OS3307_Lab5_Group1.ipynb

Kernel: Python 2 (SageMath)

# load packages
import numpy as np
import pandas as pd
import scipy.stats as stats
import matplotlib.pyplot as plt
import matplotlib as mlab
import os

# set up directory structure
cwd= os.getcwd()
wd = os.path.join(cwd, 'output')
rd = os.path.join(cwd, 'data')

# setting up bernoulli for 10,000 trials
n = 10000
p = .8
over_booked = np.random.binomial(n, p, size=None)
regular = n - over_booked

print(over_booked)
print(regular)

7960
2040

MINOR_THRESHOLD = 9691.05
MAJOR_THRESHOLD = 7627.47
p2 = .9
people = 100
total_people = 0
sum_overbooked = 0
count = 0
total_profit = 0
penalty = []
profit = []
bumpd_ppl = []
total = []
minor = 0
major = 0

for i in range(over_booked):
    total_people = np.random.binomial(people, p2, size=None)
    total.append(total_people)
    
    if(total_people < 85):
        over = 0
        
    else:
        count += 1
        over = total_people - 85
    
    bumpd_ppl.append(over)
    
    penalty = []
           
    for j in range(over):   
        penalty.append(np.random.normal(loc=500, scale=50, size=None))
    profit.append(150*people - sum(penalty))
    if ((150*people - sum(penalty)) <= MINOR_THRESHOLD):
        minor+=1
    if ((150*people - sum(penalty)) <= MAJOR_THRESHOLD):
        major+=1

for k in range(regular):
    profit.append(150*85)

print('Avg amount of people who show: %d' %np.mean(total))
print('flights with people bumped: %d' %count)
print('proportion of flights with at least one person bumped: %f' %(count /10000.00))
print('Total profit: $%f' %sum(profit))
print('Avg profit: $%f' %np.average(profit))
print('Mean number of bumped passengers: %d' %np.mean(bumpd_ppl))
print('Median number of bumped passengers: %d' %np.median(bumpd_ppl))
print('Minor: ',minor)
print('Major: ',major)

Avg amount of people who show: 90
flights with people bumped: 7664
proportion of flights with at least one person bumped: 0.766400
Total profit: $125106458.689245
Avg profit: $12510.645869
Mean number of bumped passengers: 5
Median number of bumped passengers: 5
('Minor: ', 169)
('Major: ', 1)

import scipy as stats
# Histogram of avg profits
plt.hist(profit, bins=20, color='b', label = "Profits")
plt.xlabel('Profit per flight in dollars')
plt.ylabel('Frequency')
plt.show()

import scipy as stats

# Boxplot of avg profits
fig, ax = plt.subplots()
ax.set_ylabel('Avg Profit per Flight')
ax.boxplot(profit)
plt.show()

df = pd.DataFrame(profit)
df.describe()

	0
count	10000.000000
mean	12510.645869
std	1264.216672
min	7473.379200
25%	11664.940479
50%	12750.000000
75%	13097.768792
max	15000.000000

# Boxplot of number of people bumped
fig, ax = plt.subplots()
ax.set_ylabel('People Bumped per Flight')
ax.boxplot(bumpd_ppl)
plt.show()

# Boxplot of people who show for a flight
fig, ax = plt.subplots()
ax.set_ylabel('People Who Show to Overbooked Flights')
ax.boxplot(total)
plt.show()

# If never overbooked
raw_profit = (85*150*10000)
print('profit if never overbooked: $%d' %raw_profit)
print('avg profit per flight: $%d' %(raw_profit/10000))

profit if never overbooked: $127500000
avg profit per flight: $12750

# Extra Credit to optimize profit
p3 = .9
flights = 10000
people2 = 93
total_people2 = 0
count2 = 0
penalty2 = []
optimal = []
bumpd_ppl2 = []

for j in range(flights):
    total_people2 = np.random.binomial(people2, p3, size=None)
    if(total_people2 < 85):
        over2 = 0
    elif(total_people2 > 100):
        count2 += 1
        over2 = 100
    else:
        count2 += 1
        over2 = total_people2 - 85
    bumpd_ppl2.append(over2)  
    penalty2 = []
    for j in range(over2):   
        penalty2.append(np.random.normal(loc=500, scale=50, size=None))
    optimal.append(150*people2 - sum(penalty2))

print('flights with people bumped: %d' %count2)
print('proportion of flights with at least one person bumped: %f' %(count2 /10000.00))
#print(total_profit)
print('Total profit: $%f' %sum(optimal))
print('Avg profit: $%f' %np.average(optimal))
print('Mean number of bumped passengers: %f' %np.mean(bumpd_ppl2))
print('Median number of bumped passengers: %f' %np.median(bumpd_ppl2))
print('Optimal number of tickets: %d' %people2)

# Histogram
plt.hist(optimal, bins=20, color='b', label = "Profits")
plt.xlabel('Profit per flight in dollars')
plt.ylabel('Frequency')
plt.show()

flights with people bumped: 4031
proportion of flights with at least one person bumped: 0.403100
Total profit: $136540559.097811
Avg profit: $13654.055910
Mean number of bumped passengers: 0.590900
Median number of bumped passengers: 0.000000
Optimal number of tickets: 93