Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 249-273 |
| Number of pages | 25 |
| Journal | Transportation Research Part C: Emerging Technologies |
| Volume | 102 |
| DOIs | |
| State | Published - May 1 2019 |
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Keywords
- Congestion
- Economies-of-scale
- GRASP
- Hub-and-Spoke design network
- Lagrangian relaxation
- Mixed Integer Nonlinear programming
ASJC Scopus subject areas
- Civil and Structural Engineering
- Automotive Engineering
- Transportation
- Computer Science Applications
Cite this
A Lagrangian heuristic and GRASP for the hub-and-spoke network system with economies-of-scale and congestion. / Alkaabneh, Faisal; Diabat, Ali; Elhedhli, Samir.
In: Transportation Research Part C: Emerging Technologies, Vol. 102, 01.05.2019, p. 249-273.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A Lagrangian heuristic and GRASP for the hub-and-spoke network system with economies-of-scale and congestion
AU - Alkaabneh, Faisal
AU - Diabat, Ali
AU - Elhedhli, Samir
PY - 2019/5/1
Y1 - 2019/5/1
N2 - 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.
AB - 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.
KW - Congestion
KW - Economies-of-scale
KW - GRASP
KW - Hub-and-Spoke design network
KW - Lagrangian relaxation
KW - Mixed Integer Nonlinear programming
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UR - http://www.scopus.com/inward/citedby.url?scp=85063077528&partnerID=8YFLogxK
U2 - 10.1016/j.trc.2018.12.011
DO - 10.1016/j.trc.2018.12.011
M3 - Article
AN - SCOPUS:85063077528
VL - 102
SP - 249
EP - 273
JO - Transportation Research Part C: Emerging Technologies
JF - Transportation Research Part C: Emerging Technologies
SN - 0968-090X
ER -