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@JimDuggan
JimDuggan committed Oct 10, 2024
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152 changes: 152 additions & 0 deletions Code/06 Modelling Introduction/Advertising Impact Stella Model.stmx
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<?xml version="1.0" encoding="utf-8"?>
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<header>
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<name>Advertising Impact Stella Model</name>
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<outflow>Loss_of_Impact</outflow>
</stock>
<flow name="Loss of Impact">
<eqn>Advertising_Impact*Loss_Fraction</eqn>
<non_negative/>
</flow>
<aux name="Loss Fraction">
<eqn>.1</eqn>
</aux>
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<pt x="630" y="328"/>
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<aux x="569" y="239" name="Loss Fraction"/>
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<from>Loss_Fraction</from>
<to>Loss_of_Impact</to>
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<from>Advertising_Impact</from>
<to>Loss_of_Impact</to>
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<table interval="DT" report_balances="beginning" report_flows="instantaneous" width="350" height="250">
<item type="time"/>
<item>
<entity name="Advertising_Impact"/>
</item>
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</model>
</xmile>

24 changes: 24 additions & 0 deletions Code/06 Modelling Introduction/Advertising_Euler.py
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import numpy as np
import pandas as pd


# define the function. For teh numerical solution, the function runs the
# entire simulation

def sim_advertising_impact_euler(init, time, DT, loss_fraction):
sim_out = np.zeros(len(time))
sim_out[0] = init
print(sim_out)
for i in range(1,len(time)):
net_flow = -sim_out[i-1]*loss_fraction
sim_out[i] = sim_out[i-1] + net_flow*DT
print("index",i,"time",time[i],"sim_out",sim_out[i])

return sim_out



DT = 0.25
time = np.arange(0,25,DT)
print(time)
sim_advertising_impact_euler(100,time,DT,0.1)
30 changes: 30 additions & 0 deletions Code/06 Modelling Introduction/Advertising_model.py
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import numpy as np
import pandas as pd

# This function needs: the initial value, the current time, and the decay rate,
def sim_advertising_impact(init_value, time,loss_fraction):
return init_value*np.exp(-loss_fraction*time)

# Create a time vector. The number of elements for this model is arbitrary.
time=np.arange(25)

# Create the simulation output array
sim=np.zeros(25)
# print("Time",time)
# print("Sim",sim)

# Set the initial condition for advertising impact = 100 (Percent)
init = 100

# Set the decay rate of 10% per time unit
lf = .1

# Run the model.
for i,t in enumerate(time):
sim[i] = sim_advertising_impact(init,t,lf)

# print("Sim",sim)

# Plot the results
s = pd.Series(sim, index=time);
s.plot(style="ko--",title="Advertising Impact",grid=True);
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