Profit optimization of public transit operators: examining both interior and boundary solutions

Abstract

We concern the modal choice of commuters in a transport system comprising a highway and two transit lines. For the operation of the transit lines, two market structures are considered: monopolistic and duopolistic. The problem of optimizing the profit of each transit operator is formulated as an optimization model with equilibrium constraints. We theoretically prove that, to obtain both the interior and boundary solutions of the optimization model, it is sufficient to solve an alternative optimization model with equality constraints. For each market structure, we propose a period-to-period transit fare and auto toll scheme to maximize the profit of each transit operator and to simultaneously make the profit of each transit operator more than a certain value. Finally, by numerical examples, we show the effectiveness of the scheme in each market and the necessity of examining both the interior and boundary solutions of the optimization model.

KEYWORDS:

• Day-to-day dynamics
• period-to-period adjustment
• monopoly
• Bertrand-Nash duopoly
• bus fare and auto toll scheme

Acknowledgments

The work described in this paper was jointly supported by grants from the National Natural Science Foundation of China (71622005, 71890972/71890970), a grant from the Research Grants Council of the Hong Kong Special Administrative Region of China (HKU17218916), and a grant from the University Research Committee of the University of Hong Kong (201711159034). The authors extend their sincere thanks to the four anonymous referees for their constructive comments on this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

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Funding

The work described in this paper was jointly supported by grants from the National Natural Science Foundation of China (71622005, 71890972/71890970), a grant from the Research Grants Council of the Hong Kong Special Administrative Region of China (HKU17218916), and a grant from the University Research Committee of the University of Hong Kong (201711159034).