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| Notations | Definitions |
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| Sets |
| | Set of passengers, |
| | Set of buses, |
| | Set of bus stops on the bus line, |
| | Set of bus types, , representing the vehicle type, where represents small bus and represents a larger bus |
| | Set of bus lines, |
| | Set of metro lines, |
| | Set of passengers who choose to transfer to the metro at the truncation stop |
| | Set of passengers who choose to transfer to the bus at the truncation stop |
| Parameters |
| | Length of the original bus line (km) |
| | Length of new bus line (km) |
| | Average distance between bus stops (km) |
| | Average distance between metro stops (km) |
| | Theoretical maximum length of urban bus lines (km) |
| | The average speed of buses on a metro line (km/h) |
| | The average maximum travel time of 95% of the residents (minutes) |
| | The average speed of trains on a metro line (km/h) |
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| Notations | Definitions |
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| The average travel speed of bus (km/h) |
| Constant, passenger waiting time penalty critical value (minutes) |
| Constant, maximum number of transfers for passengers |
| Constant, maximum waiting time for passengers, (minutes) |
| Constant, maximum and minimum headway of vehicles (minutes) |
| The probability of passenger transferring to bus at truncation stop , |
| Bus ride time for passenger (minutes) |
| Average wait time at bus stop for passenger (minutes) |
| Metro ride time for passenger (minutes) |
| Average wait time at metro stop for passenger (minutes) |
| Crowding penalty coefficient (CNY/stop) |
| Passenger transfer penalty coefficient (CNY/person) |
| Value of time (CNY/h) |
| The penalty factor when waiting time is longer than (CNY/person) |
| Coefficient of crowding |
| The number of buses of type at line |
| Vehicle type operating cost per kilometer (CNY/km) |
| The ticket cost of riding the type bus (CNY/person) |
| The ticket cost of passenger when riding the metro (CNY/person) |
| The purchase cost of a single bus with vehicle type that is averaged to each day based on its service life (CNY/vehicle) |
| The salary of a single driver for bus type (CNY/person) |
| The total number of passengers in the original line |
| The maximum passenger capacity for bus type (person) |
| The headway of metro line (minutes) |
| The total number of stops in the original bus line |
| Minimum and maximum truncation stop limits |
| Transfer time for passenger at stop (minutes) |
| The maximum number of buses of type required in line |
| Auxiliary variables |
| | Total operating cost of buses (CNY) |
| | Total ticket cost for passengers (CNY) |
| | Total time cost of passenger travel (CNY) |
| | Total fixed cost of the bus company (CNY) |
| | Penalized total cost (CNY) |
| | Total travel cost of passengers (CNY) |
| | Total cost of the bus company (CNY) |
| | The number of passengers in bus at stop (person) |
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| Notations | Definitions |
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| Number of total passengers in an hour of line (person/h) |
| The total number of passengers transferring at stop (person) |
| The total number of passengers transferring to bus at the truncation stop (person) |
| The total number of passengers who transferring to metro at the truncation stop (person) |
| Binary variable, 1 if passenger passes through stop , and 0 otherwise |
| Binary variable, 1 if passenger chooses vehicle at the stop , and 0 otherwise |
| Binary variable, 1 if passenger in-vehicle alights at stop , and 0 otherwise |
| Binary variable, 1 if passenger chooses metro line , and 0 otherwise |
| Decision variables |
| | The bus headway of line (minutes) |
| | Binary variable, 1 if is the truncation stop, and 0 otherwise |
| | Binary variable, 1 if the waiting time of passenger is greater than , and 0 otherwise |
| | Binary variable, 1 if the number of passengers in-vehicle exceeds at stop , and 0 otherwise |
| | Binary variable, 1 if existing at least a metro stop near bus stop , and 0 otherwise |
| | Binary variable, 1 if the vehicle of type is in the line , and 0 otherwise |
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