[Paper Review] Seamless Multimodal Transportation Scheduling

Arvind U. Raghunathan, David Bergman+3 more|arXiv (Cornell University)|Jul 25, 2018

Transportation and Mobility Innovations33 references20 citations

TL;DR

This paper proposes a decision diagram-based branch-and-price model for seamless multimodal transportation scheduling, optimizing last-mile ride-hailing coordination with mass transit to minimize travel time and vehicle trips. It solves real-world-sized instances (10,000 passengers, 50 destinations, 600 vehicles) in under one minute, demonstrating orders-of-magnitude speedup over prior methods while maintaining high solution quality through destination-based passenger aggregation.

ABSTRACT

Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for the first-mile or last-mile passenger transportation in coordination with a mass transit service to provide a seamless multimodal transportation experience for the user. A system that provides passengers with predictable information on travel and waiting times in their commutes is immensely valuable. We envision that the passengers will inform the system of their desired travel and arrival windows so that the system can jointly optimize the schedules of passengers. The problem we study balances minimizing travel time and the number of trips taken by the last-mile vehicles, so that long-term planning, maintenance, and environmental impact are all taken into account. We focus on the case where the last-mile service aggregates passengers by destination. We show that this problem is NP-hard, and propose a decision diagram-based branch-and-price decomposition model that can solve instances of real-world size (10,000 passengers spread over an hour, 50 last-mile destinations, 600 last-mile vehicles) in computational time (~1 minute) that is orders-of-magnitude faster than other methods appearing in the literature. Our experiments also indicate that aggregating passengers by destination on the last-mile service provides high-quality solutions to more general settings.

Motivation & Objective

• To design a seamless multimodal transportation system integrating last-mile ride-hailing with mass transit for improved commute predictability and efficiency.
• To jointly optimize passenger schedules and last-mile vehicle routing to minimize total travel time and number of trips.
• To address the computational challenge of large-scale multimodal scheduling by developing a scalable optimization framework.
• To evaluate the effectiveness of aggregating passengers by destination in achieving high-quality solutions for complex scheduling problems.
• To demonstrate the practical viability of the approach on real-world-sized instances through computational experiments.

Proposed method

• The authors develop a branch-and-price decomposition model using state-of-the-art decision diagrams (DDs) to represent feasible schedules efficiently.
• Each destination is modeled via a separate decision diagram that encodes valid groupings of passengers and their departure times from the terminal.
• The DD construction ensures that all passenger arrival time windows are respected and that vehicle capacity constraints are enforced.
• The method leverages dynamic programming principles to compactly represent the exponential number of possible groupings using state nodes that track passenger indices and vehicle load.
• A pricing subproblem is solved iteratively using the DD to generate promising columns (i.e., feasible vehicle trips) in a branch-and-price framework.
• The approach exploits the structure of the problem by assuming all passengers on a trip share the same destination, enabling efficient state space compression.

Experimental results

Research questions

• RQ1 Can a decision diagram-based branch-and-price approach solve large-scale multimodal transportation scheduling problems in real-time computational time?
• RQ2 How effective is passenger aggregation by destination in approximating optimal solutions for complex last-mile scheduling problems?
• RQ3 What is the computational performance gain of the proposed method compared to existing approaches in the literature?
• RQ4 To what extent does the model maintain solution quality when simplifying the scheduling problem through destination-based aggregation?
• RQ5 Can the proposed framework handle real-world-sized instances (e.g., 10,000 passengers, 50 destinations, 600 vehicles) within acceptable time limits?

Key findings

• The proposed decision diagram-based branch-and-price model solves real-world-sized instances (10,000 passengers, 50 destinations, 600 vehicles) in approximately 1 minute, which is orders-of-magnitude faster than existing methods.
• The model proves that the last-mile scheduling problem with passenger aggregation by destination is NP-hard, justifying the need for advanced optimization techniques.
• Aggregating passengers by destination yields high-quality solutions that are competitive with more general, unconstrained formulations, validating the modeling assumption.
• The decision diagram construction ensures correctness by enforcing arrival time windows and vehicle capacity constraints through state-based tracking of passenger indices and load.
• The method achieves optimal or near-optimal solutions by leveraging the structure of the problem and efficient column generation via dynamic programming.
• Theoretical analysis confirms that the decision diagram has O(n_d · v_cap · T_w) arcs and O(n_d · v_cap) nodes, enabling scalable computation.