A Lagrangian heuristic and GRASP for the hub-and-spoke network system with economies-of-scale and congestion
Autor: | Ali Diabat, Faisal Alkaabneh, Samir Elhedhli |
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Rok vydání: | 2019 |
Předmět: |
Optimal design
050210 logistics & transportation Mathematical optimization Computer science 05 social sciences GRASP MathematicsofComputing_NUMERICALANALYSIS Transportation 010501 environmental sciences 01 natural sciences Computer Science Applications Nonlinear programming symbols.namesake Nonlinear system Lagrangian relaxation 0502 economics and business Automotive Engineering symbols Convex function Integer programming Greedy randomized adaptive search procedure 0105 earth and related environmental sciences Civil and Structural Engineering |
Zdroj: | Transportation Research Part C: Emerging Technologies. 102:249-273 |
ISSN: | 0968-090X |
DOI: | 10.1016/j.trc.2018.12.011 |
Popis: | We consider a hub-and-spoke network design problem with inter-hub economies-of-scale and hub congestion. We explicitly model the economies-of-scale as a concave piece-wise linear function and congestion as a convex function. The problem is modeled as a nonlinear mixed integer program that is difficult to solve directly since the objective function has both convex and concave nonlinear terms and hence finding an optimal solution may not be easy. A Lagrangian approach is proposed to obtain tight upper and lower bounds. The Lagrangian decomposition exploits the structure of the problem and decomposes it to convex and concave subproblems. Furthermore, we add some valid inequalities to accelerate the convergence rate of the Lagrangian heuristic. To tackle large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is developed. Both the Lagrangian heuristic and GRASP provide high-quality solutions within reasonable computational time. The optimal designs of hub-and-spoke networks with nonlinear inter-hub economies-of-scale and congestion at hub locations are analyzed in comparison with other models in the literature to demonstrate the significant impact of modeling nonlinearity in economies-of-scale and congestion simultaneously rather than independently. |
Databáze: | OpenAIRE |
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