], power distribution system reconfiguration [61], stochastic joint location inventory [8], routing/location in telecommunication/hub-spoke networks [15,32], variable selection in linear regression [44], planning for plugin electric vehicle fast-charging stations [72], two-player zero sum games [55], and UAV collision avoidance [71]. We refer the reader to Lobo et al [38], Ben-Tal and Nemirovski [18], Alizadeh and Goldfarb [3] and Benson and Saglam [19] for an introduction and for more details on the applications on SOCP problems.…”

Public Transport-based Crowd-shipping with Backup Transfers

“…Finally, we consider dynamic routes to connect satellites to PT connections as opposed to static routing decisions that disregard uncertainties in demand and capacity. Some of these extensions are individually investigated in the hub network design literature (Yaman, Kara, and Tansel 2007, Alumur, Kara, and Karasan 2009, Yang 2009 Laporte 2011, Yıldız, Yaman, and Karas ¸an 2021, Bayram, Yıldız, and Farham 2022). However, to the best of our knowledge, our study is the first to consider all these extensions together.…”