﻿ 资金约束下单向共享电动汽车系统的充电站选址
 计算机系统应用  2019, Vol. 28 Issue (5): 208-214 PDF

Charging Station Location of One-way Shared Electric Vehicle System under Financial Constraints
ZHENG Jian-Guo, QI Guang-Hui
The Glorious Sun School of Business and Management, Donghua University, Shanghai 200050, China
Abstract: A method for optimizing the location of charging stations is proposed for the one-way shared electric vehicle system, with the consideration of rational capacity of charging station and the demand within the served area. Thus the problem of unbalanced vehicle inventory is solved and the customer demand is satisfied to the maximum. The method is based on the mixed integer programming model. The goal is to meet the revenue of the service, the operating cost of the station, and the depreciation cost of the vehicle. The objective function is to maximize the profit of the shared electric vehicle service provider. Finally, simulations are carried out to test the slack and performance of the method, and the model can solve large-scale problems in a reasonable time.
Key words: shared electric vehicle     shared electric vehicle system     charging station location     mixed integer programming     CPLEX

1 相关研究

2 问题定义

(1)车辆

(2)车站

(3)时间间隔

(4)运营操作

① 该系统是在预定的基础上运行并允许单程租用车辆. 在预定时, 用户的出发地点、到达地点、出发时间、到达时间是可获得的. 在预定做出的时间段, 车辆在用户在出发地点可访问的车站获得车辆; 并在到达地点可访问的车站停放. 假定每一次租赁都是从一个时间间隔的开始时开始, 然后在一个时间间隔结束时结束.

② 本文所建立的模型采用了电动汽车. 为了对电动汽车充电时间进行建模, 假设车辆返回车站后, 必须在车站停留一段固定的时间, 这代表了车辆的充电时间.

(5)需求中心(潜在车站)

(6)需求

① 在出发时间间隔开始时可从起始位置相应的车站获得车辆;

② 在到达时间时间间隔结束时到达位置相应的车站拥有停车位.

(7)成本和收入

3 实验分析

3.1 输入

(1) 索引和集合:

$p,j \in J$ : 潜在站点的索引;

$h,k \in H$ : 需求订单索引.

(2) 参数定义:

$V = \{ 1,\cdots,n\}$ : 为节点的集合;

$J = \{ 1,\cdots,m\}$ : 潜在车站的集合, 其中 $J \in V$ ;

${f_j}$ : 开放车站 $j$ 的成本, 它是关于充电站车位数量 ${C_j}$ 的线性函数;

${F_j}$ : 建造车站 $j$ 的固定成本;

$g$ : 电动汽车运行成本;

$G$ : 电动汽车购买成本;

$T = \{ 0,\cdots,\tau \}$ : 时间节点;

$k = \{ {O_k},{D_k},{T_k},{T_k} + {d_k},{P_k},{\delta _{ij}}\}$ : ${O_k}$ 为请求 $k$ 的起点; c为请求 $k$ 的终点, ${T_k}$ 为请求 $k$ 的起始时间, ${T_k} + {d_k}$ 为请求 $k$ 的终止时间, ${P_k}$ 为请求 $k$ 的利润; ${\delta _{ij}}$ 为请求 $k$ 的电量.

(3) 辅助变量:

 图 1 T时间内的需求K

 图 2 请求订单三部分

 图 3 请求最终的可行结果

1) Π←Φ

2) for k←1 to K

3) HkΦ

4) for i←1 to m

dOkiβ

6) for j←1 to m

7) if dDkiβ

8) b[h][Tk]=1

9) u[j][Tk+dk]=1

10) λ[h][j][Tk+dk+dk/ρ]=1

11) Ph={i, j, Tk+dk}

12) Hk=HkPh

13) H=HHk

14) return b, u, λ, H

$u_{hj}^t = 1$ : 请求 $h$ 所使用的车辆在 $t$ 时刻已经在车站 $j$ 充电, 否则为0;

$b_{hj}^t$ =1: 请求 $h$ 所要使用的车辆在 $t$ 时刻从车站 $j$ 出发, 否则为0;

$\lambda _{hj}^t$ =1: 请求 $h$ 所要使用的车辆在 $t$ 时刻已经在车站 $j$ 充电完成, 否则为0;

(4) 决策变量:

${u_h} = 1$ : 请求 $h$ 被服务;

$L_j^t$ : 车站 $j$ $t$ 时刻拥有的电动汽车的数量;

$L_j^0$ : 车站 $j$ 在0时刻拥有的电动汽车的数量;

${C_j}$ : 站点 $j$ 的能力;

${y_j}$ : 车站 $j$ 是否打开.

3.2 模型建立
 $Max(z) = \sum\limits_{h \in H} {{P_h}{u_h}} - \sum\limits_{p \in P} {{f_p}} {C_p}{y_p} - g\sum\limits_{p \in P} {L_p^0}$ (1)

s.t.

 $\sum\limits_{p \in P} {(\alpha + \beta {C_p}){y_p} + G\sum\limits_{p \in P} {L_p^0 \leqslant W} }$ (2)
 $\sum\limits_{h \in H} {{u_h} \leqslant 1}$ (3)
 ${u_h} \leqslant {y_p},\begin{array}{*{20}{c}} {}&{\forall h \in H,p \in {P_h}} \end{array}$ (4)
 $\sum\limits_{h \in H} {b_{hp}^t{u_h} \leqslant L_p^t}, \begin{array}{*{20}{c}} {}&{\forall p \in P,t \in T} \end{array}$ (5)
 $L_p^t + \sum\limits_h {(u_{hp}^t - b_{hp}^t){u_h} \leqslant {C_p}{y_p},\begin{array}{*{20}{c}} {}&{\forall p \in P,t \in T} \end{array}}$ (6)
 $L_p^t = L_p^{(t - 1)} + \sum\limits_{h \in H} {(\lambda _{hp}^t - b_{hp}^{(t - 1)}){u_h},\begin{array}{*{20}{c}} {}&{\forall p \in P,t \geqslant 1} \end{array}}$ (7)
 $0 \leqslant L_p^t \leqslant {C_p}{y_p},\begin{array}{*{20}{c}} {}&{\forall p \in P,t \geqslant 1} \end{array}$ (8)
 $L_p^0,{C_p} \in {{\rm Z}^ + }$ (9)
 ${u_h} \in \{ 0,1\}, \begin{array}{*{20}{c}} {}&{\forall h \in H} \end{array}$ (10)
 ${y_p} \in \{ 0,1\}, \begin{array}{*{20}{c}} {}&{\forall p \in P} \end{array}$ (11)

4 仿真实验

5 结论和展望

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