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Single Allocation Hub Location with Heterogeneous Economies of Scale

Borzou Rostami(brostami***at***wlu.ca)
Masoud Chitsaz(masoud.chitsaz***at***hec.ca)
Okan Arslan(okan.arslan***at***hec.ca)
Gilbert Laporte(gilbert.laporte***at***cirrelt.ca)
Andrea Lodi(andrea.lodi***at***polymtl.ca)

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 non-linear program, which we then reformulate as a mixed integer linear program (MILP) and also 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 dataset. The results confirm the efficacy of our solution methods in solving large-scale instances.

Keywords: Single allocation, hub location, economies of scale, quadratic program, Benders decomposition, Lagrangian relaxation

Category 1: Applications -- OR and Management Sciences

Category 2: Combinatorial Optimization

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation:

Download: [PDF]

Entry Submitted: 10/17/2019
Entry Accepted: 10/17/2019
Entry Last Modified: 10/17/2019

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