Challenge simulating adoption of efficient technologies

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Thomas Fiddaman
Posts: 152
Joined: Thu Jan 15, 2009 6:55 pm
Location: Bozeman, MT

Re: Challenge simulating adoption of efficient technologies

Post by Thomas Fiddaman » Mon Nov 01, 2010 4:35 pm

After bumping into this thread at the Vensim forum I played with the models a bit.

The matrix seems promising, in that it directly tackles the question of what replacement choices people make. I implemented it (I think) in one of the attached models. However, I think there are some potential limitations.

First, the replacement cycle is possibly not the only constraint or driver of switching. For example, incandescent bulbs turn over quickly, but fixture compatibility is really the constraint on alternatives, so perhaps we should forget about bulbs, and model fixtures, driven by some kind of longer-term renovation cycle. (This is more a representation question than an equation issue I guess.)

Second, the specific choice matrix is a bit too nonlinear. The relationship between replacement and (equilibrium stock)/(actual stock) is continuous, but has a discontinous derivative - for example it abruptly hits a floor at (equilibrium stock) = (actual stock). Also, the fact that there is 100% replacement when a stock is below its equilibrium value seems at odds with the interpretation as randomized choice, which would imply at least some switching behavior even when a stock is near equilibrium.

Third, modeling purchases as the aggregate of replacements neglects the stock level itself as a driver of purchases. In other words, if sales[tech] = share[tech]*retirements, things are fine as long as bulbs are conserved. But as soon as there's some other mechanism for bulb disappearance (a vandal shatters them?) there needs to be a stock adjustment process to restore balance. In that case, another term is needed, e.g.: sales[tech] = share[tech]*retirements + (desired stock[tech] - actual stock[tech])/time to adj stock. (This may be how the Analytica version works, but I didn't check). Similarly, people might decide to switch technologies independent of bulb lifecycle, thereby idling some bulbs and causing the total stock in use to exceed that needed to fill all sockets, but a replacement-only approach won't do that.

It might help to write down the reality checks that a good formulation would observe. (Several are already in the .doc specification attached above, but a succinct list is nice.) The ones in the Vensim documentation of allocation problems are at least partially relevant.

I've posted two model variants (Vensim .vpm) that implement the replacement-matrix approach (my interpretation) and something closer to "standard" sd (which has its own limitations). An interesting test for both is to override the "change in attractiveness" for incandescents with a sin wave from -1 to 1 with a period of about 10. These are based on JJ's version from the Vensim forum ... p?tid=4257 and may be found in the same thread. They use arrays, so they require the Model Reader or an advanced version to run.


Reality Checks for allocation (from the Vensim documentation):

1. Conservation of Matter: The amount received by the demanders (summed across all demanders) must be equal to the amount provided by the suppliers (summed across all suppliers).

2. Nonnegative: All quantities allocated must be positive or zero.

3. Conservation of Intent: No supplier shall provide more than it desired to supply and no demander shall receive more than it has chosen to demand. (Less, however, is possible).

4. No Loopholes: Under conditions of adequate supply, each demander should receive its stated demand. Under conditions of adequate demand, each supplier should supply its stated supply.

5. Clear Differentiation: When there is insufficient supply, extremely low priority demanders should receive little or nothing and extremely high priority suppliers should receive everything or almost everything. Conversely, when there is excess supply extremely unattractive suppliers should provide little or nothing and extremely attractive suppliers should provide the bulk of the demand.

6. Continuity: Small changes in priorities, supply and demand should cause small changes in the resulting allocations. Smoothness, which requires that small changes cause only small changes in the derivative of the allocations is also often desirable.

Jean-Jacques Lauble

Re: Challenge simulating adoption of efficient technologies

Post by Jean-Jacques Lauble » Wed Nov 03, 2010 12:44 pm

Hi Tom

I studied both of your models. Both converge more quiclky than mine, because I was initially presuming that the total amount of light bulbs in service could be varying.
The standard approach works a little better than the matrix one. But the real problem is that one presumes that the people replacing the bulbs are acting to reach a certain percentage of technogy use.
How is it possible to predict this? AS Bob said it is the rate of replacement that will determine how each technology will be used and not the reverse.
One should add some more informations about the conditions of installing the bulbs, their cost, how much it costs to change the installation etc..
The time horison is too irrealistic. But I presume that it is only a mathematical problem with no relation with any reality.
And even if it is the goal of vendors, nothing guarantees that the buyers will act correspondingly.
There is something missing in the definition of the problem as explained by Cory. This is a bit simplistic and too easy. By the way, he seems to have disappeared!
Building the model using reality checks may work well, but at the condition that one has sufficient information about how the reality could behave in the future or eventually behaved in the past, supposing that the behaviour stays the same.

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