Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

Abstract

The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USApHMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.

A Multimodal Passenger-and-Package Sharing Network for Urban Logistics

“…Hub location problems are firstly proposed by O'Kelly in 1980s [22][23][24]. Typical HLPs can be classified based on their objectives: the p-hub median problems locate p hubs to minimize the total routing cost [25][26][27][28][29][30][31]; the p-hub center problems locate p hubs so that the maximum cost between any OD pair can be minimized [25,32]; and the p-hub covering problems aim to maximize the total flow between all OD pairs covered by p hub facilities [33]. In these studies, the number of hubs to be established, i.e., p, is prespecified.…”

“…In these studies, the number of hubs to be established, i.e., p, is prespecified. Instead of predetermining the number of hubs, some works assume a setup and operation cost for each hub with the objective of minimizing the sum of hub cost and routing cost [29,34] or maximizing the system profit [35]. Comprehensive reviews can be found in Alumur and Kara [36], Campbell and O'Kelly [37], and Farahani et al [38].…”

Spatial Separability in Hub Location Problems with an Application to Brain Connectivity Networks

“…Therefore, we compare the performance of SPATIAL algorithm (r 25) with state-of-the-art heuristics. We consider three heuristics: (1) the VNS of Ilić et al (2010), (2) Euclidean Projection Method of Meier and Clausen (2017), and (3) Bender decomposition of Ghaffarinasab and Kara (2019). Table 6 provides a comparison in terms of the optimality gap and computational time.…”

“…Proposed solution methodologies range from decomposition-based methods, such as Lagrangian relaxation (Aykin 1994, Pirkul and Schilling 1998, Elhedhli and Hu 2005, branch-and-price (Contreras et al 2011c), and Benders decomposition (de Camargo et al 2009a, Contreras et al 2011a, Ghaffarinasab and Kara 2019 to heuristics, such as genetic algorithms (Topcuoglu et al 2005), tabu search, greedy randomized adapted search procedure (GRASP) (Klincewicz 1992, Mayer andWagner 2002), Variable Neighborhood Search (VNS) (Ilić et al 2010), and Euclidean projection (Meier and Clausen 2017). On the application side, HLPs have been introduced in the context of airline transportation (O'Kelly 1987, Martin andRomán 2004), postal delivery (Ernst and Krishnamoorthy 1996), and telecommunication (Klincewicz 1998).…”

“…320-346, © 2020 It is worth mentioning that despite the limitations mentioned above on using these formulations with generalpurpose solvers for large problem instances, it is well known that decomposition algorithms usually work well to handle such formulations. In fact, there has been recent progress in the development of algorithms capable of optimally solving large-size instances for the considered problem (Meier andClausen 2017, Ghaffarinasab andKara 2019) and heuristically solving even larger ones (Ilić et al 2010, Guan et al 2018).…”