Joint Ship Schedule Design and Sailing Speed Optimization for a Single Inland Shipping Service with Uncertain Dam Transit Time

Inland shipping has received extensive attention in practice and is a high energy-consuming service sensitive to the river streamflow speed and the uncertain lock traversing time of dams. In this study, we propose a joint ship schedule design and sailing speed optimization problem for a single inland shipping service by incorporating the effects of nonidentical streamflow speed and the uncertain dam transit time. A bi-objective programming model is developed for the proposed problem to simultaneously minimize the total bunker consumption and the ship round-trip time with service level constraints. The service level at each port call is captured by the punctual arrival probability of the ship not less than a predefined value. By introducing the term of buffer times, we analytically derive the Pareto optimal solutions of the ship sailing speeds and schedule. The theoretical method is extended to the case with an arbitrary number of dams and the uncertain port service and leg voyage time. We also examine the relationship between the Pareto optimal solution in this study and the solutions of the previous joint sailing speed and schedule optimization problems in the liner shipping service design. Numerical experiments based on the Yangtze River are conducted.