QUERY Age of material in a stock

[Richard Dudley <richard.dudle]

Posted by Richard Dudley <richard.dudley@attglobal.net>

Little's law can tell us about the length of time material is in a stock when the stock is in equilibrium.

Is there any way to _estimate_ the the length of time material is in a stock
when that stock is not in equilibrium? Or is this a complete unknown?

[ For those who don't recognize it - as I didn't - Little's law is simply

stock = average delivery delay * inflow

which I tend to think of as Jay's formulation that

average delivery delay = stock / outflow

where outflow = inflow in steady state. Jay's formulation is always
exactly true if the underlying delay distribution is exponential
(outflow = level/delay) - if not then only in equilibrium just like
Little's Law.]

Richard

____________________________

Richard G. DudleyPosted by Richard Dudley <richard.dudley@attglobal.net> posting date Fri, 13 Apr 2007 14:20:06 +0700 _______________________________________________

[Jean-Jacques Laublé <jean-jac]

Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr>

Hi Richard

As soon as the inputs and the outputs are varying you must consider if the material inside the stock is undifferentiated or not.
It can follow a FIFO law and you can then use discreet functions as you will find in Vensim.

If the material is undifferentiated and you use a first order exponential delay, I do not see any analytical solution (I am not sure that the Vensim functions do not work numerically).

You must calculate the time in stock using Jay's formulation and integrating it step by step.

This average time delivery will vary each time period, depending on the future inputs and outputs still to come.

I have a model that calculates the average time in stock with varying inputs and outputs for the material in the stock at the start of the simulation.
It must be reinitialised every day, to recalculate the new average.
Of course you must predict the inputs and outputs.

The average is becoming more and more precise as the time passes.
It becomes sufficiently precise after 100 days.

The model can be dowloaded from:

http://www.ventanasystems.co.uk/forum/

under the Sytem Dynamics Discussion forum and can be used with Vensim PLE.

I will build as soon as I have the time, a model that calculates the average time in stock not only for the initial stock, but for each new inputs to come.

It will probably use subscripts.

Regards.
Jean-Jacques Laublé
Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr> posting date Sat, 14 Apr 2007 18:16:32 +0200 _______________________________________________

[""Jack Homer"" <jhomer@comcas]

Posted by ""Jack Homer"" <jhomer@comcast.net>

Calculating average age of material in a stock is a special case of calculating any average attribute of a stock, for which the solution is a co-flow structure. See Sterman, Business Dynamics, Chapter 12.
The incoming attribute in this case is the time at which the material arrives into the stock. The co-flow structure gives the average time of arrival. Subtract that average time of arrival from the current time to get the average age.

Jack Homer
Posted by ""Jack Homer"" <jhomer@comcast.net> posting date Sun, 15 Apr 2007 09:01:34 -0400 _______________________________________________

[""Will Glass-Husain"" <wglass]

Posted by ""Will Glass-Husain"" <wglass@forio.com>

Dear Richard,

Good responses by both Jean-Jacques and Jack.

Actually, I'd say that the technique to estimate the age of materials in a stock depends on the type of stock.

For a homogeneous pool of materials, e.g. a classic ""bathtub"", then Jack's point is absolutely correct. Use a coflow structure to calculate the average time the material comes into each stock, then subtract from current time to calculate the average length the material is in the stock.

For a stock that represents a more sequential process, e.g. a shipping process, or a project management process, then the average time approach often doesn't make sense. The average time calculation will be incorrect if tasks in a project are executed in a FIFO (first-in-first-out) order inside the stock. This is more visible with some behavior patterns then others.
(for example, an inflow that shuts off completely will show a declining instead of constant time to process while material is still in the stock).

The iThink/STELLA software has a sophisticated cycletime capability, which trackes ""batches"" of items flowing into the stock at each DT. The modeler clicks a stopwatch at an upstream flow which invisibly timestamps each batch. The actual cycletime (amount of time from stopwatch to current time) can then be reported at any point downstream.

You can track the same information using a parallel stock/flow structure that is arrayed over time. I've created this using Forio Brodcast's simulation language but the concept would work with any modeling tool that supports arrays. The behavior of this model exactly replicates the results from the iThink cycletime function.

The link below is a simple web page showing one specific simulation run.
The model can be downloaded and applied to any stock/flow structure.

http://forio.com/simulation/cycletime/

Best regards,

WILL

--
Forio Business Simulations
Posted by ""Will Glass-Husain"" <wglass@forio.com> posting date Mon, 16 Apr 2007 11:14:49 -0700 _______________________________________________

[Tom Fiddaman <tom@ventanasyst]

Posted by Tom Fiddaman <tom@ventanasystems.com>

Another coflow approach:

There's no general rule that applies for all inputs.

One possibility is to add a coflow to the model to track time spent in the stock. This is implemented the way you'd track average experience of staff in a workforce model. In Vensim lingo that might look like:

average residence time= ZIDZ(stuff time,stuff) ~ weeks ~ |
stuff= INTEG ( stuff in-stuff out, 0) ~ widgets ~ |
stuff in= 1 ~ widgets/week ~ |
stuff out= stuff/time const ~ widgets/week ~ |
stuff time= INTEG ( time in-time out, 0) ~ widgets*weeks ~ |
time const= 3 ~ weeks ~ |
time in= stuff ~ widgets*weeks/week ~ |
time out= stuff out*average residence time ~ widgets*weeks/week ~ |

Note that I've initialized things to 0 for ease; initializing stuff_time needs special attention if the model's not starting in some obvious steady-state condition. Also, time in has an implicit dimensionless parameter (widget*weeks accrued per widget per passage of time). Whether this is appropriate depends on whether the underlying assumption that the stuff is well mixed is appropriate. If not, it's easy to extend this structure to a higher-order delay (e.g., tracking vintages of capital). If you go the vintaging route, it may not be critical to t rack the coflow, as summing the Little's Law assumption across the vintages is usually a pretty good approximation of the truth (as always, it's best to test though).

If you play with this, you'll find the expected steady state response. Replacing stuff_in with a pulse, a ramp, and exponential growth is interesting. It becomes apparent that for particular inputs, it is possible to create a rule of thumb, but I'll leave that for someone else to tackle.

Tom
Posted by Tom Fiddaman <tom@ventanasystems.com> posting date Mon, 16 Apr 2007 09:11:21 -0600 _______________________________________________

[""Jack Homer"" <jhomer@comcas]

Posted by ""Jack Homer"" <jhomer@comcast.net>

Tom Fiddaman writes:
""If you play with this, you'll find the expected steady state response. Replacing stuff_in with a pulse, a ramp, and exponential growth is interesting. It becomes apparent that for particular inputs, it is possible to create a rule of thumb, but I'll leave that for someone else to tackle.""

I addressed this topic in an appendix on co-flows in my 1983 doctoral thesis, looking at step changes and exponential growth in particular. If the fractional growth rate in the stock is 'G' and the average time-to-outflow is 'To', then with straightforward algebra one may show that the steady-state age in the stock 'As' is expressed simply as:

As = 1 / (G + (1/To))

In the case of zero stock growth (G=0), this reduces, as one would expect, to As = To. Positive growth in the stock leads to As<To, while negative growth in the stock leads to As>To.

This derivation assumes a first-order (single stock) process, with perfect mixing as Tom notes.

Jack Homer
Posted by ""Jack Homer"" <jhomer@comcast.net> posting date Tue, 17 Apr 2007 09:02:42 -0400 _______________________________________________

[Jean-Jacques Laublé <jean-jac]

Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr>

Hi everybody.

There is an ambiguity in the question of Richard.
Does he mean, the average total time material was in the stock or average delivery delay?
Or the current average age a material in a stock?
By the formulation of Little's law Richard probably means the first
formulation:
Average delivery delay = stock / outflow.
In equilibrium where inflow = outflow the average age of material in stock = Average delivery delay / 2.
A good approximation of the average delivery delay is the maximum age of material in stock.
If the distribution of the age is uniform in the stock, the maximum or delivery delay will be the double of the average.
This way surveying the average age of material in stock by a co-flow gives a good indication about how the delivery delay is moving if there is no sudden change in the input or output process and the input approximately equals to the output.
If the input is greater than the output, the non uniform distribution will make the average age less than half of the maximum and the approximation of the delivery delay by the average age in stock * 2 will underestimate the reality, and the opposite if the input is less than the output.
But I did not find any way to calculate the precise average delivery delay or total time in stock using co-flows.
The only way I found to calculate the average delivery delay is the model in the Vensim forum.
Regards.
Jean-Jacques Laublé
Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr> posting date Tue, 17 Apr 2007 12:43:24 +0200 _______________________________________________

[jhomer@comcast.net >]

Posted by jhomer@comcast.net

>Jean-Jacques Lauble writes:
>""In equilibrium where inflow = outflow the average age of material in
>stock = Average delivery delay / 2.

The above comments are accurate only in the case of a fixed or conveyor-belt delay, where the age distribution is uniform, but not in the case of standard bathtub structures in which perfect mixing within the stock is implicitly assumed, and the age distribution is exponential. With the perfect mixing assumed in a bathtub, the average age of material in an unchanging stock is equal to the average time-to- outflow (As=To), whereas in a conveyor-belt delay the average age of material in an unchanging stock is one-half of the time-to-outflow.

Jack Homer
Posted by jhomer@comcast.net
posting date Wed, 18 Apr 2007 12:24:40 +0000 _______________________________________________

[Tom Fiddaman <tom@ventanasyst]

Posted by Tom Fiddaman <tom@ventanasystems.com>

It's worth noting a few consequences of Jack's analysis:

- The fractional growth rate G is only constant for exponential growth or decay. Growth in the stock leading to As<To means the average age of material is younger than you'd expect from Little's Law because a disproportionate amount of material arrived recently. Little's law remains a good approximation as long as G is small compared to 1/To - that is, as long as growth is slow with respect to the lifetime of the stock.

- It would seem that As becomes negative when growth is negative, with -G > 1/To. Fortunately that can't happen; the inflow to the stock could quickly approach zero at some large negative growth rate, but the stock can decay at most as fast as the time constant of the outflow, To.
In that case, As = 1/0, and if you run the model with zero input, you will find that the average residence time does grow without bound. This makes sense - if you look in a box that's had zero inflow for a long time, anything in there has clearly been there for a long time.

- If the inflow is an increasing ramp, the stock comes into a different steady state. In this case the rate of increase in the stock is constant at S*To (where S is the slope of the input ramp), while the stock grows without bound. That means G (net increase rate divided by the stock) falls to zero, so after an initial transient, Little's Law holds as usual, As = To.

Tom
Posted by Tom Fiddaman <tom@ventanasystems.com> posting date Wed, 18 Apr 2007 08:59:25 -0600 _______________________________________________

[""Jay W. Forrester"" <jforest]

Posted by ""Jay W. Forrester"" <jforestr@MIT.EDU>

There has been much discussion recently about the proper way to evaluate age of items in a stock.

But there has been no discussion of why the answer matters.
Can someone supply some examples of where the way of computing age in a stock will alter the direction of policy recommendations to improve the behavior of a system?

---------------------------------------------------------
Jay W. Forrester
Professor of Management
Sloan School
Massachusetts Institute of Technology
Room E60-156
Cambridge, MA 02139
Posted by ""Jay W. Forrester"" <jforestr@MIT.EDU> posting date Thu, 19 Apr 2007 11:07:34 -0400 _______________________________________________

[""Jack Homer"" <jhomer@comcas]

Posted by ""Jack Homer"" <jhomer@comcast.net>

Jay Forrester asks:

""Can someone supply some examples of where the way of computing age in a stock will alter the direction of policy recommendations to improve the behavior of a system?""

My doctoral thesis in 1983 dealt with recommendations for government regulation and multi-year assessment (registry) of new medical products.
Registries are complicated by the fact that over time the range of product applications (sometimes called off-label usages) may change, which can, in turn, affect registry findings. In order to understand that effect, it was necessary to calculate the average time of follow-up of patient outcomes, that is, the average time since patients had entered the registry. That calculation affected my recommendations with respect to how the registry should be implemented; for example, the question of whether the registry should operate for only the first couple of years after first launch of the product, or for a longer period of time.

I didn't consider various different ways of computing the average time of patient follow-up. I was able to prove in my thesis that the co-flow approach was computationally correct, and so that's the approach I used.

Jack Homer
Posted by ""Jack Homer"" <jhomer@comcast.net> posting date Fri, 20 Apr 2007 08:14:26 -0400 _______________________________________________

[Tom Fiddaman <tom@ventanasyst]

Posted by Tom Fiddaman <tom@ventanasystems.com>

Pardon me while I dodge Jay's question and pursue the technical details a little further.

Richard Dudley and I wondered if Jack Homer's arrival-time-coflow structure
(ATCS) was equivalent to my time-integrating-coflow structure (TICS).
Richard got motivated and built the two versions in the same model for comparison. (The ATCS is appended to the end of this note; the other was in my original message, SD6403.)

It turns out that the two are nearly equivalent. Probably they are equivalent in principal as dt -> 0. However, there are minor differences in real world use. If you feed the structures a step in arrivals, they reach the same equilibrium, but differ in the first few time steps from the input step occurrence. This is because ATCS immediately yields a difference between arrival time and current time, while TICS needs a time step for time spent waiting to accumulate. This difference goes away as the time step gets small, as one would hope. I think the only occasion for worry would be if you were using a discrete time model and trying to replicate some sort of real-world data reporting mechanism in order to calibrate to it.

However, ATCS is subject to numerical problems, particularly with a small time step that is not a power of 2, and when time is large compared to the time constant (as if your model runs from 1980-2020 and your time constant is a few years). Then, ATCS calculates the average residence time as (current time - average accession date). This is a small difference of two big numbers, so roundoff error rears its ugly head, and the average age can be incorrect

Tom

time const= 3 ~ Year ~ |
average age= Time-average accession date ~ Year ~ | stuff in= 0 ~ widgets/Year [0,10,1] ~ | stuff out= stuff/time const ~ widgets/Year ~ |
stuff time= INTEG ( time in-time out, (INITIAL TIME-time const)*stuff) ~ widgets*Year ~ |
stuff= INTEG ( stuff in-stuff out, stuff in*time const) ~ widgets ~ |
time in= stuff in*Time ~ Year*widgets/Year ~ | average accession date= XIDZ(stuff time,stuff,Time) ~ Year ~ |
time out= stuff out*average accession date ~ widgets*Year/Year ~ |
Posted by Tom Fiddaman <tom@ventanasystems.com> posting date Fri, 20 Apr 2007 19:08:06 -0600 _______________________________________________

[""John W. Rodat"" <jwr@signal]

Posted by ""John W. Rodat"" <jwr@signalhealth.com>

Length of time of patients in a nursing home or institution can influence the potential for their discharge to home or other community based services.

The longer the time in the institutional stock, the higher the probability that patients' home supports have dissipated and that they themselves have become ""institutionalized."" Once a threshold is reached, such patients are no longer candidates for discharge.

John W. Rodat
Posted by ""John W. Rodat"" <jwr@signalhealth.com> posting date Fri, 20 Apr 2007 07:26:06 -0400 _______________________________________________

[""Magne Myrtveit"" <magne@myr]

Posted by ""Magne Myrtveit"" <magne@myrtveit.com>

Jay Forrester writes:


>>Can someone supply some examples of where the way of computing age in
>>a stock will alter the direction of policy recommendations to improve
>>the behavior of a system?

In Dynaplan we recently created a model to study the behaviour of the DSO (days sales outstanding) key figure. It is used to measure how long (in
average) it takes from a sale is made until payment is received from the customer. If sales go up or down, payment terms are changed, or customers change behaviour, this will be reflected in the account receivables stock (and hence, in the DSO). Different ways to compute the DSO might influence the (transient) behaviour of this key figure when sales and/or payment flows change.

Since investors make use of the DSO measure (together with other key
figures) to make investment decisions, the particular way to measure DSO might actually influence decisions.

In our concrete case, the objective was not to come up with the best way to compute the DSO, but rather to understand how the DSO would react over time in different scenarios (decreasing sales, increasing number of unhappy customers who delay payments or refuse to pay, extension of payment terms, etc.)

Best regards,

Magne Myrtveit

PS
I have made two blogs that might interest people who work with system dynamics and spreadsheets.

Why is the spreadsheet so popular when it is so bad?
http://www.dynaplan.com/blog.php?page=thread&tid=572

Why is system dynamics used by so few when it is so good?
http://www.dynaplan.com/blog.php?page=thread&tid=574

Comments are welcome
Posted by ""Magne Myrtveit"" <magne@myrtveit.com> posting date Fri, 20 Apr 2007 14:45:40 +0200 _______________________________________________

[Jean-Jacques Laublé <jean-jac]

Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr>

Hi Jack

You write:
> but not in the
> case of standard bathtub structures in which perfect mixing within the
> stock is implicitly assumed

You are absolutely right and I was wrong.

I was even persuaded that the equation As = To / 2 was true even in a perfect mixed outflow.

In fact it is not easy to understand that for instance in a 10 people stock where every day one new person is getting in and one person is getting out, in the case of a pipeline stock, if you ask anybody how much time he has been already waiting, the average answer will be 5 days, and in the case of an outflow where the person getting out is chosen by chance, the answer will be 10. And in both case that the average To will be the same.

I should have built a co-flow and verified what I said.
In fact I had to build the co-flow to get persuaded of it.
Simulation is sometimes useful.

But I still did not really understand the reason of the difference of the As in both cases.

In fact when you ask the persons in a pipeline, the sample is complete and all the persons that have entered the last ten days are there. In the case of the perfect mix, the only people still there are the unlucky ones, and to compare both cases, one should too ask the people that had the luck to be picked up already and who are no more there.

I have added the co-flow to my model in the Vensim Forum.

But when the input and output change as in the case of seasonal variations, it would be interesting to tell anybody entering the stock, how much time he will have to wait on average.

Of course one must be able to forecast the inputs and the outputs.
One can forecast the future As, but there is no way to predict from the As, the future To, the number everybody wants to know before entering the stock.

To calculate the future To, I do not see another way than to integrate step by step Jay's Law, using probability calculations.
I think that it is too an example where probability and conditional Bayesians probability is close to SD.
Regards.
Jean-Jacques Laublé.
Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr> posting date Fri, 20 Apr 2007 11:46:30 +0200 _______________________________________________

[<richard.dudley@attglobal.net]

Posted by <richard.dudley@attglobal.net>

Yes.... I neglected to mention _why_ I am interested in this question: How can we determine the mean time material remains in a stock?

In my particular case I am working on a fishery model. Many fishery models are cohort models, but some are single stock biomass models. While cohort models tend to be more widely used in fisheries analysis, in some ways single stock biomass models are more like the real world. When fishing takes place we are really dipping into multi-cohort mass of fish. Also, we often don't have sufficient data to look at cohorts by numbers and weight.

So I'm interested in how could we better use single stock biomass models as the basis for looking at larger fishery issues with system dynamics models.
Inflow to biomass in the single stock models is typically a constant fraction of the biomass... although in a system dynamics model we could have that fraction change for various reasons.

One issue is that the inflow to a stock of fish biomass can be considered as being from two components: additions due to growth of biomass already present, and additions due to recruitment-- that is, the addition of new biomass in the form of new fish -- what fisheries people might call recruitment biomass.

In a cohort model it's fairly likely that there is a relationship between the numbers of older fish and the amount of recruitment biomass. In the biomass model this is less likely to be clear. Traditional one stock biomass models do not address this question. In those models additions to biomass are usually a constant fraction of biomass. But we can partition this fraction into two components. (Basically I am continuing work on a paper I presented at the New York meeting in 2003).

==> So I am interested in the relationship between the mean age of the biomass and the addition of new biomass due to recruitment. There are two feedback issues here. Most importantly, I think, is the fact that as the age of biomass decreases the proportion of new biomass due to recruitment will increase. That is, biomass with a mean age of say 2 years will be influenced more by an influx of new biomass and a biomass of the same size with a mean age of say 7 years. This is particularly important if there are fluctuations in the recruitment component of the inflow. This is important in fisheries because as the stock declines natural fluctuations in recruitment additions will have a larger and larger effect.

There is also another affect whereby the same biomass of older fish may produce more young than that biomass made up of younger fish. However this is probably less of an issue than the first.


Richard
Posted by <richard.dudley@attglobal.net> posting date Sat, 21 Apr 2007 14:04:05 +0700 _______________________________________________

[Khalid Saeed <saeed@wpi.edu&g]

Posted by Khalid Saeed <saeed@WPI.EDU>

Jay's refreshing comment is timely. It tells us that analysis is a means to an end, not an end in itself.

Khalid Saeed
Posted by Khalid Saeed <saeed@WPI.EDU>
posting date Fri, 20 Apr 2007 10:37:41 -0400 _______________________________________________

[""d.mckelvie@virgin.net"" <d.]

Posted by ""d.mckelvie@virgin.net"" <d.mckelvie@virgin.net>

In response to Prof. Forrester, one example is capacity planning in the UK health service.

Having built (with Eric Wolstenholme) several models of acute hospital systems, it is clear that most policy-makers / planners have little idea about the simple relationships between admission rates, lengths of stay and numbers of people who are in-patients. In particular, their measures of length of stay are often substantially ""trimmed"" to exclude the statistical outliers (which would be fine if they were designing services from which these outlier-patients are to be excluded).

Among the many other errors that it is possible to make, they might ""observe""
a measure of length of time since admission of patients who are still in beds at a point in time (i.e. the average age of material in the stock) and mistake that for the average length of stay (when it is actually half of the length of stay).

So it's not so much that we need to be able to compute the age of material in a stock. It is that we need to explain to people that if what they have actually done is to measure the age of material in that stock, they still have not got a proper measure of length of stay.

Relating this back to ""improving the behaviour of a system"", the improvement in this case is improved understanding on the part of those responsible for operating a system of some of its simplest dynamics (input rate, occupancy / capacity, length of stay). Admittedly, that is a modest claim.

Douglas McKelvie
Posted by ""d.mckelvie@virgin.net"" <d.mckelvie@virgin.net> posting date Fri, 20 Apr 2007 10:08:10 +0000 (UTC) _______________________________________________

[Bob Eberlein <bob@vensim.com&]

Posted by Bob Eberlein <bob@vensim.com>

Hi Everyone,

I know some of us are still a little bit confused by Jack Homer's correct assertion that the average age of material in a stock and the outflow age are the same.

The confusion comes because it is often easiest to think of a stock as getting distinct chunks of ""stuff"" in one end, and that those chunks might break up a bit, and maybe pass one or two chunks from an earlier inflow, but they basically flow through the stock and get sent out the other end.

What perfect mixing means is that once the chunks get put in they are actually completely broken down. Think of pouring red water into a bucket of clear water - perfect mixing keeps all the water the same color. That color builds from clear to red very slowly, and what comes out the drain looks just like the water in the bucket.

Perfect mixing does not depend on the equation determining the outflow - though it is completely consistent with outflow = stock/drain time - which gives an exponential distribution of age within the stock. But any delay process from input to output could also apply.

Clearly, perfect mixing is not always what happens. Jay asks if this matters to the final results. Unfortunately I am not sure there is a way to answer that question without doing the model two or more different ways and seeing what the results are.

Bob Eberlein
Posted by Bob Eberlein <bob@vensim.com
posting date Sat, 21 Apr 2007 13:46:30 -0500 _______________________________________________

[George Richardson <gpr@albany]

Posted by George Richardson <gpr@albany.edu>


>On Apr 20, 2007, at 5:33 AM, SDMAIL Jay W. Forrester wrote:
> Can someone supply some examples of where the way of computing age in
>a stock will alter the direction of policy recommendations to improve
>the behavior of a system?


Great question. We have at least one really good example: Being able to keep track of the average lengths of stay in stocks was crucial to all of our modeling efforts to help NYS counties cope with welfare reform (see Using Simulation Models to Address 'What If'
Questions About Welfare Reform. A.A. Zagonel, J. Rohrbaugh, G.P.
Richardson, and D.F. Andersen. Journal of Policy Analysis and Management 23,4 (2004): 889-920).

The reform legislation, passed by the Republican-dominated Congress and signed by Clinton, removed the Federal guarantee of (potentially) lifetime support for people on welfare. The legislation replaced that lifetime guarantee, in place since the depths of the Depression, with Temporary Assistance to Needy Families (TANF).

An individual is now eligible for up to five years (cumulative in one's lifetime) of TANF support from the Federal government.
Once a person uses up that five years in various spells of poverty, they are on their own, or depend on support from states and counties.

Our model-based efforts with three New York State counties was designed to help counties anticipate the system dynamics and cope with the added strains on their resources once people would begin timing out of TANF. To do it formally, we had to keep track of the years people accumulated in the various stocks in the client-flow
system. There were six stocks tracking the various ways clients
flowed through the system, and hence a pretty complicated six-stock coflow system to keep track of the average cumulative lengths of stay on TANF.

George P. Richardson
Chair of public administration and policy Rockefeller College of Public Affairs and Policy University at Albany - SUNY, Albany, NY 12222 Posted by George Richardson <gpr@albany.edu> posting date Sat, 21 Apr 2007 21:44:12 -0400 _______________________________________________

[""John Gunkler"" <jgunkler@sp]

Posted by ""John Gunkler"" <jgunkler@sprintmail.com>

Just off the top of my head, if the stock in question is inventory in a manufacturing operation -- either work in process or finished goods -- you might need to know the age of the material for a couple of reasons:

1. To put a dollar value on the inventory (which, in a Lean environment, is a measure of waste, therefore of potential savings from eliminating
inventory)

2. To know when items in inventory will ""expire"" (reach a date after which they cannot be sold), to evaluate how much money is at risk unless the inventory is reduced.

Is that the kind of answer you had in mind, Jay? Or did you want examples where one way of evaluating age leads to a different policy decision than another?


John Gunkler
Posted by ""John Gunkler"" <jgunkler@sprintmail.com> posting date Fri, 20 Apr 2007 14:34:26 -0400 _______________________________________________

[""C.A.F.M. Grutters"" <c.grut]

Posted by ""C.A.F.M. Grutters"" <c.grutters@jur.ru.nl>

Jay W. Forrester's question:

>> Can someone supply some examples of where the way of computing age in
>> a stock will alter the direction of policy recommendations to improve
>> the behavior of a system?

gave a number of interesting replies illustrating the relation age-of-stock and policy direction.

I would like to add an example of legal dynamics.

One important aspect of legal procedures is that one may appeal, i.e. go to a 'higher judge', if the result of the procedure is not acceptable to one (or
all) of the parties involved.

Such a request for an appeal, however, has to be filed within a certain period of time (for example 4 weeks). If such a request has not been filed within this period, it will be inadmissable.

This also - at least in a number of countries - works the other way around, meaning that if a certain administrative body waits too long deciding requests, it is automaticly assumed that the outcome is negative meaning that the 'appeal- route' is opened.

This implies that the existence of backlogs increases the possibility of exceeding a certain period of time-to-decide, and that means an increase of the number of 'automatically' generated negative outcomes and therefore the number of appeals.

Knowledge about the age of the stock - or backlog - then is crucial to compute the number of expected appeals. In policy terms this implies that changing handling capacity at one level indirectly influences the size of the inflow at another (appeal) level.

Carolus Grütters
Centre for Migration Law
Faculty of Law
Radboud University Nijmegen, The Netherlands Posted by ""C.A.F.M. Grutters"" <c.grutters@jur.ru.nl> posting date Sun, 22 Apr 2007 21:37:30 +0200 _______________________________________________

[Richard Stevenson <rstevenson]

Posted by Richard Stevenson <rstevenson@valculus.com>

>On 20 Apr 2007, at 10:33, SDMAIL Jay W. Forrester wrote:
> Can someone supply some examples of where the way of computing age in
>a stock will alter the direction of policy recommendations to improve
>the behavior of a system?

I think so.

In the pharmaceutical industry, value is being destroyed through longer product development times. It now takes (on average) 12-13 years to bring a new product to market as opposed to around 8 years a decade or so ago. Given that patent lives are (normally) fixed at 20 years, the double hit of increasing ""time to market"" is evident - higher R&D costs and less time at market before generic competitors are able to kick in.

""Age in a stock"" - or, more specifically, ""time to market"" - is a critical policy determinant in pharmaceuticals. In practise, drug development can be thought of as a series of stages, or stocks.
The time in any one stage is less important than the total time to market. This can be thought of as the ""cycle time"" of a project, as recently described by Will Glass-Hussain in this forum.

Large pharma companies (e.g. Pfizer, Astra Zeneca, GSK) have to make massive policy decisions based on this phenomenon. The longer a project stays in development, the more it costs and the less market value it can ultimately create. The policy conundrum is whether to ""fail fast"" - i.e. to eliminate risky projects early in development (before they consume scarce resources) , or to bet that projects can become ""blockbusters"" (i.e. massive monopoly products that generate billions of revenue each year, before they come off patent).

This is a huge and widely discussed phenomenon in the pharmaceuticals industry, that has wiped billions off market values in the past decade.

The problem is well illustrated by Pfizer, which has managed double digit growth for years. But in the next two years, some of its most lucrative drugs will come ""off patent"" whereas the pipeline of new drugs is running dry.

Policy implications? Massive. A huge and permanent shift away from internal R&D towards partnerships, licensing deals and acquisitions of more fleet-footed, more innovative biotechnology companies. Major deals are being made between ""old pharma"" companies that have empty R&D pipelines but possess the infrastructure to market new drugs, and ""new biotech"" companies having technology but no infrastructure.

Most of these deals are being made on ""faith"" rather than solid valuations - because most biotech companies still have no products at market.

Recently AstraZeneca paid nearly a billion pounds for Cambridge Antibody Group - a biotech company with no products but possessing advanced monoclonal antibody technology. But ""monoclonals"" are still highly risky - one such product caused the disastrous and highly publicised clinical trial failure that nearly killed six volunteers in London - and forced the (German) drug company into bankruptcy.
So what is the value of unproven and speculative technology? SD has much to offer here, as a tool to make the risks and opportunities of new technology more transparent - for buyers and sellers.

Recently we have been working with a large European pharmaceutical company to help to identify portfolio policy in R&D. The outcome of the ""time to market"" and risk issues identified by the SD study has been instrumental in a significant shift in R&D policy - away from internal development towards external licensing and partnerships.
Of course, that creates a whole new set of issues!

There is a short description of this work on our website - a longer paper is in development.

Richard Stevenson
Valculus Ltd
UK
Posted by Richard Stevenson <rstevenson@valculus.com> posting date Sun, 22 Apr 2007 19:03:47 +0100 _______________________________________________

[""Goncalves, Paulo"" <pgoncal]

Posted by ""Goncalves, Paulo"" <pgoncalves@exchange.sba.miami.edu>

>Jay Forrester asks:
>""Can someone supply some examples of where the way of computing age in
>a stock will alter the direction of policy recommendations to improve
>the behavior of a system?""

What an interesting question? In its essence it highlights that computing age in a stock in different ways could potentially lead to different policy implementations. We all know that poor modeling leads to poor results, but this query implies that even seemingly proper modeling might generate problems. Two formulations mentioned in the thread (and commonly used) to capture the age in a stock are coflows and Little's Law. Comparing them might be a good starting point to potentially address the question.

The first important thing to consider (in any formulation) is the Baker criterion, that is, ""what do the decision makers know, and when do they know it?"" (Sterman 2000, p.516). Traditionally, the coflow formulation assumes that decision makers know the ""steady state"" average residence time in the stock (the time constant in the arrival-time (ATCS) and time-integrating (TICS) coflow structures.) The coflow structure captures changes in the average age of the stock by the introduction of an inflow of new stock to the accumulated old one. Assuming a manufacturing setting where order flow in, accumulate in a backlog and are fulfilled as shipments are sent out, a possible use of the coflow structure would be to measure the average residence time of orders in backlog when managers know that ""on average"" orders are shipped with the desired shipment delay (time constant). In contrast, Little's Law (Jay's formulation) assumes that decision makers know (or have access
to) the outflow rate, the average age of the stock depends directly on the ouflow rate (average age = stock/ouflow). In the same setting with shipments now determined by what can be achieved by the production process, managers can use Little's Law to compute the average residence time of orders in backlog. Managers know how much they ship out every week and so they can compute the average residence time of orders in their backlog.

To compare the two formulations directly, it is possible to change the traditional coflow formulation so that it uses an ""external"" shipment rate (without an explicit assumption for the steady state average residence time.) As before, the coflow formulation (either TICS or ATCS) the average age of the stock will depend on the ratio between stock time and stock, both of which change smoothly with the accumulation of their net flows. In contrast, with Little's Law, the average age of the stock is instantaneously influenced by changes in the outflow. (Average age also depends on the inflow rate, since change in stock = inflow - outflow, but that effect is smoothed through the accumulation over
time.) Hence, the latter measure of average age will be more unstable to changing inflow and outflow rates. Managerial decisions based on average age measures obtained via Little's Law will change more rapidly to accommodate more rapid and erratic changes to the age of the stock than managerial decisions based on age of a stock obtained with coflows.


For instance, assume that managers use Little's law to estimate the average delivery delay in the same manufacturing setting. Since long delivery delays can cause customers to seek alternate sources of supply, managers will adopt policy recommendations that change rapidly to the changing environment, shifting production policies more frequently to reduce observed delivery delays. If instead, managers use a coflow formulation their measures will be adjusting more smoothly and so will their corrections. (Of course policies that managers use also depend on how customers perceive (and formulate) the average delivery delay for the orders placed, and must be taken into consideration.)

Paulo Goncalves
Posted by ""Goncalves, Paulo"" <pgoncalves@exchange.sba.miami.edu>
posting date Mon, 23 Apr 2007 07:33:55 -0400 _______________________________________________

[Bill Braun <bbraun@hlthsys.co]

Posted by Bill Braun <bbraun@hlthsys.com>

I understood Jay's question to refer to the aging in a particular stock, in other words the ""mixing"" of items within a single stock. In a number of examples offered in response to his question, John's below being a good example, I have been asking myself why we are trying to extract aging information from a single stock when multiple stocks would reveal the same information.

Using John's inventory example, why would I not establish a separate stock for each of the policy decision points? So, if I want to differentiate the age of inventory in five day increments, I would model a stock for [the first] five days, flow its contents into the second five days, into the third five days, etc. until I reach an 'X days and older' stock. Shipments would draw from the oldest stock
(FIFO) or the youngest (LIFO) or any other relevant combination. The net of all flows would be the inventory in each aging stock. At any point in time, the aging of inventory, patients in a queue, time in a trail, etc. would be known by the number of people/items in each of the aging buckets.

I think this would also suffice for Jack's new medical products scenario, as well as Bob's red water example (very helpful, thanks Bob).

This seems simple enough, so simple that I now question my understanding of the original question, and the many examples and explanations offered.
To conceptually quote Bob, I haven't actually tried this in a model, which I suppose is as close to a cardinal sin as I can get (that is, assuming I can sort this all out in my head).

Bill Braun
Posted by Bill Braun <bbraun@hlthsys.com> posting date Mon, 23 Apr 2007 15:32:21 -0400 _______________________________________________