Robust optimisation of dry port network design in the container shipping industry under uncertainty

Abstract

The concept of dry port has attracted the attention of many researchers in the field of containerised transport industry over the past few decades. Previous research on dry port container network design has dealt with decision-making at different levels in an isolated manner. The purpose of this research is to develop a decision-making tool based on mathematical programming models to integrate strategic level decisions with operational level decisions. In this context, the strategic level decision making comprises the number and location of dry ports, the allocation of customers demand, and the provision of arcs between dry ports and customers within the network. On the other hand, the operational level decision making consists of containers flow, the selection of transportation modes, empty container repositioning, and empty containers inventory control. The containers flow decision involves the forward and backward flow of both laden and empty containers. Several mathematical models are developed for the optimal design of dry port networks while integrating all these decisions. One of the key aspects that has been incorporated in this study is the inherent uncertainty of container demands from end customers. Besides, a dynamic setting has to be adopted to consider the inevitable periodic fluctuation of demands. In order to incorporate the abovementioned decision-making integration with uncertain demands, several models are developed based on twostage stochastic programming approach. In the developed models, the strategic decisions are made in the first stage while the second-stage deals with operational decisions. The models are then solved through a robust sample average approximation approach, which is improved with the Benders Decomposition method. Moreover, several acceleration algorithms including multi-cut framework, knapsack inequalities, and Pareto-optimal cut scheme are applied to enhance the solution computational time. The proposed models are applied to a hypothetical case of dry port container network design in North Carolina, USA. Extensive numerical experiments are conducted to validate the dry port network design models. A large number of problem instances are employed in the numerical experiments to certify the capability of models. The quality of generated solutions is examined via a statistical validation procedure. The results reveal that the proposed approach can produce a reliable dry port container network under uncertain environment. Moreover, the experimental results underline the sensitivity of the configuration of the network to the inventory holding costs iii and the value of coefficients relating to model robustness and solution robustness. In addition, a number of managerial insights are provided that may be widely used in container shipping industry: that the optimal number of dry ports is inversely proportional to the empty container holding costs; that multiple sourcing is preferable when there are high levels of uncertainty; that rail tends to be better for transporting laden containers directly from seaports to customers with road being used for empty container repositioning; service level and fill rate improve when the design targets more robust solutions; and inventory turnover increases with high levels of holding cost; and inventory turnover decreases with increasing robustness.