A mixed integer programming model for container selection and cargo loading problems

This study aims to provide a systematic framework of the container selection and cargo loading problems, which are currently faced by a forwarding company in Hong Kong. The forwarding company first consolidates all goods that will be shipped to overseas markets into different types of cargos. Then the company is responsible for packing the cargos into containers, which are rented from airlines a week in advance in order to obtain a cheap price from the airlines. The airlines can provide different types and numbers of containers. Therefore, the question of how to select containers from the airlines and how to pack cargos into the containers is a very important issue that the forward company faces every day. The decision-making process becomes complex because of the containers´ volume and weight limits and the fact that the rental cost is the fixed cost for using the containers plus the variable cost that depend on the total weight that each container holds. The objective in this study is to minimize the total rental cost, which is the piece-wise function. We further change it into anther form, in which the piece-wise function can be expressed as a continue one. Therefore, a mixed integer linear programming model is provided to determine the optimal container selection and cargo loading strategy. The application of the proposed model is illustrated by the practical problems from the forwarding company.