*4.1. Assumptions*

To facilitate problem formulation, several assumptions are made as mentioned in Section 3. In this section, we summarize the assumptions to develop the route guidance strategies as follows:

**Assumption 1.** *The charging demand information considered in the route guidance strategies is assumed to include drivers' travel destinations and the remaining energy of vehicles.*

**Assumption 2.** *It is assumed that travel time and energy consumption for each link are constant during a separate time slot. Such an assumption conforms to the tra*ffi*c condition characteristic if the duration for each time slot is relatively short.*

**Assumption 3.** *The charging demands are assumed to occur in the normal nodes and the charging station nodes cannot generate charging demands. Such an assumption is reasonable because drivers seek help from the charging service provider only when they have di*ffi*culty finding nearby charging stations.*

**Assumption 4.** *Each normal node is assumed to generate at most one charging demand following a uniform distribution during a time slot. Meanwhile, it is assumed that at most one EV can leave a charging station after completing charging at each time slot. The assumptions conform to the actual situations if the duration for each time slot is relatively short.*

**Assumption 5.** *The charging service provider is assumed to know the information about the travel time and energy consumption on all the links at the beginning of each time slot.*

**Assumption 6.** *Without loss of generality, it is assumed that the routes with minimum energy consumption are selected as the travel routes between departure points and charging station nodes.*

**Assumption 7.** *It is assumed that EV drivers can reach their destinations by charging their vehicles only once, because EVs with a single charge often have su*ffi*cient energy to reach their destinations in an urban road network. For the routes from origins to charging stations, EV drivers prefer to focus on reachability rather than distance.*

**Assumption 8.** *Every charging demand is assumed to have at least one reachable charging station in a road network to guarantee a solution. For the special situation in which no reachable charging station exists, extra cost* *may be incurred in transporting the vehicles, such as through trailer services, which is not discussed in the route guidance strategies.*
