Manufacturing Control Systems

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"Edward Anderson {andersone}"
Newbie
Posts: 1
Joined: Fri Mar 29, 2002 3:39 am

Manufacturing Control Systems

Post by "Edward Anderson {andersone}" »

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If Jim is taking a poll, I vote for "prolonged event." At some level, I =
think "continuing event" would be even better as it is more =
self-explanatory and avoids any perjorative connotations often =
associated with "prolonged." However, distinguishing it from =
"continuous", "continuous time", as well as the old linguistic bugbear =
"continual" is uninviting at best. However, I will be glad to side with =
whatever the majority of you all feel in order to avoid linguistic =
chaos. There is nothing I hate more in the world than trying to =
distinguish for operations students the 101 ways that "cycle time" is =
used and abused.
=20
An interesting side note with respect to Kanban stability: In my =
operations class, we simulate both a traditional Kanban and a =
traditional push system each year by hand by passing candy between =
buffers that are plastic glasses using first a push and then a Kanban =
policy. I already knew intellectually from the computer simulation work =
that Jim cited earlier that fixed Kanban systems tend to stabilize =
factory systems. But during our classroom simulation, it always amazed =
me at a "real-world level" just how difficult it was to make a Kanban =
system oscillate significantly in response to demand relative to what =
can be done with a push system. Of course, the point of this exercise =
was to illustrate not only the relative stability of the fixed Kanban =
system, but also the inability of that system to satisfy highly volatile =
demand.
=20
Best,
=20
--Ed
=20
=20
Edward G. Anderson, Ph.D.
Assistant Professor of Operations Management and
Faculty Advisor, Engineering Route to Business BBA Major
University of Texas McCombs School of Business
1 University Station B6300, CBA 4.234
Austin, Texas 78712-0210
512-471-6394; fax: 512-471-3937
edward.anderson@mccombs.utexas.edu; web: www.edsim.org
=20
=20
"Jim Hines"
Senior Member
Posts: 88
Joined: Fri Mar 29, 2002 3:39 am

Manufacturing Control Systems

Post by "Jim Hines" »

Ray says " Lets make sure we are talking about the same thing. "

So just to be clear, were talking about two separate dimensions of a
model: A time dimension and an event dimension. Time can be either
discrete or continuous. Events can either be discrete or [insert a word
here that means an event that extends over a bunch of neighboring time
points]. (Ill use the word "extended event")

Think of it as a grid:
______________________________________________
| | Event |
| | Discrete | Extended |
|_________________|____________|_______________|
| Discrete | A | B |
| Time ----------|------------|----------------
| Continuous| C | D |
|_________________|____________|_______________|

Most (but not all) of modeling done within the SD field is in cell D
(continuous time AND extended event). A lot of econometric modeling is
(or was twenty years ago) in cell B (discrete time AND extended event).
A lot of manufacturing-type modeling is in cell C (continuous time AND
discrete event). A lot of scheduling type modeling is done in cell A
(discrete time AND discrete event).

George Simpsons challenge model is in cell C -- continuous time AND
discrete event.


Time Axis:
The term "discrete time" refers to a model whos clock jumps from one
time point to the next. The clock on the wall in my fourth grade class
had a minute hand that jumped from one minute to the next. Thats
discrete time. An example would be a model in which time starts at week
0, jumps immediately to week 1, then jumps to week 2 and then to 3, etc.
Time is undefined on points between these integers -- there is no moment
at week 1.5.


Discrete time looks like this: . . . .
1 2 3 4

The term "continuous time" refers to a model whos clock moves fluidly
through the time dimension. The minute hand doesnt jump from one
minute to the next, but rather moves smoothly touching all of the
intervening moments between one minute and the next. All time points
are defined.

Continuous time looks like this __________
1 2 3 4


Event Axis:
A "discrete event" is one that happens all at once on a single point in
time -- either a single point in discrete time or a single point in
continuous time.

A discrete event in discrete time looks like this

|
. . . .
1 2 3 4


A discrete event in continous time looks like this

|
__________
1 2 3 4

An "extend event" is an event that happens (or extends) over more than
one time point -- either a series of consecutive time points in the
discrete time case or an interval of time points in the continuous time
case.

An extended event in discrete time looks like this

| |
. . . .
1 2 3 4


An extended event in continuous time looks like this

____
__________
1 2 3 4

From: "Jim Hines" <jhines@mit.edu>
Joel Rahn
Junior Member
Posts: 15
Joined: Fri Mar 29, 2002 3:39 am

Manufacturing Control Systems

Post by Joel Rahn »

Now that I know what we are talking about, and inspired by Jims
diagrams, I suggested that "repeated event" describes Jims "extended
event" when it occurs in discrete time and "interval event" describes a
Hinesian "extended event" in continuous time. Sorry it is not just one
term but the situations are different as Jims description makes clear:

either a series of consecutive time points in the
discrete time case OR an interval of time points in the continuous time
case

The OR is my emphasis and it is an exclusive OR. The fundamental
problem, as someone may have said earlier in this thread, is that there
is no way to define a series of consecutive points in an interval of
continuous time (Zenos paradox anyone?) except by a limit argument and
even then you have the problem that the cardinality of the integers
(aleph null) is smaller than the cardinality of points in a continuous
interval ( C ).

For the examples given below Jims grid, I would substitute the
following text (my substitutions are in CAPS enclosed in brackets[ ] ):

Most (but not all) of modeling done within the SD field is in cell D
(continuous time AND ([INTERVAL] event). A lot of econometric modeling is
(or was twenty years ago) in cell B (discrete time AND [INTERVAL] event).
A lot of manufacturing-type modeling is in cell C (continuous time AND
discrete event). A lot of scheduling type modeling is done in cell A
(discrete time AND discrete [or REPEATED]event).

For the first two, I dont see any difference in the kind of "extended
event". SD uses rates which can change at each time-step but are
constant over that time-step. Econometric models use totals and averages
of data over the interval between each evaluation of the model which
occurs at a fixed time-step for a given model. For the latter two
cases, cell Cs continuous time comes from the "arrival time"
distributions which are used and which are usually defined on continuous
intervals whereas cell As discrete time comes from the (often periodic)
fixing of a schedule and its subsequent revisions. In the last case (the
only one for which I could quickly see a need for a "repeated event"),
the repetition comes from the supposition that the scheduling mantra is
repeated regularly, until the next consultant comes along...

R. Joel Rahn
jrahn@sympatico.ca
Joel Rahn
Junior Member
Posts: 15
Joined: Fri Mar 29, 2002 3:39 am

Manufacturing Control Systems

Post by Joel Rahn »

Jim Hines wrote:

>Ray says " Lets make sure we are talking about the same thing. "
>
>So just to be clear, were talking about two separate dimensions of a
>model: A time dimension and an event dimension. Time can be either
>discrete or continuous. Events can either be discrete or [insert a word
>here that means an event that extends over a bunch of neighboring time
>points]. (Ill use the word "extended event")
>
>
Why do we "need" a single word to cover the two concepts included in
"extended event"? What important classification service does "extended
event" provide? In the above paragraph, the event "dimension" is
dependent on the time dimension (and nothing else) so the event
dimension is a function of time, not a completely separate dimension,
just a way to emphasize that some time effects appear at single time
points (discrete events), some appear over the whole duration of the
simulation (continuous processes) and some appear over a range of times,
i.e. between a beginning time and an end time, that is shorter than the
duration of the simulation.

An "extended event" is an event that happens (or extends) over more than
one time point -- either a series of consecutive time points in the
discrete time case or an interval of time points in the continuous time
case.

In a discrete-time case, the "extended event" is just a bunch of
discrete events. Does Jim have an example where the presence of these
bunches distinguishes the model from a discrete-event model and requires
a new descriptor?

In a continuous-time case, the "extended event" occurs over an interval
-like turning on and off a STEP function or having a PULSE function be
non-zero for an interval of more than one time-step. Does Jim have an
example where the presence of these interval effects distinguishes the
model from a standard continuous-time SD model and requires a new
descriptor?

Sign me,
Just curious

R. Joel Rahn
From: Joel Rahn <jrahn@sympatico.ca>
John Sterman
Senior Member
Posts: 117
Joined: Fri Mar 29, 2002 3:39 am

Manufacturing Control Systems

Post by John Sterman »

Jim Hines wants a model that operates in continuous time but
represents discrete events. Hazhir Rahmandad and I have developed
such a model, specifically a continuous time agent-based model of
epidemics/diffusion dynamics in which events are discrete. Based on
the classic SEIR epidemic model (see chapter 9 of Business Dynamics
for examples), it is of course simulated numerically with finite
timestep (as are all digital simulations of ODEs), but,unlike nearly
all agent-based models, the time step can be made arbitrarily small
without altering the intrinsic dynamics. The events include, for
example, "become infected (or adopt the innovation)," "become
symptomatic," "recover," "die." We explicitly compare this discrete
event, agent based model to the classical lumped nonlinear continuous
time SEIR model.

The model demonstrates how to formulate agent-based models with
discrete, stochastic events in a continuous time framework, enabling
modelers to mix agent and aggregated elements in a single model. We
also characterize the conditions under which the disaggregated,
stochastic, agent-based framework might yield different dynamics or
policy recommendations compared to the continuous lumped model (there
arent many).

We plan to present this work at the SD conference this summer and
will have a paper for the proceedings.

FYI this is not the first SD model that operates in continuous time
and also represents discrete events. Steen Rasmussen developed one
such model as part of his doctoral dissertation at the Technical
University of Denmark, under Erik Mosekilde, in the early 1980s. It
was a model of technological innovation in the context of economic
long waves. Innovations arrived in a poisson fashion. Jason
Wittenberg and I developed a model of Thomas Kuhns theory of
scientific revolutions in which new scientific theories are created
stochastically and endogenously (the discrete events); the model
operated in continuous time. Interested readers should consult

Sterman, J. and J. Wittenberg (1999). "Path Dependence, Competition,
and Succession in the Dynamics of Scientific Revolution."
Organization Science 10(3): 322-341.

The documented model is available at
http://web.mit.edu/jsterman/www/SDG/self.html

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