PuLP minimize weighted average of a selection

Question

I am stuck setting up a proper objective function for the minimization of a weighted average.

Exercise: For a portfolio of fixed income securities (ie bonds) find the selection of bonds to sell that generates a minimum gain. Within that constraint, minimize the weighted average yield of the selection of bonds.

The relevant data fields are Yield , Current Face Value and Current Profit or Loss . The weighted avg yield of the selection is the sumproduct of Yield and Current Face Value , divided by sum of Current Face Value . Continuous or Binary decision variables are acceptable.

This post is similar to my issue... Optimizing A Loan Portfolio On Weighted Average Criteria

I picked up PulP quicker than Scipy but I can use whatever package is best suited for this type of problem.

import pandas as pd
from pulp import *

d = {
      'Current Face Value':[173669.3, 219544.4, 253647.88, 256776.38, 264824.02, 348820.44, 415053.58, 475354.13, 643773.24, 781129.21, 866839.35, 866013.93, 974840.18, 1053465.32, 1074261.8, 1097979.35, 1112974.78, 1125646.64, 1216768.1, 1231914.2, 1423300.7, 1462152.67, 1642708.16, 1679005.31, 1625365.08, 1708252.62, 1765860.7, 1763888.76, 1828103.0, 1833238.25, 1796976.58, 1973474.26, 2027289.74, 2058402.54, 2186044.1, 2185605.23, 2222353.6, 2260944.05],
      'Current Profit or Loss':[-1613.81, 6546.25, 1965.83, 431.56, 1653.4, -556.95, 3192.99, 1732.18, -870.51, 16216.16, 140.5, -11624.28, 13347.67, 37106.55, 1638.02, 11903.53, 22179.76, 16074.41, 34904.67, 12146.89, 3976.73, -4810.06, -11510.87, 44416.35, 11475.39, 24260.51, 11766.51, 14648.76, 12272.55, 12255.15, -33461.55, -18799.52, 35814.91, 41468.95, 8442.11, 41645.9, 51555.44, -3333.12],
      'Yield':[2.118191, 3.381024, 3.723284, 3.567963, 3.381002, 3.554571, 1.786467, 3.585767, 2.061981, 3.395873, 1.895965, 1.41617, 2.935917, 3.140995, 3.103661, 2.157629, 2.400065, 2.231383, 2.941482, 2.172782, 2.086372, 2.128788, 2.400682, 3.497868, 2.094667, 2.667469, 2.308526, 2.513017, 2.326085, 2.306328, 2.685972, 2.001348, 2.806967, 3.659145, 2.203806, 3.201562, 2.839683, 1.462699],
    }
data = pd.DataFrame(d)

data_gains = data[data['Current Profit or Loss'] > 0].reset_index(drop=True)    # securities with gains
data_losses = data[data['Current Profit or Loss'] <= 0].reset_index(drop=True)  # securities with losses
print('Secs w/ gains:',str(len(data_gains)),'  Secs w/ losses: '+str(len(data_losses)))

prob = LpProblem('Portfolio Selection',LpMinimize)

# decision variables
decision_variables = []
for rownum, row in data_gains.iterrows():
    variable = pulp.LpVariable(str('x' + str(rownum)), lowBound = 0, upBound = 1, cat= 'Continuous')
    decision_variables.append(variable)
print ('Decision_variables: ' + str(len(decision_variables)))

# objective - minimize weighted avg yield of selection
wa_yield = []
for rownum, row in data_gains.iterrows():
    for i, flag in enumerate(decision_variables):
        if rownum == i:
            wa_yield.append(row['Current Face Value']*row['Yield']*flag)    # numerator of the proper objective
wa_yield = sum(wa_yield)
prob += wa_yield

# create constrains - total gain to be in this range
min_gain, max_gain = 100000, 150000

total_gain = []
for rownum, row in data_gains.iterrows():
    for i, flag in enumerate(decision_variables):
        if rownum == i:
            total_gain.append(row['Current Profit or Loss']*flag)
total_gain = sum(total_gain)

prob += (total_gain >= min_gain)
prob += (total_gain <= max_gain)

prob.solve()
print("Status:", LpStatus[prob.status])

result = []
for v in prob.variables():
    print(v.name, "=", v.varValue)
    result.append(v.varValue)

Answer 1

Try changing the two blocks with the string objects like so. I think you should be using optimizable functions since you already have your variables. You could also use numpy.sum

wa_yield = []
for rownum, row in data_gains.iterrows():
    for i, flag in enumerate(decision_variables):
        if rownum == i:
            wa_yield.append(row['Current Face Value']*row['Yield']*flag)    # numerator of the proper objective
wa_yield = sum(wa_field)
prob += wa_yield

...

total_gain = []
for rownum, row in data_gains.iterrows():
    for i, flag in enumerate(decision_variables):
        if rownum == i:
            total_gain.append(row['Current Profit or Loss']*flag)

total_gain = sum(total_gain)