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Coach Reservation for Groups Requests

Carlos H. Cardonha, Arvind U. Raghunathan

Abstract

Passenger transportation is a core aspect of a railway company's business, with ticket sales playing a central role in generating revenue. Profitable operations in this context rely heavily on the effectiveness of reject-or-assign policies for coach reservations. As in traditional revenue management, uncertainty in demand presents a significant challenge, particularly when seat availability is limited and passengers have varying itineraries. We extend traditional models from the literature by addressing both offline and online versions of the coach reservation problem for group requests, where two or more passengers must be seated in the same coach. For the offline case, in which all requests are known in advance, we propose an exact mathematical programming formulation that incorporates a first-come, first-served fairness condition, ensuring compliance with transportation regulations. We also propose algorithms for online models of the problem, in which requests are only revealed upon arrival, and the reject-or-assign decisions must be made in real-time. Our analysis for one of these models overcomes known barriers in the packing literature, yielding strong competitive ratio guarantees when group sizes are relatively small compared to coach capacity - a common scenario in practice. Using data from Shinkansen Tokyo-Shin-Osaka line, our numerical experiments demonstrate the practical effectiveness of the proposed policies. Our work provides compelling evidence supporting the adoption of fairness constraints, as revenue losses are minimal, and simple algorithms are sufficient for real-time decision-making. Moreover, our findings provide a strong support for the adoption of fairness in the railway industry and highlight the financial viability of a regulatory framework that allows railway companies to delay coach assignments if they adhere to stricter rules regarding request rejections.

Coach Reservation for Groups Requests

Abstract

Passenger transportation is a core aspect of a railway company's business, with ticket sales playing a central role in generating revenue. Profitable operations in this context rely heavily on the effectiveness of reject-or-assign policies for coach reservations. As in traditional revenue management, uncertainty in demand presents a significant challenge, particularly when seat availability is limited and passengers have varying itineraries. We extend traditional models from the literature by addressing both offline and online versions of the coach reservation problem for group requests, where two or more passengers must be seated in the same coach. For the offline case, in which all requests are known in advance, we propose an exact mathematical programming formulation that incorporates a first-come, first-served fairness condition, ensuring compliance with transportation regulations. We also propose algorithms for online models of the problem, in which requests are only revealed upon arrival, and the reject-or-assign decisions must be made in real-time. Our analysis for one of these models overcomes known barriers in the packing literature, yielding strong competitive ratio guarantees when group sizes are relatively small compared to coach capacity - a common scenario in practice. Using data from Shinkansen Tokyo-Shin-Osaka line, our numerical experiments demonstrate the practical effectiveness of the proposed policies. Our work provides compelling evidence supporting the adoption of fairness constraints, as revenue losses are minimal, and simple algorithms are sufficient for real-time decision-making. Moreover, our findings provide a strong support for the adoption of fairness in the railway industry and highlight the financial viability of a regulatory framework that allows railway companies to delay coach assignments if they adhere to stricter rules regarding request rejections.

Paper Structure

This paper contains 35 sections, 6 theorems, 38 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Technical Background and Challenges
  3. Contributions of this work
  4. Literature Review
  5. Problem Description and Notation
  6. Fairness Constraints
  7. First-Come, First Serviced
  8. Strict First-Come, First Serviced
  9. Online Extensions
  10. Random Order Model
  11. Arrival Rate
  12. Online Policies for $\textsc{CRP}$
  13. Mathematical Programming Formulation for the Offline $\overline{\textsc{CRP}}$
  14. $\textsc{CRP}$ in the Random Order Model
  15. Description of the Algorithm
  16. ...and 20 more sections

Key Result

Lemma 1

The expected revenue collected from request $r_i$ to OPT is $\mathop{\mathbb{E}}[ p(r_{i})] \geq \frac{OPT}{n}$.

Figures (5)

  • Figure 1: Map of the Tokyo-Shinosaka line (generated with Cartopy (Cartopy)).
  • Figure 2: Example of adversarial setting for FCFS fairness.
  • Figure 3: Performance profiles of heuristic policies for $\textsc{CRP}$-FCFS.
  • Figure 4: Performance profiles for $\textsc{CRP}$ policies over the selling horizon.
  • Figure 5: Performance of policies that observe fairness considerations.

Theorems & Definitions (12)

  • Example 1: Price of fairness
  • Remark 1: Safe assignments
  • Lemma 1: Expected Utility
  • Lemma 2: Profit per arrival
  • Theorem 1
  • Proposition 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • ...and 2 more