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This paper investigates a distance-based preferential fare scheme for park-and-ride (P&R) services in a multimodal transport network. P&R is a sustainable commuting approach in large urban areas where the service coverage rate of conventional public transport modes (e.g., train and bus) is poor/low. However, P&R services in many cities are less attractive compared to auto and other public transport modes, especially for P&R facilities sited far away from the city center. To address this issue, this paper proposes a distance-based preferential fare scheme for P&R services in which travelers who choose the P&R mode get a discount. The longer the distance they travel by train, the better the concessional price they get. A multimodal transport network equilibrium model with P&R services is developed to evaluate the impacts of the proposed distance-based fare scheme. The travelers’ mode choice behavior is modeled by the multinomial logit (MNL) discrete choice model, and their route choice behavior is depicted by the user equilibrium condition. A mathematical programming model is then built and subsequently solved by the outer approximation method. Numerical simulations demonstrate that the proposed distance-based preferential fare scheme can effectively motivate travelers to use a P&R service and significantly enhance the transport network’s performance.

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Advanced strategies for emergency logistics scheduling problems in urban transport networks have been a challenging topic for centuries. This study proposed a cluster-first route-second constructive heuristic method based on the continuous approximation (CA) for ‘one-to-many’ vehicle routing to dispatch commidities after an emergency. The objective of the study is to provide a replenish schedule and routing solution from the government/provider’s end in order to minimize the total motion cost, pipeline inventory cost, and holding cost with backorder for the disaster relief operation. The developed method can turn the complicated vehicle routing problem (VRP) into a relatively simple travel salesman problem (TSP) for pre-assigned customer sets. The CA is employed to determine the optimal replenish amount and inventory level for the route serving a given location. The Christofides method is then applied to solve the TSP for the selected cluster. Two clustering methods are investigated in this research: (1) a local-based approach where clustering and routing are determined; and (2) a K-mean clustering method where points are clustered upfront by the CA solution. A case study in Miami-Dade County in Florida to dispatch fuels from the depot to 72 gas stations is presented, demonstrating the proposed approach and comparing two clustering methods. The numerical results illustrate the effectiveness of the algorithms and conclude that the local-based clustering approach may yield a lower total cost with a higher motion cost.

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