Can someone show me the basic structure of a s-shaped growth where I can control the top growth at the time, its end and the points of minimum and maximum absolute?
Thinking in terms of productivity curve of a fruit in time, for example: we know when the trees begin to produce and what is the expected initial production, we also know when the majority should be producing and what is the maximum expected production.
Thank you in advance.
Regards,
G.
S-shaped growth with maximum and minimum absolute points
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karankhosla
- Senior Member
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- Joined: Wed Nov 26, 2008 6:12 am
Dear Geamaro,
Please take a look at Business Dynamics (Sterman) page (333):
If I understand you correctly, you want a min value for the stock of "Adopters" when the model run begins and at some point in time you want it to saturate at a max value.
1) If your stock of "Adopters" starts at a value of zero, then you should use this Bass formulation. Bear in mind, that the "adoption rate" completely drains the stock of "Potential Adopters"; therefore the max value of "adopters" at some point in time, will be whatever was the initial value of the stock of "Potential Adopters" (provided there is no inflow into this stock).
2) However, if your stock of "Adopters" does not start a value of zero, then you can just use the logistic formula and set a max capacity (see Business Dynamics p296)
3) If you want to use the Bass formulation and you want at a max value for the "Adopters" stock in a more general form, then the adoption rate should be defined such that it adjusts accordingly as the adopter population gets closer to your max vaue. To do this (see model attached) you could define the "adoption rate" as MIN("max adoption rate", ("Adoption from Advertising" + "Adoption from Word of Mouth")). Please check the formulation of max advertising rate - this needs to be verified for its validity, but I think it should be something like this.
4) In the Bass formulation, controlling the rate of growth "adoption rate", can be done by increasing "advertising effectiveness" and/or "contact rate" to move the curve ahead in time or vice versa. If you're using the logistic curve you can increase/decrease the fractional growth rate - as per the analytical solution the maximum growth rate occurs when the Adopter population reaches half the maximum capacity.
My Best,
Karan
[Edited on 7-31-2010 by karankhosla]
Please take a look at Business Dynamics (Sterman) page (333):
If I understand you correctly, you want a min value for the stock of "Adopters" when the model run begins and at some point in time you want it to saturate at a max value.
1) If your stock of "Adopters" starts at a value of zero, then you should use this Bass formulation. Bear in mind, that the "adoption rate" completely drains the stock of "Potential Adopters"; therefore the max value of "adopters" at some point in time, will be whatever was the initial value of the stock of "Potential Adopters" (provided there is no inflow into this stock).
2) However, if your stock of "Adopters" does not start a value of zero, then you can just use the logistic formula and set a max capacity (see Business Dynamics p296)
3) If you want to use the Bass formulation and you want at a max value for the "Adopters" stock in a more general form, then the adoption rate should be defined such that it adjusts accordingly as the adopter population gets closer to your max vaue. To do this (see model attached) you could define the "adoption rate" as MIN("max adoption rate", ("Adoption from Advertising" + "Adoption from Word of Mouth")). Please check the formulation of max advertising rate - this needs to be verified for its validity, but I think it should be something like this.
4) In the Bass formulation, controlling the rate of growth "adoption rate", can be done by increasing "advertising effectiveness" and/or "contact rate" to move the curve ahead in time or vice versa. If you're using the logistic curve you can increase/decrease the fractional growth rate - as per the analytical solution the maximum growth rate occurs when the Adopter population reaches half the maximum capacity.
My Best,
Karan
[Edited on 7-31-2010 by karankhosla]
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