纸浆优化问题的绝对值公式

Question

我在下面分享了我正在尝试解决的问题的简化版本。我的表述一定有问题，也许是关于决策变量。模型将所有流发送到 Destination1，但我正在尝试构建一个可以均匀分布流的模型。当我强制 Destination2 接收带有附加约束的流量时，目标值会提高，所以我不确定为什么没有找到这样的解决方案，而不是找到不太理想的解决方案。

感谢您的想法，并很乐意回答有关此模型的任何问题。

Warehouses = ["A","B","C","D"]
origin_supply = {"A": 53, "B": 62, "C": 45, "D": 65}
Destinations = ['Destination1','Destination2']
Routes = [(o,d) for o in origin_supply for d in destinations]
model = LpProblem("Testing-absolute-value-objective", LpMinimize)

supply = [53,62,45,65]
destination_mean = sum(supply) / len(destinations)

# decision variables
route_vars = LpVariable.dicts("Route",(Warehouses,Destinations),cat = "Integer", lowBound = 0)
sum_for_diff = LpVariable.dicts("sum",(Destinations),cat = "Continuous")
sum_for_diff_abs = LpVariable.dicts("sum_abs",(Destinations),cat = "Continuous", lowBound = 0)

# objective function is to minimize the absolute value of the difference supplied to the two destinations
obj_func = lpSum(sum_for_diff_abs)

# constraints
# absolute value constraints for the difference
for d in destinations:
    model += sum_for_diff_abs[d] >= sum_for_diff[d]
    model += sum_for_diff_abs[d] >= -sum_for_diff[d]

# The supply constraints (in this case all supply must be sent)
for w in Warehouses:
    model += lpSum([route_vars[w][d] for d in Destinations]) == origin_supply[w]

# calculate the difference from the average amount sent to each destination 
# the reasoning is that in the full model there will be many destinations, so this logic could scale
for d in Destinations:
    model += sum_for_diff[d] == lpSum( route_vars[w][d] for w in Warehouses) - destination_mean 
    
model.solve() 
print(LpStatus[model.status])
print(pulp.value(obj_func))
for v in model.variables():
    print (v.name + " = " + str(v.varValue))

Answer 1

您没有设置目标函数。
这一行

obj_func = lpSum(sum_for_diff_abs)

应该是

model+= lpSum(sum_for_diff_abs)