International multimodal transportation optimization considering bulk cargo containerization

Abstract

Bulk cargo containerization helps to reposition empty containers and reduce bulk cargo attrition in international trade. This paper studies an international multimodal transportation optimization problem that considers the containerization of bulk cargo in multiple planning periods. We provide a mathematical formulation for this optimization model, taking into account decisions related to equipment purchasing and bulk cargo containerization quantities. By incorporating the uncertainty of the bulk cargo demand, our basic model is extended to a two-stage stochastic mixed integer programming model. An improved Benders decomposition algorithm is proposed to solve this model. The results of numerical experiments and sensitivity analysis show that: (1) a high bulk cargo loss rate, a large number of nodes in the network, and an extensive planning period motivate carriers to pursue bulk cargo containerization; (2) when the price of the containerization equipment is reasonable, bulk cargo containerization can save costs; (3) the more complex the network, the higher the price of the equipment carriers can afford for bulk cargo containerization; and (4) considering uncertain demand with more demand scenarios can help reduce operational cost.