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| Notations | Variable description |
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| Sets and parameters |
| Set of buses heading toward the target stop, , where denotes the number of the incoming buses in the control area. Each incoming bus is denoted as bus |
| Bus whose berth index is the largest at the target stop when the optimization is conducted |
| Number of passengers alighting from bus at the target stop |
| Number of passengers boarding bus at the target stop |
| Average number of passengers on bus |
| Number of passengers on bus before arriving at the target stop |
| Weight of the delay of bus |
| A sufficiently large number |
| A sufficiently small positive value |
| Number of berths at the target stop |
| Service time for bus , s |
| Acceptable schedule delay, s |
| Safety headway between two successive buses, s |
| Time taken by a bus to decelerate to or accelerate from a berth, s |
| Time taken by a bus to traverse a berth, s |
| Earliest/latest arrival time of the arrival time window of bus at the target stop, s |
| Prescheduled departure time of bus , s |
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| Decision variables |
| Arrival time of bus at the target stop, s |
| Departure time of bus from the target stop, s |
| Berth index assigned to bus |
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| Auxiliary variables |
| 1, if bus departs later than bus arrives; otherwise, 0 |
| 1, if bus arrives earlier than bus ; 0, otherwise |
| Unacceptable schedule delay of bus to be penalized |
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