In sales forecasting, can improving forecast accuracy (1-MAPE) increase profits?
This article attempts to perform a random simulation through the classic newsboy model to observe the relationship between MAPE and profit.
1. Model setting
| Newsvendor Problem -- 30 Days |
|
| Purchase cost |
0.7 |
| Selling price |
1 |
| Salvage value |
0 |
| Demand parameter μ |
100 |
| Amount ordered each day q |
[80, 90, 100, 110, 120, 130] |
| Demand parameter ? σ |
taking values from 1 to 30 with an increment of 0.1 |
Second, the simulation code
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
#CONST
rounds = 30
c = 0.7 # purchase cost
s = 1 # selling price
u = 0 # salvage value
demand_mu = 100
color = ['b', 'g', 'r', 'c', 'm', 'y', 'k', 'w']
qs = [80]
# Demand
col = []
for demand_sigma in np.arange(1,30,0.1):
row = []
for _ in range(rounds):
demand = max(round(np.random.normal(demand_mu, demand_sigma),0),0)
while demand == 0:
demand = max(round(np.random.normal(demand_mu, demand_sigma),0),0)
row.append(demand)
col.append(row)
col = np.array(col)
df_demand = pd.DataFrame(col, columns=[ i+1 for i in range(30)])
# newsvendor model
fig = plt.figure(num=1, figsize=(10, 8),dpi=80)
i = 1
for q in [80, 90, 100, 110, 120, 130]:
df_sales_revenue = df_demand.applymap(lambda x: s * min(x, q))
df_salvage_revenue = df_demand.applymap(lambda x: u * max(0, q-x))
df_profit = df_sales_revenue + df_salvage_revenue - c * q
df_mape = df_demand.applymap(lambda x: abs(x - q)/x)
plt.subplot(2, 3, i)
plt.scatter(df_profit.mean(axis=1), df_mape.mean(axis=1), c=color[i-1])
plt.title('q = '+ str(q), size=26)
plt.xlabel('Profit', size=12)
plt.ylabel('MAPE', size=12)
i += 1
plt.legend(loc='best')
fig.tight_layout()#调整整体空白
plt.subplots_adjust(wspace =0.3, hspace =0.3)#调整子图间距
plt.savefig('./ppt素材/newsvendor_simulation.jpg') Third, the simulation results
Conclusion: At each order point, Profit increases with the decrease of MAPE and tends to stabilize.
