Optimizing inland container logistics through dry ports: A two-stage stochastic mixed-integer programming approach considering volume discounts and consolidation in rail transport

•Progressive hedging algorithm efficiently solves the stochastic instances.•Transportation costs have the biggest impact on network configuration.•Effective design should include a decentralized network with smaller dry ports.•Network design is more sensitive to the transportation costs in road than in rail.•Application of stochastic solution instead of deterministic one can provide savings. It is essential for container shipping companies to plan for the optimum number and locations of dry ports as well as efficient inland container logistics operations to reduce costs and environmental impacts while improving customer service. The plan for optimum inland container transportation network design must account for demand uncertainty to eliminate financial difficulty due to redundant investment. In this regard, this study proposed a two-stage stochastic mixed-integer programming model for optimizing inland container logistics through dry ports. The model contributes to the state of the art in current research by including a piecewise-linear cost function for railway transportation to account for volume discounts, integrating full container scheduling with transport mode selection and empty container relocation for consolidation, and reflecting the fact that the amount of import and export full containers transported between customers (consignees and consignors) and seaports are exogenously decided. The solution results demonstrated the definite performance superiority of the progressive hedging algorithm over the extensive form solution. Additionally, the value of stochastic solution calculation showed that the application of stochastic solution might result in significant cost savings compared to the application of mean value deterministic solution. The proposed model can be applied for practical necessities to design robust optimum inland container logistics operations using intermodal rail transport with the progressive hedging algorithm as an efficient solution approach.