Challenge simulating adoption of efficient technologies

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Cory Welch
Posts: 6
Joined: Wed Nov 18, 2009 10:48 pm

Challenge simulating adoption of efficient technologies

Post by Cory Welch » Fri Oct 22, 2010 11:39 am

If any brilliant SD practitioners out there have any thoughts as to how to address the challenge posed in the attached document, I would be very appreciative.

It has to do with simulating the replacement of inefficient technologies (e.g., incandescent lightbulbs) with efficient technologies (e.g., CFLs) when the replacement technology has a very different lifetime than the efficient technology.

Best regards,

Cory Welch
SalesRatioProblem.docx
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Jean-Jacques Lauble

Re: Challenge simulating adoption of efficient technologies

Post by Jean-Jacques Lauble » Fri Oct 22, 2010 2:19 pm

Hi Cory

Go to the Vensim site where i have posted a Vensim model that does not use Little's law but a fixed delay instead of an exponential flow which seems more correct.
All stocks convere much more quickly than in your example.
The model can be read with the vensim model reader.
the address of the Vensim forum is:
http://ventanasystems.co.uk/forum/
Regards.
Jean-jacques Laublé

Robert Eberlein
Site Admin
Posts: 179
Joined: Sat Dec 27, 2008 8:09 pm

Re: Challenge simulating adoption of efficient technologies

Post by Robert Eberlein » Sat Oct 23, 2010 5:50 am

Hi Cory,

I have to admit I am very confused by the whole premise of the question. It seems to me the behavioral decision points are around the rates, the actual purchases of alternative lighting formats. The split between these in the installed base is a consequence of these decisions. I don't understand the logic by which it would become a cause.

Jean-Jacques Lauble

Re: Challenge simulating adoption of efficient technologies

Post by Jean-Jacques Lauble » Sat Oct 23, 2010 6:34 am

Here is joind a zip file with both models in vpm format that can be read with the Vensim Reader. The former .mdl could not be read with the Reader.
If there is problem with downloading the zip file, you can load from the vensim site at:
http://ventanasystems.co.uk/forum/viewt ... p?tid=4257
I have added a third model that smoothes the additions to avoid its fluctuations.
Regards.
Jean-Jacques Laublé
Attachments
technologies.zip
(28.59 KiB) Downloaded 628 times

Cory Welch
Posts: 6
Joined: Wed Nov 18, 2009 10:48 pm

Re: Challenge simulating adoption of efficient technologies

Post by Cory Welch » Mon Oct 25, 2010 11:00 am

Bob,

The issue is that if one wants to use common approaches to simulate market share among competing products (e.g., random utility theory using logit functions, or even simple payback acceptance curves), I feel one must apply these approaches to the desired equilibrium share of the technology stock, NOT the desired share of the sales. For instance, if I can estimate (e.g., using random utility theory, or even simple payback acceptance curves) that 30% of the population would, in equilibrium, desire CFLs and 70% of the population would desire incandescents, then I must assume that the stocks of these technologies will ultimately approach this split (of course, I also add in diffusion, which further slows the approach to the equilibrium share). The sales of these technologies will not approach the 70/30 split -- it will approach a 91/9 split since incandescents burn out, and therefore turn over, faster (assuming a lifetime of 2 years for incandescents and 9 years for CFLs).

Perhaps this isn't yet clear, but I do believe that when you have stocks of existing technologies that are turning over, the market share that you'll typically estimate using standard techniques applies to the total population of customers, and proportionately to the total stock of the technologies owned by those customers, rather than to the sales (or flow) of the technology replacements, which depend largely on the lifetime of the technologies.

I'll separately post one proposed solution to this problem.

Best regards,

Cory

Cory Welch
Posts: 6
Joined: Wed Nov 18, 2009 10:48 pm

Re: Challenge simulating adoption of efficient technologies

Post by Cory Welch » Mon Oct 25, 2010 11:11 am

OK, I’ll answer my own question in the hopes that someone may be able to use this.

A colleague of mine, Brad Rogers, came up with the attached matrices (see Excel file) that define how retirements from multiple competing stocks with different lifetimes should transfer to the flow of “additions” of new stocks. I think it’s a pretty elegant approach and does everything I hoped it would regarding the dynamics of the transition. See my reply to Bob regarding why I believe the desired market share (at least as I'm calculating it) applies to the stocks of these technologies rather than to the flows.

I'm happy to provide, for anyone interested, a very small test model to demonstrate this approach in Analytica. I’m not sure how one would make the attached matrix formulae generic (e.g., for any number of competing stocks) in Vensim or Stella (I haven’t tried), but I know how in Analytica, which the test model demonstrates. You can read it, if so inclined, by downloading a free Analytica Player from h[url]ttp://www.lumina.com/ana/player.htm[/url]. I don't seem to be able to upload that model here, however.

Best regards,

Cory
Turnover of competing stocks.xlsx
(9.93 KiB) Downloaded 674 times

Cory Welch
Posts: 6
Joined: Wed Nov 18, 2009 10:48 pm

Re: Challenge simulating adoption of efficient technologies

Post by Cory Welch » Mon Oct 25, 2010 11:39 am

Jean-Jacques,

Thank you very much for your reply. The one issue I noticed with your "gap" approach is that it permits the new sales (the inflow) to exceed the retirements (the outflow). So, the total stock of all 3 technologies would exceed the actual stock of lightbulbs in existence.The dynamics of the turnover should, I believe, not permit the turnover to occur more quickly than would be governed by retirements (unless of course you're simulating an early retirement program, which at least in this example, I am not).

See my other post for an alternate solution.

Best regards,

Cory

Cory Welch
Posts: 6
Joined: Wed Nov 18, 2009 10:48 pm

Re: Challenge simulating adoption of efficient technologies

Post by Cory Welch » Mon Oct 25, 2010 11:49 am

Analytica test model is attached as a *.zip file, for anyone interested.
Stock_Sales_Example3.zip
(2.46 KiB) Downloaded 625 times

Jean-Jacques Lauble

Re: Challenge simulating adoption of efficient technologies

Post by Jean-Jacques Lauble » Tue Oct 26, 2010 5:20 am

Hi Cory

I join a new model that leaves the total stock of light bulbs approximately stable, which was not the case in my previous model. I changed too the time step that smoothes the process automatically.
I will try to understand the real nature of your problem, studying the files you joined.
Regards.
Jean-Jacques Laublé
Attachments
technologies4.zip
(159.74 KiB) Downloaded 566 times

Jean-Jacques Lauble

Re: Challenge simulating adoption of efficient technologies

Post by Jean-Jacques Lauble » Tue Oct 26, 2010 12:00 pm

Hi Cory

I have tried to understand your problematic. But i must confess that I do not really understand it. it should maybe be useful to explain it in plain English, without any predefined solution in it, like the equilibrium condition. What is the purpose of the model? Maybe simplifying the problem to start with might be a good idea and generate more interests from the SD community?

The models I built suppose that one is trying to find the rate of replacement that would generate a new percentage of technologie use as quickly as possible. Once the rate of replacement is found one must organize prices and commercial action so as to generate these rates of adoption. The last model supposes that the total of light bulbs stay the same in the future.
There are certainly people in the SD community that are much more competent than me to help you.
Regards.
Jean-Jacques Laublé

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