Dynamic and Stochastic Models for the Allocation of Empty Containers

TLDR

The empty container allocation problem arises in international maritime shipping, involving the dispatch of empty containers to meet export customer requests and the repositioning of containers to storage depots or ports in anticipation of future demand. This study defines the problem, outlining its basic structure and key characteristics. We present two dynamic deterministic formulations for single‑ and multicommodity cases that model space‑time dependencies, container substitutions, partner relationships, imports/exports, and large equilibration flows, and we extend the single‑commodity model to incorporate demand and supply uncertainty while discussing data requirements and algorithmic considerations.

Abstract

The empty container allocation problem occurs in the context of the management of the land distribution and transportation operations of international maritime shipping companies. It involves dispatching empty containers of various types in response to requests by export customers and repositioning other containers to storage depots or ports in anticipation of future demands. We describe the problem and identify its basic structure and main characteristics. We then introduce two dynamic deterministic formulations for the single and multicommodity cases, which offer a general modeling framework for this class of problems, and which account for its specific characteristics: the space and time dependency of events, substitutions among container types, relationships with partner companies, imports and exports, massive equilibration flows, etc. Finally, we provide a mathematical formulation for handling, in the single commodity case, the uncertainty of demand and supply data that is characteristic of container allocation and distribution problems. Various modeling choices, data requirements, and algorithmic considerations related to the implementation of the models are also discussed.