有没有最简单的多车场多车型vrp问题算例,帮我用lingo写一下
时间: 2024-02-21 08:01:22 浏览: 29
以下是一个简单的多车场多车型VRP问题算例,其中有两个车场,每个车场都有两种车型,每个车型都有一定数量的车辆。需要将一些客户点分配给这些车辆,使得每个客户点都被服务一次,并且满足车辆容量和行驶距离的限制。
```
Sets:
C set of customer points / c1*c6 /
V set of vehicle types / v1, v2 /
F set of facilities / f1, f2 /
K(V) set of vehicles for each vehicle type
v1 K(v1) = 1..3
v2 K(v2) = 1..2
P(V) set of maximum number of vehicles for each vehicle type
v1 P(v1) = 3
v2 P(v2) = 2
D maximum travel distance per vehicle / 200 /
Parameters:
d(c,*) demand of customer point c
x(c) x-coordinate of customer point c
y(c) y-coordinate of customer point c
s(v) maximum capacity of vehicle type v
t(v) travel time per unit distance of vehicle type v
c(f,v) fixed cost of using vehicle type v at facility f
c1(f) fixed cost of opening facility f
c2(c,v) variable cost of serving customer point c by vehicle type v
Variables:
q(c,k,v) quantity of customer point c served by vehicle k of type v
y(f,v) binary variable indicating whether facility f is open for vehicle type v
z(f,k,v) binary variable indicating whether vehicle k of type v is used to serve facility f
Equations:
obj objective function
cap capacity constraint
dem demand constraint
loc location constraint
open facility opening condition
serve service condition
dis distance constraint
obj.. sum((f,v), c(f,v)*y(f,v) + sum((c,k,v), c2(c,v)*q(c,k,v))) =E= sum((f), c1(f)*sum((v), y(f,v)));
cap(k,v).. sum((c), q(c,k,v)*d(c)) =L= s(v);
dem(c).. sum((k,v), q(c,k,v)) =E= 1;
loc(c,k,v).. x(c)*sum((f), z(f,k,v)) =E= sum((f), x(f)*z(f,k,v));
open(f,v).. sum((k), z(f,k,v)) =L= y(f,v)*card(K(v));
serve(c,v).. sum((k), q(c,k,v)) =L= sum((f), sum((k), z(f,k,v)));
dis(f,k,v).. sum((c1,c2), sqrt(sqr(x(c1)-x(c2)) + sqr(y(c1)-y(c2)))*sum((c), q(c,k,v))) =L= D*y(f,v);
model multidepotmultivehiclerouting /all/;
option limrow=0, limcol=0, solprint=off, sysout=off;
* Insert model instance data here
solve multidepotmultivehiclerouting using mip maximizing obj;
* Insert post-solve output display here
```
请注意,这只是一个简单的算例,实际情况可能更加复杂。在使用Lingo编写代码时,请根据您的实际需求进行相应的修改和扩展。