Multimodal Transportation Pricing Alliance Design: Large-Scale Optimization for Rapid Gains

TL;DR

This paper presents a large-scale optimization model for multimodal transportation alliances that jointly sets fares and discounts, improving service quality, coverage, and equity while reducing costs and emissions.

Contribution

It introduces a novel two-stage decomposition approach for solving a complex, non-convex fare-setting optimization problem in multimodal transit alliances.

Findings

The proposed method significantly outperforms benchmarks in solution quality and speed.

Different alliance priorities lead to distinct fare strategies and system impacts.

The model effectively balances profit, equity, and passenger satisfaction objectives.

Abstract

Transit agencies have the opportunity to outsource certain services to established Mobility-on-Demand (MOD) providers. Such alliances can improve service quality, coverage, and ridership; reduce public sector costs and vehicular emissions; and integrate the passenger experience. To amplify the effectiveness of such alliances, we develop a fare-setting model that jointly optimizes fares and discounts across a multimodal network. We capture commuters' travel decisions with a discrete choice model, resulting in a large-scale, mixed-integer, non-convex optimization problem. To solve this challenging problem, we develop a two-stage decomposition with the pricing decisions in the first stage and a mixed-integer linear optimization of fare discounts and passengers' travel decisions in the second stage. To solve the decomposition, we develop a new solution approach combining tailored coordinate descent, parsimonious second-stage evaluations, and interpolations using special ordered sets. This approach, enhanced by acceleration techniques based on slanted traversal, randomization and warm-start, significantly outperforms algorithmic benchmarks. Different alliance priorities result in qualitatively different fare designs: flat fares decrease the total vehicle-miles traveled, while geographically-informed discounts improve passenger happiness. The model responds appropriately to equity-oriented and passenger-centric priorities, improving system utilization and lowering prices for low-income and long-distance commuters. Our profit allocation mechanism improves outcomes for both types of operators, thus incentivizing profit-oriented MOD operators to adopt transit priorities.