Table 2 Parameter and variable definitions.
Symbol type | Symbol | Meaning |
|---|---|---|
Set | \(V_{0,N + 1}\) | Vertex set,\(V_{0,N + 1} = V \cup \{ o\} \cup \{ N + 1\}\) |
\(V\) | Customer set,\(V = \{ 1,2,...,N\}\) | |
\(F\) | Charging station cluster,\(F = \{ 1,2,...,n\}\) | |
\(K\) | Vehicle Assembly,\(K = \{ 1,2,...,k\}\) | |
\(A\) | Graph Arc Set,\(A = \{ (i,j)|i \in V_{0,N + 1} \cup F,j \in V_{0,N + 1} \cup F,i \ne j\}\) | |
Parameter | \(R\) | Hazard area radius of impact |
\(S_{ij}\) | Area of the hazard area | |
\(d_{ij}\) | Distance between demand points \((i,j)\) | |
\(N_{ij}\) | The number of people at risk | |
\(P_{ij}\) | Probability of dangerous accidents | |
\(w_{ij}\) | The vehicle load from node \(i\) to node \(j\) | |
\(R_{th}\) | Risk threshold | |
\(P_{th}\) | Accident probability threshold | |
\(W\) | Vehicle capacity | |
\(h_{i}\) | The demand of node \(i\) | |
\(t_{i}^{k}\) | The time when vehicle k arrives at customer node \(i\), \(i \in V\),\(k \in K\) | |
\(t_{i,wait}^{k}\) | The possible waiting time for the vehicle at node \(i\),\(i \in V\) | |
\(C_{veh}\) | Unit vehicle use cost (YUAN) | |
\(C_{pelec}\) | Average unit charging cost (YUAN/kW•h) | |
\(T_{i}^{1}\) | Earliest time window for customer \(i\),\(i \in V\) | |
\(T_{i}^{2}\) | Latest time window for customer \(i\),\(i \in V\) | |
\(b_{ij}\) | Unit distance power consumption coefficient (kW•h/km) | |
\(C_{wait}\) | Waiting cost per unit time (YUAN/hour) | |
\(C_{penal}\) | Punishment cost per unit time (YUAN/hour) | |
\(C_{buy}\) | Vehicle purchase cost (YUAN) | |
\(B\) | Electric vehicle power battery capacity (kW•h) | |
\(B_{j}^{k}\) | Vehicle k’s battery level when leaving node \(j\),\(j \in V\) | |
Decision variable | \(x_{ij}^{k}\) | \(x_{ij}^{k} = 1\) indicates that vehicle k is in use, otherwise \(x_{ij}^{k} = 0,k \in K,j \in V \cup F\) |
\(y_{ij}^{k}\) | \(y_{ij}^{k} = 1\) Indicates that vehicle \(k\) goes to charging station \(j\) for charging after visiting node \(i\), otherwise \(y_{ij}^{k} = 0,k \in K,i \in V_{0} ,N + 1,j \in F\) | |
\(u_{j}^{k}\) | Represents the amount of electricity that vehicle k replenishes at charging station \(j\) | |
Intermediate variable | \(r_{ij}\) | The risk of vehicle k from node \(i\) to node \(j\) |
\(R_{total}\) | Total Transportation Risk | |
\(C_{fixed}\) | Vehicle fixed costs | |
\(C_{ch\arg e}\) | Charging cost | |
\(C_{time}\) | Time window penalty cost | |
\(\rho\) | Population density |
