Liner fleet deployment and slot allocation problem: A distributionally robust optimization model with joint chance constraints

In this paper, we address the classical liner fleet deployment and slot allocation joint optimization problem in the maritime field with uncertain container transportation demand. We relax the assumption in existing studies that the demand distribution function is known because container transportation demand is deeply affected by the world’s economic and political landscape. With the help of advances in distributionally robust optimization theory, we develop a two-stage data-driven robust chance-constrained model. This distribution-free model requires only limited historical demand data as input and jointly optimizes the class (i.e., capacity) and number of liners assigned on each route and the scheme for allocating containers on each leg to maximize the profit (container transportation revenue minus fleet operating costs, voyage costs, and capital costs) of the liner company. The joint chance constraint in the model requires that the transportation demand of the contract shipper be satisfied with a pre-determined probability. We then reformulate the model as a second-order cone programming and design a customized algorithm to explore the global optimal solution based on the outer approximation algorithm framework. This paper can serve as a baseline distribution-free model for solving liner fleet deployment and slot allocation joint optimization problems.