Profit Maximization Model with Fare Structures and Subsidy Constraints for Urban Rail Transit

Qing Wang,Lianbo Deng,Paul Schonfeld

doi:10.1155/2021/6659384

Abstract

This paper analyzes government subsidies based on the service design (i.e., headway) and fare structures of an urban rail transit system while considering necessary financial support from the government. To capture the interactions among the operator performance, government subsidies, and passengers in an urban rail transit system, a profit maximization model with nonnegative profit constraint is formulated to determine the optimal fare and headway solutions. Then, the social welfare that results from the operator profit maximization model is analyzed. Finally, a numerical example from Changsha, China, is employed to verify the feasibility of the proposed model. The major results consist of optimized solutions for decision variables, i.e., the fares and train headways, as well as subsidies to the operator. The fare elasticity factor under two fare structures significantly affects fares and demand. As the fare elasticity factor increases, the social welfare gradually decreases and a deficit occurs at low fares and demand, while subsidies rise from 0 to ¥24658.00 and ¥38089.16 under the flat fare and distance-based fare structures.

Highlights

In recent decades, large-scale investment by local authorities in China has greatly promoted the pace of urban rail transit (URT) construction and operation
Since fares are closely related to operator profit and subsidies, the implementation of fare differentiation is one of the practical policies adopted in public transport management [6]
A model was developed to optimize the transit fare structure with demand elasticity, but with a fixed service frequency [7]. en, Chien and Spasovic [8] proposed a model that optimized fares by considering demand without excessively simplifying spatial characteristics and demand patterns. e work of Chien and Spasovic [8] was extended by Sharaby and Shiftan [9], who studied the impacts of fares on demand and travel behavior. e optimization of fares has often been related to the service frequency, which has been investigated by many researchers

Summary

Introduction

Large-scale investment by local authorities in China has greatly promoted the pace of urban rail transit (URT) construction and operation. Wang and Deng [12] developed a model for optimizing distance-based fare structure (DBF) and headway by considering the maximum operator profit and minimum per capita subsidy for passengers. E present study only considers FF and DBF since these two are the most widely used fare structures in public transportation Another stream of the literature related to our work focuses on operator performance and passenger travel behavior. (i) is research comprehensively considers subsidy constraints and fare structures of URT system optimization to determine the operator performance and passenger travel behavior. (iii) We investigate the operator performance under the government’s subsidy constraints and different fare structures and compare the effectiveness of the two fare structures at attracting passenger demand and maximizing social welfare.

Preliminaries

Model Formulation

Numerical Study

Subsidy Discussion and Operator Performance

Findings

Proof Progress