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| Indices | Definition |
|
| Index of depot instances and every route starts at and ends at |
| Index of nodes, |
| Index of physical link between two adjacent nodes, |
| Sets |
| Set of recharging station |
| Set of dummy vertices of |
| Set of recharging visits including depot instance |
| Set of customers |
| Set of customers including depot instance |
| Set of nodes including customers and recharging stations, |
| Set of customers and recharging stations including depot instance , |
| Set of customers and recharging stations including depot instance , |
| Set of customers and recharging visits including depot instance and , |
| Parameters |
| Distance of link |
| Travel time of link |
| Recharging rate |
| The power demand for one electric car in node |
| Battery capacity for mobile charging service car |
| Charge consumption rate in traveling |
| Demand number of node and if does not belong to set V |
| Earliest start of service at node |
| Latest start of service at node , it is always a positive number of infinity |
| Service time at node |
| The node can provide the upper limit of electricity for recharging |
| The sufficiently large constant |
| Variables |
| The time of arrive at node |
| The recharging amount of electricity at node |
| if arc is traveled; otherwise |
| if arc is utilized; otherwise, is unrestricted |
| The remaining battery on arrival at node |
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