A decomposition-based matheuristic for the passenger-oriented integrated passenger-freight transport problem

Integrating passenger and freight transport has become increasingly important for improving the efficiency of urban mobility systems, as planning them separately often results in underutilized capacity and redundant vehicle movements. Coordinating the two enables more effective use of existing transport resources for public transport operators, helps logistics providers maintain cost-effective and reliable deliveries, and assists public authorities in alleviating urban congestion. When implementing such integration, railway stations play a key role as urban hot-spots with limited access, where road–rail connections can facilitate efficient intermodal operations. In this work, we introduce a passenger-oriented pickup and delivery problem with explicit road–rail connections and a fleet of shared-use light vehicles. The problem is formulated as a mixed-integer linear program to jointly determine fleet size, routing, and scheduling plans, ensuring a balanced service quality for both passengers and freight. A decomposition-based matheuristic is developed that iteratively coordinates a routing-oriented master problem and a scheduling-oriented subproblem, with feasibility partially restored through a schedule-shifting strategy. The master problem is tackled using an adaptive large neighborhood search enhanced with variable neighborhood search, featuring a novel adaptive selection mechanism based on the relative contributions of service quality indicators. The resulting routing decisions are then passed to the scheduling subproblem, which is solved efficiently using a propagation-based approach that guarantees local optimality. Extensive sensitivity and benchmark analyses demonstrate the benefits of integrated transport in reducing delays, in particular in resource-constrained and demand-uncertain contexts.