Discrete Event vs. DiffEq Models
Posted: Wed Nov 19, 2003 9:31 am
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
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