如何在Pyomo中实现此价格弹性问题的需求约束？

Question

我目前是一名SAS用户，正在过渡到Python，我正在尝试转换一个程序，该程序可以根据先前的需求、价格和弹性系数来优化价格。

然而，我在制定需求约束时遇到了一些麻烦。

在这个问题中，我卖的是苹果和/或橙子；但是，我只能卖出100种商品的总和。此外，这两个项目的价格必须是相同的价格，因为我只允许一个价格。

以前，我以5.00美元的价格卖出了60个苹果，以5.00美元的价格卖出了30个橙子，弹性系数分别为-2.5和-1.5；然而，我之前卖了90个水果，但我被允许卖出100个水果的总和。那么，优化收入所需的价格是多少？

我使用的是来自https://pyomocontrib-simplemodel.readthedocs.io/en/latest/的pyomocontrib-simplemodel，我使用的求解器是来自https://www.coin-or.org/download/binary/Ipopt/的Ipopt二进制文件，并且我运行了示例问题，没有出现任何问题。

我已经测试了各种示例问题，并且能够很好地运行它们。

在SAS中，用于约束的公式最初来自这里：http://support.sas.com/documentation/cdl/en/ormpex/66104/HTML/default/viewer.htm#ormpex_ex21_sect009.htm

我根据需要修改了SAS代码，使其看起来像这样(我验证了它在SAS中工作正常)：

   con Demand_con {i in PRODUCTS}:
      (Demand[i] - prev_demand[i]) / prev_demand[i]  
     = sum {PRODUCTS} elasticity[i] * (Price - prev_price[i]) / prev_price[i];

但是，我一直在尝试使用Python中的pyomocontrib-simplemodel包来复制这个约束。

在Pyomo中，我的尝试如下所示：

m += ((demand[i]-prev_demand[i])/prev_demand[i] for i in products) == sum(elasticity[i] * ( price - prev_price[i]) / prev_price[i] for i in products)

下面是完整的代码：

# Price Elasticity
from pyomo.contrib.simplemodel import *

# Input Variables
products = {'Apples','Oranges'}
prev_demand = {'Apples':60, 'Oranges':30}
elasticity = {'Apples':-2.5, 'Oranges':-1.5}
prev_price = {'Apples':5.00, 'Oranges':5.00}
supply = 100

# Create empty model
m = SimpleModel(maximize=True)

# Variables
price = m.var('price', within=NonNegativeReals)
demand = m.var('demand', products, within=NonNegativeReals)

# Objective
m += sum(price*demand[i] for i in products)

# Demand Constraint - Broken
m += ((demand[i]-prev_demand[i])/prev_demand[i] for i in products) == sum(elasticity[i] * ( price - prev_price[i]) / prev_price[i] for i in products) 

#Supply Constraint
m += sum(demand[i] for i in products) <= supply

# Optimize
status = m.solve('ipopt')

# Print the status of the solved NLP
print("Objective = %f" % value(m.objective()))

下面是我在制定需求约束时遇到的错误: AttributeError：'generator‘对象没有属性'is_expression_type’

我还尝试了这个语法：

# Demand Constraint - Broken
for i in products:
    m += ((demand[i]-prev_demand[i])/prev_demand[i]) == sum(elasticity[i] * ( price - prev_price[i]) / prev_price[i])

我得到的错误是: TypeError：'ProductExpression‘对象不可迭代

正确的答案应该是苹果和橙子的价格应该在4.87美元左右。

Answer 1

    # Price Elasticity
    from pyomo.contrib.simplemodel import *

    # Input Variables
    products = {'Apples','Oranges'}
    prev_demand = {'Apples':60, 'Oranges':30}
    elasticity = {'Apples':-2.5, 'Oranges':-1.5}
    prev_price = {'Apples':5.00, 'Oranges':5.00}
    supply = 100

    # Create empty model
    m = SimpleModel(maximize=True)

    # Variables
    price = m.var('price', within=NonNegativeReals)
    demand = m.var('demand', products, within=NonNegativeReals)

    # Objective
    m += sum(price*demand[i] for i in products)


    # Demand Constraint - Broken
    for i in products:
        m += (demand[i]-prev_demand[i])/prev_demand[i] == sum(elasticity[i]  * ( price - prev_price[i])  / prev_price[i] for i in products)


    #Supply Constraint
    m += sum(demand[i] for i in products) <= supply

    # Optimize
    status = m.solve('ipopt')

    # Print the status of the solved NLP
    print("Status = %s" % status.solver.termination_condition)
    print("Objective = %f" % value(m.objective()))
    for i in products:
        print("%s = %f" % (demand[i], value(demand[i])))
    print("%s = %f" % (price, value(price)))

这使我得到了以下输出：

状态=最佳，目标= 486.111115，demandApples = 66.666667，demandOranges = 33.333334，价格= 4.86111

足够接近，我相信像XPRES而不是IPOPT这样的商业求解器可能会输出不同的答案。