Fleet deployment and demand fulfillment for container shipping liners

This paper models and solves a fleet deployment and demand fulfillment problem for container shipping liners with consideration of the potential overload risk of containers. Given the stochastic weights of transported containers, chance constraints are embedded in the model at the strategic level. Several realistic limiting factors such as the fleet size and the available berth and yard resources at the ports are also considered. A non-linear mixed integer programming (MIP) model is suggested to optimally determine the transportation demand fulfillment scale for each origin-destination pair, as well as the ship deployment plan along each route, with an objective incorporating revenue, fixed operation cost, fuel consumption cost, holding cost for transhipped containers, and extra berth and yard costs. Two efficient algorithms are then developed to solve the non-linear MIP model for different instance sizes. Numerical experiments based on real-world data are conducted to validate the effectiveness of the model and the algorithms. The results indicate the proposed methodology yields solutions with an optimality gap less than about 0.5%, and can solve realistic instances with 19 ports and four routes within about one hour.