Ventana software support forum

Posted by Bill Braun <bbraun@hlthsys.com>
Is there a general rule of thumb for discerning the difference between modeling a series of first order delays and using an Nth order delay?

For example, as an over simplification, an order structure could be described as:

SIP = SIP + dt * (PO - PR) where

PO is Products Ordered (by the customer at some rate)
PR is Products Received (by the customer after some delay)
SIP is Somewhere in Process

and PR = SIP / AT (Average Time [between placing product order and product
receipt])

Suppose that SIP is disaggregate into:

POIT - Product Order in Transit (to producer)
PIP - Product in Process (by producer)
PIT - Product in Transit (from producer)

My understanding is that if the average outflows from POIT, PIP, and PIT are all different each outflow would be a first-order delay (e.g., POIT / AT1, PIP / AT2, and PIT / AT3). If, on the other hand, the average delay between the stocks is the same the desegregation could be treated as a third order delay with the outflows equal to POIT / (AT / 3), PIP / (AT / 3), and PIT / (AT / 3) respectively.

Is this a correct understanding?

Bill Braun
Posted by Bill Braun <bbraun@hlthsys.com>
posting date Fri, 30 Sep 2005 11:08:37 -0500

Posted by Joel Rahn <jrahn@sympatico.ca>
Your interpretation is basically correct with a couple of added comments. 1. The rule of thumb for the delay times here is AT = AT1 + AT2 + AT3 2. The difference between the sequence of explicit first-order delays and an 'equivalent' third-order delay is in the details: You would use the sequence if you were interested in the details of the levels and rates in the chain. A third-order delay (or any Nth-order delay) is a special function in most SD languages that lets you *approximate* the detailed dynamics by using an average delay time for each internal level of the structure with the total delay time being the same for both the whole sequence of first-order delays and for the approximating Nth-order delay.

A rule of thumb for deciding which structure to use is to ask yourself: Are there specific policies that apply to each of the first-order delays in the sequence or is the sequence pretty much a black-box at the level of detail I am using in my model?

Posted by Joel Rahn <jrahn@sympatico.ca>
posting date Sat, 01 Oct 2005 08:30:24 -0400

Posted by ""geoff coyle"" <geoff.coyle@btinternet.com>
Sorry for this late rely to Bill Braun's query, but I've been struggling with sun, food (and the odd glass of wine) in Cyprus. It was tough, believe me!

It is, of course, true that cascading N first order delays will produce the same dynamics as an Nth order delay. That is, however, only true if the delay magnitude for each and every first order delay is DEL/N, where DEL is the delay used in the Nth order delay. That does not affect the correct value for DT (what we now wrongly call TIMESTEP).

You might sometimes want to model a different type of delay response in which, say the first part of the delay is long (or short) and later parts speed up (or slow down). For a two stage delay that would be done as

SIP1=SIP1+dt*(in- out1)
out1=SIP1/DEL1
SIP2=SIP2+dt*(out1-out2)
out2=SIP2/DEL2

etc.

Regards,

Geoff

Visiting Professor of Strategic Analysis,
University of Bath
Posted by ""geoff coyle"" <geoff.coyle@btinternet.com>
posting date Mon, 17 Oct 2005 11:01:45 +0100