Modelling containerisation of air cargo forwarding problems

This study presents a decision-making framework for modelling containerisation of air cargo forwarding problems. The objective is to help logistics managers make decisions about how to rent air containers from air carriers and how to load air cargos into these containers optimally. The air carriers can provide different types of air containers with differing weight and volume limits. The problem is further complicated by the cost charged by the air carriers: this is based on a fixed cost for using the container and a variable cost that depends on the weight that the container will hold. A mathematic programming model is formulated to minimise the total rental cost while satisfying the customer's shipping requirements. The objective function in the model, however, is a non-decreasing piece-wise linear one. The model is changed into a mixed integer linear programming model by introducing two new sets of variables, and the new model can be solved by employing many mathematical programming software packages available today. The model is illustrated with a practical problem faced by a logistics company and sensitivity analysis of three different scenarios.