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Integrated User Matching and Pricing in Round-Trip Car-Sharing

Avalpreet Singh Brar, Rong Su, Gioele Zardini, Jaskaranveer Kaur

TL;DR

The paper tackles fleet inefficiency in round-trip car-sharing by enabling one-way requests through an integrated N-user matching and pricing framework. It formulates a Two-Stage ILP model that first determines incentive-based prices and then maximizes profit through chain-based matchings, with chain activation governed by a risk factor $\alpha$ and Gaussian price thresholds. Three objective variants—service rate, profit, and expected profit—are analyzed, with the expected-profit approach combining activation probability and chain value. Empirical results on real-world NYC data show the method significantly increases fleet utilization and profits, achieving up to a 35% boost in demand fulfillment and robust performance across parameter variations, underscoring practical relevance for dynamic fleet rebalancing and pricing in round-trip settings.

Abstract

Traditional round-trip car rental systems mandate users to return vehicles to their point of origin, limiting the system adaptability to meet diverse mobility demands. This constraint often leads to fleet under-utilization and incurs high parking costs for idle vehicles. To address this inefficiency, we propose a N-user matching algorithm which is designed to facilitate one-way trips within the round-trip rental framework. Our algorithm addresses the joint problem of optimal pricing and user matching through a Two-Stage Integer Linear Programming (ILP)-based formulation. In the first stage, optimal rental prices are determined by setting a risk factor that governs the likelihood of matching a set of N-user. The second stage involves maximizing expected profit through a novel ILP-based user-matching formulation. Testing our algorithm on real-world scenarios demonstrates an approximate 35\% increase in demand fulfillment. Additionally, we assess the model robustness under uncertainty by varying factors such as the risk factor (probability of user ride acceptance at the offered price), cost factor (rental cost-to-fare ratio), and maximum chain length.

Integrated User Matching and Pricing in Round-Trip Car-Sharing

TL;DR

The paper tackles fleet inefficiency in round-trip car-sharing by enabling one-way requests through an integrated N-user matching and pricing framework. It formulates a Two-Stage ILP model that first determines incentive-based prices and then maximizes profit through chain-based matchings, with chain activation governed by a risk factor and Gaussian price thresholds. Three objective variants—service rate, profit, and expected profit—are analyzed, with the expected-profit approach combining activation probability and chain value. Empirical results on real-world NYC data show the method significantly increases fleet utilization and profits, achieving up to a 35% boost in demand fulfillment and robust performance across parameter variations, underscoring practical relevance for dynamic fleet rebalancing and pricing in round-trip settings.

Abstract

Traditional round-trip car rental systems mandate users to return vehicles to their point of origin, limiting the system adaptability to meet diverse mobility demands. This constraint often leads to fleet under-utilization and incurs high parking costs for idle vehicles. To address this inefficiency, we propose a N-user matching algorithm which is designed to facilitate one-way trips within the round-trip rental framework. Our algorithm addresses the joint problem of optimal pricing and user matching through a Two-Stage Integer Linear Programming (ILP)-based formulation. In the first stage, optimal rental prices are determined by setting a risk factor that governs the likelihood of matching a set of N-user. The second stage involves maximizing expected profit through a novel ILP-based user-matching formulation. Testing our algorithm on real-world scenarios demonstrates an approximate 35\% increase in demand fulfillment. Additionally, we assess the model robustness under uncertainty by varying factors such as the risk factor (probability of user ride acceptance at the offered price), cost factor (rental cost-to-fare ratio), and maximum chain length.
Paper Structure (25 sections, 3 theorems, 34 equations, 10 figures, 1 table)

This paper contains 25 sections, 3 theorems, 34 equations, 10 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. N-User Matching Problem
  3. Round-Trip Car-Sharing System
  4. Components of N-User Matching Model
  5. Starting Station
  6. End Station
  7. Starting Timeslot
  8. End Timeslot
  9. Base Rental Price
  10. Travel Cost
  11. Price Threshold and Offered Price
  12. Mathematical Model
  13. Decision Variable
  14. Feasible Chain
  15. Chain Activation
  16. ...and 10 more sections

Key Result

Theorem III.1

If the price offered to each inactive user is $\hat{P}_{\hat{u}_i} = \mathcal{P}(\theta_{\hat{u}_i}, \alpha)$ such that $\mathbb{P}(P^*_{\hat{u}_i} < \mathcal{P}(\theta_{\hat{u}_i}, \alpha)) = \alpha$, then the probability that the chain $c$, becomes active is given by: where, $\hat{c} \subseteq c$ is a set of inactive users in $c$

Figures (10)

  • Figure 1: Graphic representation of a chain of matched users.
  • Figure 2: Price threshold function For inactive users.
  • Figure 3: $f_{P^*_{u_i}}(w)$: PDF of $P^*_{u_i}$ with parameters $(\mu_{u_i}, \sigma_{u_i})$.
  • Figure 4: Served user count vs. model.
  • Figure 5: Profit (USD/h) vs risk factor $\alpha$.
  • ...and 5 more figures

Theorems & Definitions (7)

  • Theorem III.1
  • proof
  • Example III.1
  • Theorem III.2
  • proof
  • Theorem III.3
  • proof