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

Table 1

Related studies.

Citation	Considering social welfare	Fare structures		Considering subsidy	Demand pattern
		FF	DBF		Many-to-many elastic demand
Chien and Spasovic [8]	✓	✓	—	—	✓
Chien and Tsai [10]	—	✓	✓	—	✓
Wang and Deng [12]	—		✓	✓	✓
Huang et al. [17]	—		✓	✓	✓
Jara-Díaz and Gschwender [19]	✓	✓	—	✓	—
Basso and Silva [20]	—	✓	—	✓	—
Zhou et al. [23]	—	✓	—	✓	—
Wang et al. [24]	—	✓	✓	✓	✓
Sun et al. [25]	✓	✓	—	✓	—
Ling et al. [26]	—	✓	—	✓	—
This study	✓	✓	✓	✓	✓