Title: A bi-level stochastic liner shipping network design optimization considering seasonal water level fluctuations

Inland port capacities are profoundly influenced by prevailing weather conditions, primarily attributed to water level fluctuations. During severe droughts or floods, the utilization of planned barge and tug sizes becomes constrained. This study addresses the intricate challenge of liner shipping network design, encompassing the determination of optimal sailing routes, effective management of return journeys, repositioning of empty containers and vessels, all while accommodating the stochastic element of seasonal water level fluctuations.

To tackle this multifaceted problem, we employ an operational research approach utilizing a two-stage mixed-integer non-linear programming framework. The model is formulated as a capacitated flow maximization problem, incorporating the critical aspects of empty vessel routing and turnaround time optimization. Benders decomposition, a specialized technique, is leveraged to attain an exact optimal solution for the decision variables. To illustrate the model's efficacy, we present a case study involving multiple scenarios, replicating the impact of water level fluctuations on liner shipping operations. This research provides valuable insights and tools for optimizing liner shipping networks in the face of variable and unpredictable environmental conditions. The results of this study suggest the use of optimally sized flatbed barges to mitigate the hindrances caused by severe water level fluctuations as a recourse.