Emergency response to patients with medical needs after a disaster is a critical aspect of public safety and community resilience. An effective response to emergency medical patients can be achieved by designing a system that - Allocates limited resources such as ambulances in resource-constrained settings, - Leverages data and triage information to inform the design of response districts, and - Sheds light on how these decisions change after a disaster. In this talk, Dr. Laura Albert will discuss how analytical methods can be used to design emergency response systems and provide guidance into how to design data-driven emergency response systems. She will discuss how system design decisions must change after weather disasters when the system is congested and critical infrastructure is impaired.

1. Designing emergency medical service
systems to enhance community resilience
Laura Albert
Industrial & Systems Engineering
University of Wisconsin-Madison
laura@engr.wisc.edu
punkrockOR.com
@lauraalbertphd
1This work was in part supported by the National Science Foundation under Award No. 1054148, 136,1448, 1444219, 1541165.

2. An introduction
I’m an industrial and systems engineering professor and
assistant dean at the University of Wisconsin-Madison
Punk Rock Operations Research (punkrockOR.com) blogger
@lauraalbertphd on twitter
Laura Albert 2AAAS 2018

3. I study systems
A system is a set of things—people, vehicles, travelers going
through checkpoint security, or whatever—interconnected in
such a way that they produce their own pattern of behavior
over time.
My discipline is operations research: the science of making
decisions using advanced analytical methods.
AAAS 2018 Laura Albert 3

4. The road map
• How do emergency medical service (EMS) systems work?
• How do we know when EMS systems work well?
• How can we improve how well EMS systems work?
• How can EMS systems enhance community resilience after
disasters?
4

5. Collaborators
Maria Mayorga
North Carolina State University
Students / Former students
Sardar Ansari
Soovin Yoon
Suzan Afacan
Eric Dubois
5

6. Anatomy of a 911 call
Response time
Service provider:
Emergency 911 call
Unit
dispatched
Unit is en
route
Unit arrives
at scene
Service/care
provided
Unit leaves
scene
Unit arrives
at hospital
Patient
transferred
Unit returns
to service
6
Response time from the patient’s point of view

7. Anatomy of a 911 call
Call arrives to
call center
queue
Call answered
by call taker
Triage / data
entry
Call sent to
dispatcher
Information
collected from
caller
Instructions to
caller
Call taker
ends call
Dispatcher
answers call
First unit
assigned
Additional
units assigned
Pre-arrival
instructions to
service providers
Dispatcher
ends call
Response time
Service provider:
Dispatcher:
Call taker:
Dispatch time
Dispatch time
Emergency 911 call
Unit
dispatched
Unit is en
route
Unit arrives
at scene
Service/care
provided
Unit leaves
scene
Unit arrives
at hospital
Patient
transferred
Unit returns
to service
7

8. EMS design varies by community:
One size does not fit all
8McLay, L.A., 2011. Emergency Medical Service Systems that Improve Patient Survivability. Encyclopedia of Operations Research in the area of
“Applications with Societal Impact,” John Wiley & Sons, Inc., Hoboken, NJ (published online: DOI: 10.1002/9780470400531.eorms0296)
Fire and EMS vs. EMS
Paid staff vs. volunteers
Publicly run vs. privately run
Emergency medical technician
(EMT) vs. Paramedic (EMTp)
Mix of vehicles
Mutual aid

9. Performance standards come from the
National Fire Protection Agency (NFPA)
• NFPA 1710 guidelines for departments with paid staff
• 5 minute response time for first responding vehicle
• 9 minute response time for first advanced life support vehicle
• Must achieve these goals 90% of the time for all calls
• Similar guidelines for volunteer agencies in NFPA 1720 allow
for 9-14 minute response times
• Guidelines based on medical research for cardiac arrest
patients and time for structural fires to spread
• Short response times only critical for some patient types:
cardiac arrest, shock, myocardial infarction
• Most calls are lower-acuity
• Many communities use different response time goals
9

10. Operationalizing recommendations when
sending ambulances to calls
Priority dispatch:
… but which ambulance when there is a choice?
10
Type Capability Response Time
Priority 1
Advanced Life Support (ALS) Emergency
Send ALS and a fire engine/BLS
E.g., 9 minutes
(first unit)
Priority 2
Basic Life Support (BLS) Emergency
Send BLS and a fire engine if available
E.g., 13 minutes
Priority 3
Not an emergency
Send BLS
E.g., 16 minutes

11. Performance standards
National Fire Protection Agency (NFPA) standard yields a
coverage objective function for response times
Most common response time threshold (RTT):
9 minutes for 80% of calls
• Easy to measure
• Intuitive
• Unambiguous
11

12. Response times vs. cardiac arrest survival
12
CDF of
calls for
service
covered
Response time (minutes) 9
80%

13. Response times vs. cardiac arrest survival
13
CDF of
calls for
service
covered
Response time (minutes) 9
80%

14. What is the best response time threshold?
• Guidelines suggest 9 minutes
14

15. What is the best response time threshold?
• Guidelines suggest 9 minutes
• Medical research suggests ~5 minutes
• But this would disincentive 5-9 minute responses
15
Responses
no longer
“count”

16. What is the best response time threshold?
• Guidelines suggest 9 minutes
• Medical research suggests ~5 minutes
• But this would disincentive 5-9 minute responses
• Which RTT is best for design of the system?
16

17. What is the best response time threshold
based on retrospective survival rates?
Decision context is locating and dispatching ALS ambulances
• Discrete optimization model to locate ambulances *
• Markov decision process model to dispatch ambulances
17
* McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service Performance Measures. Health Care
Management Science 13(2), 124 - 136

18. Survival and dispatch decisions
18
Across different ambulance configurations
McLay, L.A., Mayorga, M.E., 2011. Evaluating the Impact of Performance Goals on Dispatching Decisions in
Emergency Medical Service. IIE Transactions on Healthcare Service Engineering 1, 185 – 196
Minimize un-survivability when altering dispatch decisions

19. Ambulance Locations, N=7
Best for patient survival / 8 Minute RTT
= one ambulance
= two ambulances
McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service
Performance Measures. Health Care Management Science 13(2), 124 - 136
Suburban area –>
(vs. rural areas)
<– Interstates
19

20. Ambulance Locations, N=7
10 Minute RTT
= one ambulance
= two ambulances
McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service
Performance Measures. Health Care Management Science 13(2), 124 - 136
20

21. Ambulance Locations, N=7
5 Minute RTT
= one ambulance
= two ambulances
McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service
Performance Measures. Health Care Management Science 13(2), 124 - 136 21

22. Dispatching models
22

23. Ambulance dispatching must consider
tradeoffs across patients
Tradeoffs exist in real-time decision-making between patients
at hand and patients that may arrive
AAAS 2018 Laura Albert 23
911 call
Unit
dispatched
Unit arrives
at scene
Service/care
provided
Unit leaves
scene
Unit arrives
at hospital
Patient
transferred
Unit returns
to service
Send ambulance based on
triage information
Patient
triage
Ambulance unavailable for other patients
Response time /
“Coverage”
True
priority
HT or LT

24. Optimal dispatching policies
using Markov decision process models
Optimality equations:
𝑉𝑉𝑘𝑘 𝑆𝑆𝑘𝑘 = max
𝑥𝑥𝑘𝑘∈𝑋𝑋(𝑆𝑆𝑘𝑘)
𝐸𝐸 𝑢𝑢𝑖𝑖𝑖𝑖
𝜔𝜔
𝑥𝑥𝑘𝑘 + 𝑉𝑉𝑘𝑘+1 𝑆𝑆𝑘𝑘+1 𝑆𝑆𝑘𝑘, 𝑥𝑥𝑘𝑘, 𝜔𝜔
Formulate problem as an undiscounted, infinite-horizon, average reward
Markov decision process (MDP) model.
Information changes over the course of a call
• Decisions made based on classified priority.
• Performance metrics based on true priority.
• The state 𝒔𝒔𝒌𝒌 ∈ 𝑆𝑆 describes the combinations of busy and free ambulances.
• 𝑋𝑋(𝒔𝒔𝑘𝑘) denotes the set of actions (ambulances to dispatch) available in state 𝒔𝒔𝒌𝒌.
• Reward 𝑢𝑢𝑖𝑖𝑖𝑖
𝜔𝜔 depend on true priority.
• Transition probabilities: the state changes when (1) one of the busy servers completes service or
(2) a server is assigned to a new call.
Select
best
ambulance
to send
Value in
current
state
Values in
(possible)
next states
(Random)
reward based
on true patient
priority

25. Under- or over-prioritize
• Assumption: classify calls as high or low priority and
respond uniformly to each type
• Assumption: No priority 3 calls are truly high-priority
Case 1: Under-prioritize medium priority calls with different
classification accuracy
Pro: fewer classified high priority calls leads to better resource
allocation
Cons: Slower response to some true high
priority calls misclassified as low-priority
Pr1
High
Pr2
Low
Pr3
Low
HT
Pr1
High
Pr2
Low
Pr3
Low
HT
High accuracy
 𝛼𝛼 =
𝑃𝑃 𝐻𝐻𝑇𝑇 𝐻𝐻
𝑃𝑃(𝐻𝐻 𝑇𝑇|𝐿𝐿)
25
Classified high-priority
Classified low-priority
Low accuracy

26. Under- or over-prioritize
• Assumption: classify calls as high or low priority and
respond uniformly to each type
• Assumption: No priority 3 calls are truly high-priority
Case 2: Over-prioritize medium priority calls
Pro: All true high priority calls are classified as high priority
Con: most calls are classified as high priority, which makes it
difficult to allocate resources according to risk
Pr1 Pr2 Pr3
HT
26
Classified high-priority
Classified low-priority

27. Structural properties
RESULT
It is more beneficial for an ambulance to be idle than busy.
RESULT
It is more beneficial for an ambulance to be serving closer
patients.
RESULT
It is not always optimal to send the closest ambulance, even for
high priority calls.

28. System Performance
Fraction of High-Priority calls covered in 9 minutes
0 10 20 30 40 50
0.405
0.41
0.415
0.42
0.425
0.43
0.435
0.44
0.445
α
Expectedcoverage
Optimal Policy, Case 1
Optimal Policy, Case 2
Closest Ambulance
28
Better accuracy

29. How do we use that goal to send ambulances to
prioritized patients in real-time?
AAAS 2018 Laura Albert 29
Case 2: First to send to high-priority calls
Station
1
2
3
4
Case 2: Second to send to high-priority calls
Station
1
2
3
4
Rationed for
high-priority calls
Rationed for low-
priority calls
Insight: Service can be improved via optimization of backup service and response to
low-priority patients

30. Should we replace an ambulance (2 EMTp/EMT) with two quick
response vehicles (1 EMTp)?
• Double response = both types of vehicles dispatched
• Patient downgrades / upgrades
AAAS 2018 Laura Albert 30
Coordinating multiple types of vehicles
with prioritized patients is not intuitive
Mix of vehicles
Emergency medical technician
(EMT) vs. Paramedic (EMTp)

31. Should we replace an ambulance
with two quick response vehicles?
31
Optimization models suggest that quick response vehicles are a good idea
Sometimes both vehicles
must go to hospital (tying up
3 EMTs/EMTps instead of 2)
Sending both vehicles to a
call can overcome initial
uncertainty about patient
needs and better match
resources to health needs
Double response: Send both types of vehicles because quick
response vehicles cannot take patients to hospital

32. Application in a real setting: 5% more high-priority calls
were responded to in less than 9 minutes without an
increase in cost!
Achievement Award Winner for Next-Generation Emergency Medical Response
Through Data Analysis & Planning (Best in Category winner), National
Association of Counties, 2010.
McLay, L.A., Moore, H. 2012. Hanover County Improves Its Response to Emergency Medical 911 Calls. Interfaces 42(4),
380-394.
AAAS 2018 Laura Albert 32

33. What about natural disasters and severe
weather events?
33

34. How does severe weather affect emergency response?
• What is different during severe weather:
• there may be a surge of patients,
• critical infrastructure is impaired or destroyed, and
• there are cascading failures in the system.
• Motivates the need for new models to support data-driven
decisions in new situations
1. Delay service to some calls when the system is congested
2. Coordinate emergency response efforts with network restoration
efforts after a disaster
AAAS 2018 Laura Albert 34

35. Emergency response in congested networks
• Models implicitly assume patients receive immediate care.
• Patients with time-critical conditions are more vulnerable to
the delay of service resulting from congestion.
• When the system is congested, the response to less urgent
emergency calls can be delayed.
Goal: response plans that depend on the level of available
resources in the system as well as the specific needs of the
patients.
35

36. EMS with a cutoff priority queue:
A dynamic response plan that depends on the level of
resources available in the system
Triage
• A call taker classifies each call as high-priority or low-priority
• High-priority calls receive an immediate response
• Low-priority calls only receive an immediate response if the system
is not congested
• Low-priority calls are either queued or “lost” when the number of
available servers is less than the number of reserved servers
New spatial hypercube queueing approximation that can
captures the dynamics for losing and queueing calls
Mixed integer linear programming (MILP) model that uses
queueing approximation to locate ambulances on a network

37. Expected coverage as a function of how many servers
are reserved (𝑠𝑠𝑅𝑅) for high-priority calls with 𝑠𝑠 = 16
servers
Note: this figure assumes low-priority calls have no
value so there is no penalty for “losing” calls
Base case:
reserve
no servers
The number of servers in reserve
Loss system:
Neighboring regions
serve low-priority
calls through
mutual aid

38. How to select the number of servers to
reserve for high-priority calls
Expected total coverage for different weights 𝑤𝑤 for low-priority calls
relative to high priority calls with weight 1.0
𝑠𝑠𝑅𝑅 = 12 when 𝑤𝑤 = 0.1
𝑠𝑠𝑅𝑅 = 8 when 𝑤𝑤 = 0.2
𝑠𝑠𝑅𝑅 = 5 when 𝑤𝑤 = 0.5
Coverage worsens if
too many servers
are reserved

39. How can we optimally restore a network
while providing service?
39

40. How can we optimally restore a network
while providing service?
40
Two types of service providers:
1) Repair crews who install of network components over a time horizon
2) Emergency responders who deliver time-sensitive commodities
Model gives insight into how to priority restoration efforts to deliver critical services
after a disaster

41. Locating emergency responders on a
network
Issues:
1. The canonical models
consider one-shot decisions
2. The network has missing
components (arcs)
3. We want to relocate
emergency responders as
network is restored.
4. Need to restore the most
critical network
components first.
Our model
1. Series of location decisions
over the restoration time.
2. Repair crews install arcs in
the network over a time
horizon.
3. That’s a good idea. Let’s do
it.
4. Minimize the time-
cumulative weighted
distance between
emergency responders and
demand to reach this goal.
41

42. 𝑡𝑡 = 0
42

43. 𝑡𝑡 = 5
43

44. 𝑡𝑡 = 10
44

45. 𝑡𝑡 = ∞
45

46. Objective function versus time
46

47. What are the next challenges?
• Emergency response to
support critical and
interdependent infrastructure
• Interdependent
infrastructure provides an
opportunity for resilience
47
Emergency
Response &
Healthcare
Infrastructure
Disasters

48. 48

49. Thank you!
49
1. McLay, L.A., Mayorga, M.E., 2013. A model for optimally dispatching ambulances to emergency calls with classification errors in
patient priorities. IIE Transactions 45(1), 1—24.
2. McLay, L.A., Mayorga, M.E., 2011. Evaluating the Impact of Performance Goals on Dispatching Decisions in Emergency Medical
Service. IIE Transactions on Healthcare Service Engineering 1, 185 – 196
3. McLay, L.A., Mayorga, M.E., 2014. A dispatching model for server-to-customer systems that balances efficiency and equity. To appear
in Manufacturing & Service Operations Management, doi:10.1287/msom.1120.0411
4. Ansari, S., McLay, L.A., Mayorga, M.E., 2015. A Maximum Expected Covering Problem for District Design, Transportation Science
51(1), 376 – 390.
5. McLay, L.A., Moore, H. 2012. Hanover County Improves Its Response to Emergency Medical 911 Calls. Interfaces 42(4), 380-394.
6. McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service Performance Measures. Health Care Management
Science 13(2), 124 – 136
7. Yoon, S., Albert, L. 2017. An Expected Coverage Model with a Cutoff Priority Queue. To appear in Health Care Management Science.
8. Afacan, S. I., Albert, L.A. 2017. An Integrated Network Design and Scheduling Problem for Network Recovery and Emergency
Response. Under review at European Journal of Operational Research.
laura@engr.wisc.edu
punkrockOR.com
@lauraalbertphd