Uses Monte Carlo Simulation to maximize profit. -- Newspaper demand per day is normally distributed. Can be done easily on excel.

0MonteCarloSimulationNewsvendor.py

import numpy as np
import math

'''Using MonteCarlo Simulation to maximize profit. 

A Newspaper boy can buy 100, 120, 140, or 160 newspapers/day/month.
He will only be able to buy same number of newspapers for the whole month.

For example, if he buys 100 newspapers/day/month, then he will not be able to 
buy 120, 140, or 160 newspapers in any day in that month.

The demand for newspaper in a day is normally distributed with mean of 135.70
and standard deviation of 27.10. 
 
Newspaper boy can buy at a Whole sale price of $0.55/paper. 
He can sell at a retail price of $1/paper.
He can sell the leftover newspapers at a scrap price of $0.03/paper.
 
In this problem, we want to find out whether the newspaper buy should buy
100, 120, 140, or 160 newspapers/day/month in order to maximize his average profit 
for the month (30 days).


T-Distribution for 95% confidence intervals.
alpha=0.025, dof=29 -> t=2.045
 '''
np.random.seed(0)

Days = 30

NewspaperBuyOptions = [100, 120, 140, 160]

WholeSalePrice = 0.55
RetailPrice = 1
ScrapPrice = 0.03

MeanDemand = 135.70
SDDemand = 27.10


AverageProfitForNewspaperBuy = [0, 0, 0, 0]

ProfitValues = [[], [], [], []]

StandardDeviation = []

ConfidenceIntervalsNewspaperBuy = [[], [], [], []]



# checks and gives error if this is not satisfied
assert len(NewspaperBuyOptions) == len(AverageProfitForNewspaperBuy) == len(ConfidenceIntervalsNewspaperBuy)



for day in range(Days):

    Demand = round(np.random.normal(MeanDemand, SDDemand))

    for i in range(len(NewspaperBuyOptions)):

        profit = (min(Demand, NewspaperBuyOptions[i]) * RetailPrice) + (max(NewspaperBuyOptions[i] - Demand, 0) * ScrapPrice) - \
                                           (NewspaperBuyOptions[i] * WholeSalePrice)

        AverageProfitForNewspaperBuy[i] += profit

        ProfitValues[i].append(profit)



for i in range(len(NewspaperBuyOptions)):
    AverageProfitForNewspaperBuy[i] /= Days



for i in range(len(ProfitValues)):
    StandardDeviation.append(np.std(ProfitValues[i], ddof=1))



for i in range(len(ConfidenceIntervalsNewspaperBuy)):
    ConfidenceIntervalsNewspaperBuy[i].append(AverageProfitForNewspaperBuy[i] -
                                              (2.045 * StandardDeviation[i])/math.sqrt(Days))
    ConfidenceIntervalsNewspaperBuy[i].append(
        AverageProfitForNewspaperBuy[i] + (2.045 * StandardDeviation[i]) / math.sqrt(Days))



for i in range(len(NewspaperBuyOptions)):
    print("\nIf {} newspaper/day/month is bought: \nAverage profit is {} "
          "\n95% Confidence Interval on Average Profit: {} ".format(NewspaperBuyOptions[i],
                                                                    AverageProfitForNewspaperBuy[i],
                                                                    ConfidenceIntervalsNewspaperBuy[i]))


print("\n140 newspapers/day/month seems to be the best choice to get maximum profit.")