Exact Set Packing in Multimodal Transportation with Ridesharing System for First/Last Mile

TL;DR

This work addresses improving first/last mile transit by integrating public transit with ridesharing in a centralized system (MTRS). It formulates two core optimization problems—MTRS-minDist and MTRS-minNum—using a hypergraph-based ILP and proves NP-hardness, while offering approximation algorithms (GreedyMinDist, GreedyMinNum, LS) and a clustering heuristic (CL) to scale to city-wide data. The authors provide rigorous theoretical analyses and practical evaluations on real Chicago data, showing substantial rider time savings and favorable trade-offs between solution quality and computation time, especially when clustering is employed. The study demonstrates that ridesharing-enabled FM/LM coordination can meaningfully reduce total driving distance and number of designated drivers, enhancing urban mobility and reducing emissions.

Abstract

We propose a centralized transportation system that integrates public transit with ridesharing to provide multimodal transportation. At each time interval, the system receives a set of personal drivers, designated drivers, and public transit riders. It then assigns all riders to drivers, ensuring that pick-ups and drop-offs occur at designated transit stations. This effectively replaces first-mile/last-mile (FM/LM) segments with a ridesharing alternative, reducing overall commuting time. We study two optimization problems: (1) minimizing the total travel distances of drivers and (2) minimizing the number of designated drivers required to serve all riders. We show the optimization problems are NP-hard and give hypergraph-based integer linear programming exact algorithm and approximation algorithms. To enhance computational efficiency, we introduce a clustering heuristic that utilizes both spatial and temporal aspects of the input data to accelerate rider-to-driver assignments. Finally, we conduct an extensive computational study using real-world datasets and surveys from Chicago to evaluate our model and algorithms at a city-wide scale.

Figures (2)

• Figure 1: The hypergraph $H(U\cup V,E,w)$ with $k = \lambda$. The blue edges belong the solution found by Algorithm LS, the red edges belong to an optimal solution, and black edges are the rest of edges in $H$. Since there are $\lambda^2$ blue edges and $\lambda$ red edges, the approximation ratio is $\lambda$.
• Figure 2: The road-map is viewed as 8 sectors of cells, centered at $g(3,3)$. The blue area is the diagonal sector $sec_1$, the green area is the diagonal sector $sec_2$, and the orange area is the right horizontal sector, and so on.

Theorems & Definitions (18)

• Lemma 2.1
• proof
• Theorem 2.1
• proof
• Lemma 2.2
• Theorem 2.2
• Lemma 3.1
• proof
• Lemma 3.2
• proof