A two-stage stochastic optimization model for synchronized two-echelon routing problems

In this study, we address uncertainty within the context of city logistics to improve service reliability through a two-echelon modeling framework. The goal is to minimize lateness as a measure of customer inconvenience, logistics costs for LSPs, and road mode share for reaching greener logistics systems. We propose a two-stage stochastic optimization method with a mixed-integer recourse problem and employ logical cuts for the convergence to tackle the complexity issue for synchronized two-echelon systems without storage options. A scenario-based stochastic optimization is tested on a small network to gain insights into multimodal city logistics under uncertainty. The goal is to quantify the risks associated with the integrated systems with or without storage options. The scenarios are generated to represent delay cases in transshipment lead times. The proposed scenario generation approach shows stability over time as the variance of the scenarios within the sample decreases with an increasing number of scenarios. The proposed stochastic programming model reduces the expected costs by 37% overall across all instances compared to the deterministic approach. Furthermore, it is shown that even relocating storage units in case of delays cannot match the performance of flexible sailing services in terms of congestion, reliability, and greener modal share in cities.