Technical Note—Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations

AbstractMaritime transportation is the backbone of the global economy and one of its most important segments is liner shipping. To design a liner shipping network is notoriously difficult but also very important since an efficient network can be the difference between prosperity and bankruptcy. In this paper, we propose a branch-and-price algorithm for the liner shipping network design problem, which is the problem of designing a set of cyclic services and to deploy a specific class of vessels to each service so that all demand can flow through the network at minimal cost. The proposed model can create services with a complex structure and correctly calculate the transshipment cost. The formulation of the master problem strengthens a known formulation with valid inequalities. Because of multiple dependencies between ports that are not necessarily adjacent and no defining state at any of the ports, the subproblem is formulated and solved as a mixed integer linear program. Strategies to improve the solution time of the subproblem are proposed. The computational study shows that the algorithm provides significantly tighter lower bounds in the root node than existing methods on a set of small instances.

Download Full-text

A Branch-And-Price Algorithm for Solving The Single-Hub Feeder Network Design Problem

European Journal of Operational Research ◽

10.1016/j.ejor.2021.08.046 ◽

2021 ◽

Author(s):

Erik Orm Hellsten ◽

David Sacramento ◽

David Pisinger

Keyword(s):

Network Design ◽

Design Problem ◽

Network Design Problem ◽

Branch And Price ◽

Price Algorithm

Download Full-text

Using branch-and-price approach to solve the directed network design problem with relays

Omega ◽

10.1016/j.omega.2011.11.006 ◽

2012 ◽

Vol 40 (5) ◽

pp. 672-679 ◽

Cited By ~ 10

Author(s):

Xiangyong Li ◽

Y.P. Aneja ◽

Jiazhen Huo

Keyword(s):

Network Design ◽

Design Problem ◽

Network Design Problem ◽

Directed Network ◽

Branch And Price ◽

Price Approach

Download Full-text

Dynamic Network Design Problem under Demand Uncertainty: An Adjustable Robust Optimization Approach

Discrete Dynamics in Nature and Society ◽

10.1155/2014/739656 ◽

2014 ◽

Vol 2014 ◽

pp. 1-16 ◽

Cited By ~ 6

Author(s):

Hua Sun ◽

Ziyou Gao ◽

Fangxia Zhao

Keyword(s):

Linear Programming ◽

Robust Optimization ◽

Network Design ◽

Design Problem ◽

Demand Uncertainty ◽

Network Design Problem ◽

Transmission Model ◽

Optimization Approach ◽

Robust Network Design ◽

Adjustable Robust Optimization

This paper develops an adjustable robust optimization approach for a network design problem explicitly incorporating traffic dynamics and demand uncertainty. In particular, a cell transmission model based network design problem of linear programming type is considered to describe dynamic traffic flows, and a polyhedral uncertainty set is used to characterize the demand uncertainty. The major contribution of this paper is to formulate such an adjustable robust network design problem as a tractable linear programming model and justify the model which is less conservative by comparing its solution performance with the robust solution from the usual robust model. The numerical results using one network from the literature demonstrate the modeling advantage of the adjustable robust optimization and provided strategic managerial insights for enacting capacity expansion policies under demand uncertainty.

Download Full-text