我正在一个项目中，我需要根据百分比值数组细分整数值。 我的最终数组必须包含整数值，并且数组的总和必须等于初始整数。
下面是一个伪造的例子。我们列出了带有某些“潜力”的汽车，我们需要将此潜力分配给特定的邮政编码。邮政编码分配是由一些售罄信息决定的。
SELLOUTS_PER_P_CODE规定了每个邮政编码分配的权重。例如，对于第一辆车（car 1），p_code_3的权重很大，p_code_2的权重更小，p_code_1的权重更小，因此应该分别分配用于汽车1 p_code_1=1，p_code_2=2，p_code_3=4。
贝勒是问题的数学形式。
在这里，我正在使用pyomo来实现此公式，但是不会产生预期的结果。该模型未考虑来自SELLOUTS_PER_P_CODE
from pyomo.environ import *
from pprint import pprint
def distribute(total,weights):
scale = float(sum(weights.values())) / total
return {k: v / scale for k,v in weights.items()}
Cars = ["car 1","car 2","car 3"]
Locations = ["p_code_1","p_code_2","p_code_3"]
POTENTIALS = {"car 1": 7,"car 2": 2,"car 3": 14}
SELLOUTS = {"p_code_1": 0.2,"p_code_2": 0.3,"p_code_3": 0.5}
SELLOUTS_PER_P_CODE = {}
for car in Cars:
pot = POTENTIALS[car]
scaled_sellout = distribute(pot,SELLOUTS)
t = {(car,p_code): v for p_code,v in scaled_sellout.items()}
SELLOUTS_PER_P_CODE.update(t)
pprint(SELLOUTS_PER_P_CODE)
model = ConcreteModel(name="Breakdown Potential to Postal Code")
model.Cars = Set(initialize=Cars)
model.Locations = Set(initialize=Locations)
model.a = Param(model.Cars,model.Locations,initialize=SELLOUTS_PER_P_CODE)
model.p = Param(model.Cars,initialize=POTENTIALS)
model.X_pos = Var(model.Cars,within=NonNegativeIntegers)
model.X_neg = Var(model.Cars,within=NonNegativeIntegers)
def objective_rule(model):
return sum(
(model.X_pos[i,j] - model.a[i,j] * model.p[i])
- (model.X_neg[i,j] * model.p[i])
for i in model.Cars
for j in model.Locations
)
model.objective = Objective(rule=objective_rule,sense=minimize)
def sum_maintained_rule(model,i):
return (
sum(model.X_pos[i,j] for j in model.Locations)
+ sum(model.X_neg[i,j] for j in model.Locations)
== model.p[i]
)
model.sum_maintained = Constraint(model.Cars,rule=sum_maintained_rule)
def pyomo_postprocess(options=None,instance=None,results=None):
model.pprint()
if __name__ == "__main__":
opt = SolverFactory("glpk")
results = opt.solve(model)
results.write()
print("\nDisplaying Solution\n" + "-" * 80)
pyomo_postprocess(None,model,results)
最后这是不正确的输出。注意X_neg和X_pos的输出分配。
Displaying Solution
--------------------------------------------------------------------------------
5 Set Declarations
Cars : Dim=0,Dimen=1,Size=3,Domain=None,Ordered=False,Bounds=None
['car 1','car 2','car 3']
Locations : Dim=0,Bounds=None
['p_code_1','p_code_2','p_code_3']
X_neg_index : Dim=0,Dimen=2,Size=9,Bounds=None
Virtual
X_pos_index : Dim=0,Bounds=None
Virtual
a_index : Dim=0,Bounds=None
Virtual
2 Param Declarations
a : Size=9,Index=a_index,Domain=Any,Default=None,Mutable=False
Key : Value
('car 1','p_code_1') : 1.4000000000000001
('car 1','p_code_2') : 2.1
('car 1','p_code_3') : 3.5
('car 2','p_code_1') : 0.4
('car 2','p_code_2') : 0.6
('car 2','p_code_3') : 1.0
('car 3','p_code_1') : 2.8000000000000003
('car 3','p_code_2') : 4.2
('car 3','p_code_3') : 7.0
p : Size=3,Index=Cars,Mutable=False
Key : Value
car 1 : 7
car 2 : 2
car 3 : 14
2 Var Declarations
X_neg : Size=9,Index=X_neg_index
Key : Lower : Value : Upper : Fixed : Stale : Domain
('car 1','p_code_1') : 0 : 7.0 : None : False : False : NonNegativeIntegers
('car 1','p_code_2') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 1','p_code_3') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 2','p_code_1') : 0 : 2.0 : None : False : False : NonNegativeIntegers
('car 2','p_code_2') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 2','p_code_3') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 3','p_code_1') : 0 : 14.0 : None : False : False : NonNegativeIntegers
('car 3','p_code_2') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 3','p_code_3') : 0 : 0.0 : None : False : False : NonNegativeIntegers
X_pos : Size=9,Index=X_pos_index
Key : Lower : Value : Upper : Fixed : Stale : Domain
('car 1','p_code_1') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 1','p_code_1') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 2','p_code_1') : 0 : 0.0 : None : False : False : NonNegativeIntegers
('car 3','p_code_3') : 0 : 0.0 : None : False : False : NonNegativeIntegers
1 Objective Declarations
objective : Size=1,Index=None,active=True
Key : active : Sense : Expression
None : True : minimize : X_pos[car 1,p_code_1] - 9.8 - (X_neg[car 1,p_code_1] - 9.8) + X_pos[car 1,p_code_2] - 14.700000000000001 - (X_neg[car 1,p_code_2] - 14.700000000000001) + X_pos[car 1,p_code_3] - 24.5 - (X_neg[car 1,p_code_3] - 24.5) + X_pos[car 2,p_code_1] - 0.8 - (X_neg[car 2,p_code_1] - 0.8) + X_pos[car 2,p_code_2] - 1.2 - (X_neg[car 2,p_code_2] - 1.2) + X_pos[car 2,p_code_3] - 2.0 - (X_neg[car 2,p_code_3] - 2.0) + X_pos[car 3,p_code_1] - 39.2 - (X_neg[car 3,p_code_1] - 39.2) + X_pos[car 3,p_code_2] - 58.800000000000004 - (X_neg[car 3,p_code_2] - 58.800000000000004) + X_pos[car 3,p_code_3] - 98.0 - (X_neg[car 3,p_code_3] - 98.0)
1 Constraint Declarations
sum_maintained : Size=3,active=True
Key : Lower : Body : Upper : active
car 1 : 7.0 : X_pos[car 1,p_code_1] + X_pos[car 1,p_code_2] + X_pos[car 1,p_code_3] + X_neg[car 1,p_code_1] + X_neg[car 1,p_code_2] + X_neg[car 1,p_code_3] : 7.0 : True
car 2 : 2.0 : X_pos[car 2,p_code_1] + X_pos[car 2,p_code_2] + X_pos[car 2,p_code_3] + X_neg[car 2,p_code_1] + X_neg[car 2,p_code_2] + X_neg[car 2,p_code_3] : 2.0 : True
car 3 : 14.0 : X_pos[car 3,p_code_1] + X_pos[car 3,p_code_2] + X_pos[car 3,p_code_3] + X_neg[car 3,p_code_1] + X_neg[car 3,p_code_2] + X_neg[car 3,p_code_3] : 14.0 : True
11 Declarations: Cars Locations a_index a p X_pos_index X_pos X_neg_index X_neg objective sum_maintained