Discrete Event vs. DiffEq Models

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"Timothy Quinn"
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Posts: 1
Joined: Fri Mar 29, 2002 3:39 am

Discrete Event vs. DiffEq Models

Post by "Timothy Quinn" »

Here is the problem that got me into the field of System Dynamics.

A common measure of outpatient clinic access in the healthcare industry is
Time to Third Available Appointment; that is, how many days from today--when
you call your doctor to schedule an appointment--is the third open
appointment slot on your doctors calendar. Poorly run systems have TTAA in
months, good ones have TTAA in days.

Clinics want to know what their appointment template should look like, given
the acutity profile of their physician panels (stocks of patients that each
doctor takes care of). Sicker patients require more time (longer service
time in the sysem), as do new patients (because an H&P must be taken for the
first time). Emergent cases need to be seen immediately, usually by
overbooking appointment slots at the last minute (like the airlines do).

My discrete event model took a schedule template as input, replicated every
week for as long as the simulation time horizon. Patients would arrive
according to a Poisson process. Each patient was randomly assigned an
acuity level, based on the functional health status distribution of the
panel, which was translated into how many 15-minute blocks of service time
were required for each patient. I assigned patients to appointment slots
with different policies in two sets of simulation runs: (1) give each
patient the first available appointment slot of appropriate length, or (2)
give each patient the first available appointment slot of appropriate length
after a stochastically determined (lognormal distribution) number of days
(assuming that patients like to schedule in advance). Emergent cases were
overbooked, but no more than 2 patients could be overbooked in the same
slot(s). If an appointment time was not available before a certain
threshold, the patient balks and goes elsewhere.

Using the existing template, the clinic was interested in what the TTAA
graph looked like over time. In particular, how long before most patients
are balking and going elsewhere? Next, the clinic wanted to know if certain
appointment slots should be reserved for emergent cases.

Here is the challenge: Im not sure how one would model assigning patients
to appointment slots given that the time order and vacancy of those slots is
important for calculating a running measure of TTAA.

Thanks,
Tim Quinn

System Dynamics Group
Massachusetts Institute of Technology
Sloan School of Management

30 Wadsworth Street
Bldg E53, Rm 358A
Cambridge, MA 02142

Telephone: 617-258-5585
Email:
tdquinn@mit.edu
=?iso-8859-1?Q?Jean-Jacques_Laub
Junior Member
Posts: 16
Joined: Fri Mar 29, 2002 3:39 am

Discrete Event vs. DiffEq Models

Post by =?iso-8859-1?Q?Jean-Jacques_Laub »

Hi Timothy

I did not understand if you did model correctly your problem, and what
method or software you used, or what method is supposed to be used if you
did not .
I have the same kind of problem than yours.
I have a rental car company, and I try to model the way people reserve cars,
depending on the availability of cars, the need of the client and of course
the price given etc...
I am still not sure if it is a continuous SD method or a discrete method
that will do the job better
Regards.

From: =?iso-8859-1?Q?Jean-Jacques_Laubl=E9?= <JEAN-JACQUES.LAUBLE@WANADOO.FR>
"Keith Linard"
Newbie
Posts: 1
Joined: Fri Mar 29, 2002 3:39 am

Discrete Event vs. DiffEq Models

Post by "Keith Linard" »

This problem is virtually identical to the one I routinely set my 3rd year
Civil Engineering students (as part of a 27 hr course - about 10% of
semester workload). I am happy to make the models, built in Powersim,
available on request.

NOTE: This model combines low level mechanistic control engineering
elements as well as high level policy feedback levers. My aim was to make
SDM seem relevant to hard systems civil engineers. It worked.

The student problem related to perceived productivity shortfalls in a
Concrete Batching Plant. Key actors included shareholders, management,
competing unions and workers (clerical, batching plant, truck drivers).

Student tasks included:
1. Cognitive mapping / group decision exercise:
OBJECTIVE: to understand the soft system: worldview(s), owners,
clients, actors, transformation processes and environmental constraints;
system boundaries; decision levers within control of owners / management.

2. Build System Dynamics Flight Simulator
OBJECTIVE: Understand stock-flow dynamics ; understand system
interrelationships; create a flight simulator which illustrated the
consequences of feedback effects of key decision levers; learn the power
and flexibility of the SD software (Powersim).

3. Components of the System Dynamics Model (The bare bones - ignoring the
key policy feedback levers).
Time step: 1 minute over 1 week operation.

a. Build a minute-hour-day clock which controlled client order times, batch
plant working hours and driver working hours.
b. Build a log-normal probability module to drive order inter-arrival
times.
c. Build random probability modules to drive order size and delivery
time-distance (both based on data)
d. Build the order arrival module, office-telephonist module and
transformation of potential order into logged order taking into account
telephonist availability with 1 or 2 staff (key decision variable: orders
lost if staff on rostered breaks or unscheduled toilet breaks).
e. Build batch plant module: plant operates if: staff available & plant
free & empty truck available. Plant takes variable time to fill order.
f. Build trip module: trucks change state between available, at Batch
Plant or En Route.
g. Build Loose Customer Module: If order not acted on (dispatched to
Batch Plant) within 1 hour, loose order.
h. Build Order prioritising module: Orders placed previous day get first
priority next day.


Whats lacking in this compared with the challenge.
1. No queue jumping by urgent cases: But the order prioritising module is
entirely flexible (based on manipulating the index number of an order in a
time queue) and could readily be used to ramp up priority of randomly
assigned high value customers.
2. Time slot reservation: But dead easy to implement given the above
structures.
3. The model is essentially continuous (in that orders are undifferentiated
in the various order-states), except for unactioned orders which go into a
60 level array to determine lost orders at the end of 1 hour; and
priority queue for next day actioning.

Models made available on the understanding that they are not fully
bug-proofed (after all theyre only Civil Engineering undergraduates; it
was their lowest credit unit; and it wasnt perceived as real
engineering - especially by my academic colleagues). Paper to Engineering
Education Coference on this course is also available.

Keith Linard
Visiting Fellow
University of New South Wales
(Australian Defence Force Academy)
Phone: -61 (0)3-9747-6682
Fax: -61 (0)3-9747-6697
Mobile: 0412-376-317
Email:
k.linard@adfa.edu.au

Home Address:
5 Blackwood Drive
Melton South
Vic 3338
"geoff coyle"
Senior Member
Posts: 94
Joined: Fri Mar 29, 2002 3:39 am

Discrete Event vs. DiffEq Models

Post by "geoff coyle" »

1


This is a common class of problem that arises in many domains - the workload
in a machine shop is but one of many cases. It is usually addressed, as you
have done, by discrete event simulation (DES) using any one of a number of
DES languages. (CSL was a good one but Im not sure what is now available).
The usual output is a distribution of such variables as queue length at a
work station, time to go through the system etc. The characteristics of that
distribution, such as its mean, mode, variance, probability that a given
value will be exceeded, and its shape are indicators of the relative
merits of different operating rules. For example, in a machine shop (which
is a case I have dealt with) is it better to take the largest job first, the
smallest first, the one that has waited longest, or whatever? The other
input is, of course, the numbers of machines at each manufacturing stage,
size of storage areas etc. All these can be taken into the simulation to see
that happens to the distribution. It would be unusual to be interested in
the time profile of, say, queue length; what normally matters is the nature
of the performance over some period of time, as measured by the
distribution.

For your TTTA problem, you seem to be on the right track with distributions
of patient needs and arrivals and your two decision rules on patient
allocations. Other factors are, of course, the numbers of doctors (and
nurses) available, the size of the facility in terms of consulting rooms and
beds, the capacity of the support services such as patient records and no
doubt other factors. You could simulate this over a year, say, to allow for
winter epidemics and so forth. You could even separate out the different
seasons and look at how the numbers of available resources might need to
vary over the year.

Im not at all sure that SD is an appropriate methodology for this class of
problem and Id be interested in knowing why you think that it is. Of
course, SD is great for all sorts of problems and it is not hard to
represent discrete events within an SD model, when it is appropriate to do
so (see the literature) but SD does not do everything and I always urge
students (force is closer to it) to justify the choice of a methodology with
respect to the type of problem being addressed.

I hope that helps.

Regards,

Geoff
From: "geoff coyle" <
geoff.coyle@btinternet.com>

Professor Geoff Coyle
Visiting Professor of Strategic Analysis, University of Bath.

Telephone 44 (0) 1793 782817
Fax 44 (0) 1793 783188
Bill Braun
Senior Member
Posts: 73
Joined: Fri Mar 29, 2002 3:39 am

Discrete Event vs. DiffEq Models

Post by Bill Braun »

5

>My discrete event model took a schedule template as input, replicated every
>week for as long as the simulation time horizon. Patients would arrive
>according to a Poisson process.

Tim,

Do you mean the patients actually arrive at the clinic according to a
Poisson distribution, or their request for service and their respective
severity of illness (which, I assume, correlates to length of service
requested) is according to a Poisson distribution, and appointments are
schedule accordingly?

If it is the first, are you assuming that the clinic does not require an
appointment in order to request service at the clinic?

Bill Braun
From: Bill Braun <medprac@hlthsys.com>
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