A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem

Abstract

Containerized liner trades have been growing steadily since the globalization of world economies intensified in the early 1990s. However, these trades are typically imbalanced in terms of the numbers of inbound and outbound containers. As a result, the relocation of empty containers has become one of the major problems faced by liner operators. In this paper, we consider the dynamic empty container allocation problem where we need to reposition empty containers and to determine the number of leased containers needed to meet customers' demand over time. We formulate this problem as a two-stage stochastic network: in stage one, the parameters such as supplies, demands, and ship capacities for empty containers are deterministic; whereas in stage two, these parameters are random variables. We need to make decisions in stage one such that the total of the stage one cost and the expected stage two cost is minimized. By taking advantage of the network structure, we show how a stochastic quasi-gradient method and a stochastic hybrid approximation procedure can be applied to solve the problem. In addition, we propose some new variations of these methods that seem to work faster in practice. We conduct numerical tests to evaluate the value of the two-stage stochastic model over a rolling horizon environment and to investigate the behavior of the solution methods with different implementations.

Optimization of empty container movements in intermodal transport

“…Unexpected transportation requests may be made at the last moment by important customers. Finally, uncertainty may arise from network performance measures, such as transportation times and equipment failures (Dejax and Crainic, 1987;Cheung and Chen, 1998;Olivo et al, 2005;.…”

“…A dynamic single commodity two-stage stochastic network is formulated by Cheung and Chen (1998). In the first stage, all parameters are assumed to be deterministic, while in the second stage empty container supplies and demands and ship capacities are stochastic variables.…”

Designing Container Shipping Network Under Changing Demand and Freight Rates

“…is seems impractical and not in keeping with the practice of dealing with long-term leased containers as the owned ones. Cheung and Chen (1998) also considered the sea-borne empty container allocation problem. In their paper, the dynamic container allocation problem was formulated as a two-stage stochastic network model.…”

Multiple Periods Minimal Cost Programming Optimization Model for Empty Containers Repositioning with Stock Level

“…Secondly it adopts the dynamic network programming methods to solve this problem [13][14][15]. Cheung and Chen [2] model ECR as a two-stage stochastic optimization model. They propose a time space network model which is the opening maritime ECR network modeling for discussion.…”