Single Allocation Hub Location with Heterogeneous Economies of Scale

Borzou Rostami (), Masoud Chitsaz (), Okan Arslan (), Gilbert Laporte () and Andrea Lodi ()
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Borzou Rostami: Lazaridis School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C7, Canada; Canada Excellence Research Chair (CERC) in Data Science for Real-Time Decision Making, Polytechnique Montréal, Montreal, Quebec H3C 3A7, Canada; Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3T 1J4, Canada
Masoud Chitsaz: HEC Montréal, Montreal, Quebec H3T 2A7, Canada; Kinexis, Ottawa, Ontario K2V 1C3, Canada
Okan Arslan: Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3T 1J4, Canada; HEC Montréal, Montreal, Quebec H3T 2A7, Canada; Group for Research in Decision Analysis, Montreal, Quebec H3T1J4, Canada
Gilbert Laporte: Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3T 1J4, Canada; HEC Montréal, Montreal, Quebec H3T 2A7, Canada; Group for Research in Decision Analysis, Montreal, Quebec H3T1J4, Canada; School of Management, University of Bath, Bath BA2 7AY, United Kingdom
Andrea Lodi: Canada Excellence Research Chair (CERC) in Data Science for Real-Time Decision Making, Polytechnique Montréal, Montreal, Quebec H3C 3A7, Canada; Jacobs Technion-Cornell Institute, Cornell Tech and Technion, Cornell University, New York, New York 10044

Operations Research, 2022, vol. 70, issue 2, 766-785

Abstract: We study the single allocation hub location problem with heterogeneous economies of scale (SAHLP-h). The SAHLP-h is a generalization of the classical single allocation hub location problem (SAHLP), in which the hub-hub connection costs are piecewise linear functions of the amounts of flow. We model the problem as an integer nonlinear program, which we then reformulate as a mixed integer linear program (MILP) and as a mixed integer quadratically constrained program (MIQCP). We exploit the special structures of these models to develop Benders-type decomposition methods with integer subproblems. We use an integer L-shaped decomposition to solve the MILP formulation. For the MIQCP, we dualize a set of complicating constraints to generate a Lagrangian function, which offers us a subproblem decomposition and a tight lower bound. We develop linear dual functions to underestimate the integer subproblem, which helps us obtain optimality cuts with a convergence guarantee by solving a linear program. Moreover, we develop a specialized polynomial-time algorithm to generate enhanced cuts. To evaluate the efficiency of our models and solution approaches, we perform extensive computational experiments on both uncapacitated and capacitated SAHLP-h instances derived from the classical Australian Post data set. The results confirm the efficacy of our solution methods in solving large-scale instances.

Keywords: Transportation; single allocation; hub location; economies of scale; quadratic program; Benders decomposition; Lagrangian relaxation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:2:p:766-785

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