PulP:添加聚合变量的约束

import pulp

# 创建一个线性规划问题实例
model = pulp.LpProblem("Production_Planning", pulp.LpMaximize)

# 定义决策变量
x_A = pulp.LpVariable('Product_A', lowBound=0, cat='Continuous')
x_B = pulp.LpVariable('Product_B', lowBound=0, cat='Continuous')

# 定义目标函数（总利润）
profit_A = 10  # 每单位产品A的利润
profit_B = 15  # 每单位产品B的利润
model += profit_A * x_A + profit_B * x_B, "Total_Profit"

# 添加资源约束（例如，原材料限制）
resource_limit = 100  # 总原材料限制
model += 2 * x_A + 3 * x_B <= resource_limit, "Resource_Constraint"

# 添加需求约束
demand_A = 40  # 产品A的需求量
demand_B = 30  # 产品B的需求量
model += x_A <= demand_A, "Demand_Constraint_A"
model += x_B <= demand_B, "Demand_Constraint_B"

# 定义聚合变量
x_Total = pulp.LpVariable('Total_Production', lowBound=0, cat='Continuous')

# 添加聚合变量的约束
model += x_Total == x_A + x_B, "Aggregated_Variable_Constraint"

# 添加总产量约束
max_total_production = 70  # 最大总产量限制
model += x_Total <= max_total_production, "Max_Total_Production_Constraint"

# 求解模型
model.solve()

# 输出结果
print("Status:", pulp.LpStatus[model.status])
print("Product A:", pulp.value(x_A))
print("Product B:", pulp.value(x_B))
print("Total Production:", pulp.value(x_Total))
print("Total Profit:", pulp.value(model.objective))