Cargo routing and empty container repositioning in multiple shipping service routes

This paper considers the problem of joint cargo routing and empty container repositioning at the operational level for a shipping network with multiple service routes, multiple deployed vessels and multiple regular voyages. The objective is to minimize the total relevant costs in the planning horizon including: container lifting on/off costs at ports, customer demand backlog costs, the demurrage (or waiting) costs at the transhipment ports for temporarily storing laden containers, the empty container inventory costs at ports, and the empty container transportation costs. The laden container routing from the original port to the destination port is limited with at most three service routes. Two solution methods are proposed to solve the optimization problem. The first is a two-stage shortest-path based integer programming method, which combines a cargo routing algorithm with an integer programming of the dynamic system. The second is a two-stage heuristic-rules based integer programming method, which combines an integer programming of the static system with a heuristic implementation algorithm in dynamic system. The two solution methods are applied to two case studies with 30 different scenarios and compared with a practical policy. The results show that two solution methods perform substantially better than the practical policy. The shortest-path based method is preferable for relatively small-scale problems as it yields slightly better solution than the heuristic-rules based method. However, the heuristic-rules based method has advantages in its applicability to large-scale realistic systems while producing good performance, to which the shortest-path based method may be computationally inapplicable. Moreover, the heuristic-rules based method can also be applied to stochastic situations because its second stage is rule-based and dynamical.