Comments on: Math on the simplified market adoption s-curve for Excel

By: Juan Carlos Méndez-García

Juan Carlos Méndez-García — Thu, 20 Nov 2008 05:18:53 +0000

Jaimin – Apologize for the delay responding – I’ve been swamped with work. Could you please elaborate on your comment? Take a look at http://www.lieb.com/NEWS22/2nd.htm
Is that along the lines you need?

By: Jaimin Mahadevia

Jaimin Mahadevia — Mon, 17 Nov 2008 19:41:52 +0000

Anyone have a macro for the “broken stick rule” which describes impact of order of entry.

By: Juan Carlos Méndez-García

Juan Carlos Méndez-García — Thu, 24 Jul 2008 06:40:59 +0000

@Edward – I have trouble understanding your problem description.
“during the life of the project, it is estimated to use 45GB of space” — Are you going to add data each month data[m] so SUM(data[m] for m=1..24) ~= 45GB, right?
Then, Growth is NOT =f(m) as you tried.

If I understand correctly, total_data[m] = f(m), where f is my formula with parameters saturation=45 [GB], hypergrowth=4, takeover=14.

It is somewhat counter intuitive to define takeover in terms of a takeover_rate applied over a growth table. takeover is simply an assessment of when you believe the technology is “mature” or “quite adopted”.

With that you would have an S-shaped curve that grows from 0GB to ~45GB by month 24.

The rest of your variables, you would derive backwards, and it would be something like
data[m]=growth[m]=total_data[m]-total_data[m-1] assuming total_data[0]=0
growth_pct[m]=growth[m]/total_data[m] if I define growth_pct as the percentage by which the data grows each month versus the accumulated data. Other ways to define growth (month over month, etc) can be also derived backwards very easily.

However, that doesn’t jive with your other statements “What I need, is the month Growth total never to exceed estimated total size (45GB) and total Growth % to equal 100%. Make sense?”

Nope. I’m confused.

Is 45GB then the maximum allowable growth for a month? That would be described as follows:
For any i in 1..24 data[i]< =45GB, which is quite different from SUM(data[m] for m=1..24) ~= 45GB

With that formulation, it explains that you got ~151GB for total space.

Two more questions...
"total Growth % to equal 100%"... at which month?
Why you chose saturation = 25%

Hope it helps. I would recommend to check http://en.wikipedia.org/wiki/System_dynamics to help you clarify which variables you want to model as “stocks” and which ones are “flows”

By: Edward

Edward — Mon, 21 Jul 2008 18:57:55 +0000

Thanks a lot… I worked on the formula over the weekend and figured it out.

However, I’m now having one other problem… hope you don’t mind looking at.
————————
Let’s say you have a project starting on 1/1/07 and during the life of the project, it is estimated to use 45GB of space. I want to calculate monthly growth and track total growth. My table has 3 columns (Month, Growth, % Growth). Month should be 1 – 23, Growth = % * Data_Volume, and % Growth = f(month).

I’ve tried several different things:
1. Calculating % Growth = f(month) – ends up getting 151GB & 335% for total space.
2. Calcuating % Growth = current f(month) – prior f(month) – now get 11GB and 24% for total space.

What I need, is the month Growth total never to exceed estimated total size (45GB) and total Growth % to equal 100%. Make sense?

Thanks for all your help.

Conditions:
1. Base_month = 1
2. # of Project Months = 24
3. Saturation = 25%
4. Hypergrowth = 4 (=ROUND(takeover*0.3,0))
5. Taekover = 14 (=ROUND((MAX(Monthly_Growth_Table[Month])*takeover_rate),0))
6. takeover_rate = 60%
7. Data_Volume = 45GB

By: Juan Carlos Méndez-García

Juan Carlos Méndez-García — Fri, 18 Jul 2008 05:41:02 +0000

@Edward The model works regardless the time units, as long as everything is consistent. Let's say saturation is 25, hypergrowth is month 8, and takeover is month 28. So when you use the same formula f(month)=saturation/(1 + 81^((hypergrowth + takeover/2 - month)/takeover)) you would have for different months


Month   f(Month)
5 1.62
10 3.30
15 6.25
20 10.55
25 15.39
30 19.46
35 22.12

By: Edward

Edward — Thu, 17 Jul 2008 19:40:26 +0000

Juan,

Your example shows in years. However, I need to do my calculations in months, tried to convert, but doesn’t work correct. Any suggestions?

By: Juan C. Mendez’s pages » Blog Archive » System dynamics interpretation of the logistic and Bass models

Fri, 21 Dec 2007 20:08:49 +0000

[...] regarding the Simplified Excel Model for market adoption that I published a few months ago. Reader Vince asked how to extend the math behind it to comprehend effects like cross-segment [...]

By: Vince

Vince — Thu, 20 Dec 2007 14:03:44 +0000

Juan,

I was wondering if there is a way to develop a Bass Model to predict how a technology cascades (technology spillover) from one segment to another segment within a given industry. For example, how a technology cascades from a luxury segment to a compact segment within the automotive industry.

By: Juan C. Mendez

Juan C. Mendez — Thu, 01 Nov 2007 03:07:38 +0000

I just posted a screencast that should help with using the model

By: Juan C. Mendez

Juan C. Mendez — Tue, 31 Jul 2007 03:14:40 +0000

Bob – Thanks for your comment. I just posted an entry that addresses your question. http://jcandkimmita.info/jc/2007/07/business/relationship-between-the-bass-and-the-logistic-market-adoption-models/.

By: Bob

Bob — Tue, 31 Jul 2007 00:16:56 +0000

Very interesting. How does this relate to the Bass diffusion model? ( http://en.wikipedia.org/wiki/Bass_diffusion_model ). I suppose I could examine the formulas to find out, but thought you might have already looked into this?

By: Juan C. Mendez’s pages » Blog Archive » Modeling market adoption in Excel with a simplified s-curve

Sat, 07 Jul 2007 03:30:49 +0000

[...] is a simple implementation in Excel that can be easily added to your spreadsheets. It reduces all the math to just three [...]

Month	f(Month)
5	1.62
10	3.30
15	6.25
20	10.55
25	15.39
30	19.46
35	22.12