SD knowledge/Text Based Models

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"geoff coyle"
Senior Member
Posts: 94
Joined: Fri Mar 29, 2002 3:39 am

SD knowledge/Text Based Models

Post by "geoff coyle" »

Folks,

Some of you will have noticed concerns Ive expressed in the past months about erroneous models, that is to say, models in which the equations are technically incorrect or which calculate incorrectly for a number of other reasons. Last week, I mentioned rate-dependent-rates and Ive now received the following query. I quote it verbatim as nothing in it identifies its author, other than to himself.

Would you elaborate on rate-dependent-rates? I think myself and other
people new to SD dont know the definition. Thanks.

I can only say that this worries me deeply. When I was a newcomer to SD, more than 30 years ago, I read a textbook (Forresters masterpiece) and went to lectures to find out about this new subject. I did the same when I learned about calculus (that was at school, with a most gifted maths master, Mr Whitehead (aka Sir), long since dead but still honoured in my mind and acknowledged in one of my books). I did the same when I learned about linear programming and so on. I dont want to be rude to this enquirer but it amazes me that someone new to a subject should try to pick it up by such casual enquiry and should expect me to devote time to writing notes about this topic, and many others in SD, one of which is the correct use of DT.

Rate-dependent-rates are specifically mentioned in the following textbooks: Forrester, 1961; Coyle 1977, 1966 (which has much more on correct modelling techniques, as does my Equations for Systems), Richardson and Pugh, 1981; Wolstenholme 1990. I could not find it in the index of Sterman 2000, but Im sure its there somewhere.

I can only urge newcomers to SD to study the subject properly, rather than trying to pick it up from half-reading a software manual. Excellent though those are, their purpose is to explain the use of software, not to teach SD. Maybe the Society needs to think again about its training and educational needs because, as this enquiry might be paraphrased other people new to SD dont know much about it.

Geoff Coyle
From: "geoff coyle" <
geoff.coyle@btinternet.com>
John Sterman
Senior Member
Posts: 117
Joined: Fri Mar 29, 2002 3:39 am

SD knowledge/Text Based Models

Post by John Sterman »

The question of whether rate-to-rate connections are proper in SD
models has recently come up.

First, what is a rate-to-rate connection?

Consider a classic inventory management model, where

Inventory = INTEGRAL(Production - Shipments)

To keep this as simple as possible, ignore work in process and all
resources needed to produce (labor, materials, etc.), so that
production is determined only by desired production. A simple
inventory control rule might then be

Production = Shipments + (Desired Inventory - Inventory)/Inv. Adjustment Time

The logic of the formulation is that the firm should produce enough
to replace the quantity shipped, with an adjustment above or below
that rate to correct any discrepancy between the desired and actual
inventory. (There are several problems with this formulation, for
example, Production should be constrained to be nonnegative.
However, lets ignore that for illustration; correcting it doesnt
affect the point.)

The use of the actual shipment rate in the formulation for production
constitutes a rate-to-rate connection: one rate (shipments) appears
in the formulation for another (production). More generally, all
feedback loops consist of rates that accumulate into or out of
stocks; the stocks then generate the information upon which the
decisions that alter the rates are based. That is, all loops are in
the form Stock -> Rate -> Stock. You cant have Rate -> Rate.

Forrester pointed out in Industrial Dynamics that theoretically there
can be no such direct and immediate dependence of one rate on
another. Shipments is the instantaneous rate of outflow from
inventory. As the instantaneous rate it cannot be measured. If it
cannot be measured, its instantaneous value cannot be an input to any
decision anywhere else in the system: By what I call the "Baker
Criterion", decisions can only be based on information that is
actually available to the decision maker (after former senator Howard
Baker, who asked during the Watergate scandal "what did the President
know, and when did he know it?; see chapter 13 of Business Dynamics).
Any measuring device or process necessarily involves some
accumulation or averaging, introducing a stock somewhere in the
information feedback channel between the actual, instantaneous rate
of shipments and the measured, reported, and perceived value of
shipments. Note that any type of average must include at least one
stock (see Business Dynamics Ch. 11).

In the inventory example, a more correct formulation would be:

Production = Reported Shipments + (Desired Inventory -
Inventory)/Inv. Adjustment Time

Reported Shipments = AVERAGE(Shipments, Shipment Reporting Interval)

where the AVERAGE() function represents some type of average of the
shipment rate over the Shipment Reporting Interval. For example, the
firms IT systems may report shipments on a weekly basis; in this
case reported shipments would be the sum (accumulation) of all
shipments over the past week. In practice, it is often realistic to
use a moving average over a period of time greater than the reporting
interval to capture perception and decision-making delays that add to
the measurement
eporting delay. Often some type of exponential
smoothing is a fine way to model the delay between shipments and
reported/perceived shipments. Such delays are often deliberately
introduced to filter out noise in the actual shipment rate so that
production does not bounce around too much. In fact, the shorter the
measurement
eporting delays for a rate, the more the reported rate
will bounce around with short-term noise, and the longer the
deliberate averaging managers introduce will/should be to ensure that
the noise is filtered out. (As a side issue, many firms fail to
realize this when implementing IT systems that dramatically shorten
measurement
eporting delays, then wonder why their operations seem
to be so much more variable and costly. By shortening the reporting
delays they have reduced the extent to which the measurement process
filtered out unwanted high-frequency noise; this noise is then passed
on to other decisions such as production scheduling, raw materials
ordering, and hiring. Taking delay out of a system can be
destabilizing and costly.)

Note that the nonexistence of direct rate-to-rate connections is a
theoretical issue that applies to all rates, not only information in
business or human systems. For example, the speedometer in your car
does not report the instantaneous velocity of the car but a (quite
short term) average. The averaging arises because the speedometer
mechanism contains some inertia. Moving from an old-fashioned
mechanical speedometer to an electronic one may shorten the delay but
can never eliminate it - there is always some inertia in the
electronic elements as well. Similarly, moving from a traditional
accounting system to a scanner based point of sale system may reduce
the delay in reporting sales from a week to a day or even an hour,
but there is still some delay in the measurement of shipments.

Now, as with all good rules, there are exceptions. There are no
exceptions to the principle that there cannot be direct Rate-to-Rate
connections. In theory, all rates depend only on other stocks
(though perhaps through a chain including auxiliary variables; note
that any such auxiliaries eventually trace back to stocks or
parameters outside the system boundary).

In practice, however, it is sometimes the case that the delays in
reporting and reacting to the value of a rate are so short that they
can be safely ignored. In such a case it is acceptable modeling
practice to include a direct rate-to-rate connection in your model.
For example, the delay in the reporting of velocity by the
speedometer of your car may be so short relative to your reaction
time and the inertia of the car that it is not an important
contributor to the delays in the negative loop through which you
regulate your speed on the highway. If so, you can have a
rate-to-rate connection in your model to avoid having to represent a
delay with a time constant much, much shorter than the other time
constants in the system. Whether it is appropriate to omit the delay
and permit a direct rate-to-rate connection is an empirical question
that can only be answered by considering the length and impact of the
delays against the purpose of the model. Note, however, that there is
a big difference between a deliberate modeling decision to omit the
measurement/decisionmaking delays for a rate and ignoring the delays
out of ignorance about rate-to-rate connections. People (including
modelers) often underestimate the lengths of delays, so may tend to
omit them from their models when they actually should be included.
In particular, even when reporting delays are short, there are often
important managerial decision making delays so that decisions do not
respond to short-term noise in the reported rates.

To summarize, as a theoretical matter, there are no direct,
rate-to-rate causal links in nature because it is impossible to
measure the instantaneous rate of change of any quantity (take its
derivative). There is always some delay or averaging in the
measurement and reporting of a rate. Thus there is always at least
one stock intervening between a rate and other decisions that depend
on that rate. In practice, however, it is sometimes acceptable to
omit these delays in a model if they are sufficiently short relative
to the time scale of interest for the purpose of the study. It is
not automatically an error to have a direct rate-rate connection in a
model. Modelers should, however, carefully examine any rate-rate
connections to be sure that the delays in the measurement
eporting
of the rate are in fact short enough to be ignored relative to the
model purpose.

John Sterman
From: John Sterman <jsterman@MIT.EDU>
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