This document provides an overview of emergency medical services (EMS) systems and how operations research can help improve them. It discusses how EMS systems work, how their performance is evaluated, and ways to enhance performance. Some key points: - EMS design varies by community and involves decisions around staffing, vehicle types, and ambulance locations. - National guidelines recommend response times of 5 minutes for cardiac arrests and 9 minutes for other calls. - Operations research models can help determine optimal ambulance locations and dispatching policies to maximize coverage and patient survival based on response times. These models account for uncertainty in call priorities. - Simulation and optimization techniques have found policies that improve coverage and better prioritize true high-priority calls

1. Delivering emergency medical services:
Research, theory, and application
Laura Albert
Industrial & Systems Engineering
University of Wisconsin-Madison
laura@engr.wisc.edu
punkrockOR.com
@lauraalbertphd
1
This work was in part supported by the U.S. Department of the Army under Grant Award Number W911NF-10-1-0176
and by the National Science Foundation under Award No. 1054148, 1444219, 1541165.

2. 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?
• Where is EMS search in operations research going?
• Where do they need to go?
2

3. Collaborators
Maria Mayorga
North Carolina State University
Students
Sardar Ansari
Ben Grannan
Soovin Yoon
3

4. One sentiment in the 1960s in the US
“If we can land a man on the moon…”
...why can't we attack fundamental societal problems using
math and operations research?
4

5. OR in EMS, fire & policing
5
The President’s
Commission on Law
Enforcement and the
Administration of Justice
(1965)
Al Blumstein chaired the
Commission’s Science
and Technology Task
Force (CMU)
Richard Larson did
much of the early
work (MIT)
1972
1972

6. A golden age of public safety research began
in the 1960s
• New York City / RAND Institute Collaboration
• Between 1963 – 1968, fire alarms in NYC increased 96% while
operating expenses remained the same
• New York City used simulation for the first time!
• The research was put into practice
• Public safety research applications were influential and
productive in the field of operations research
• Queueing, integer programming, simulation, data analytics
• Many applied operations research papers appeared in the
best journals
• The research won major awards (Lanchester, Edelman,
NATO Systems Science Prize)
6

7. Early urban operations research models
7
Set cover / maximum cover models
How can we “cover” the maximum
number of locations with
ambulances?
Church, R., & ReVelle, C. (1974). The maximal covering
location problem. Papers in regional science, 32(1),
101-118.
Markov models
How many fire engines should we send?
Swersey, A. J. (1982). A Markovian decision model for deciding how
many fire companies to dispatch. Management Science, 28(4), 352-
365.
Analytics
How far will a fire
engine travel to a call?
Kolesar, P., & Blum, E. H.
(1973). Square root laws
for fire engine response
distances. Management
Science, 19(12), 1368-1378.
Hypercube queueing models
What is the probability that our first choice
ambulance is unavailable for this call?
Larson, R. C. (1974). A hypercube queuing model for facility location
and redistricting in urban emergency services. Computers &
Operations Research, 1(1), 67-95.

8. 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
8
Response time from the patient’s point of view

9. EMS design varies by community:
One size does not fit all
9McLay, 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
Ambulance location,
relocation, and relocation
on-the-fly
Mutual aid

10. 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
10

11. Operationalizing recommendations when
sending ambulances to calls
Priority dispatch:
… but which ambulance when there is a choice?
11
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

12. 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
12

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
• Medical research suggests ~5 minutes
• But this would disincentive 5-9 minute responses
14
Responses
no longer
“count”

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
• Which RTT is best for design of the system?
15

16. 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
16
* McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service Performance Measures. Health Care
Management Science 13(2), 124 - 136

17. Survival and dispatch decisions
17
Across different ambulance
configurations
Across different call
volumes
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

18. 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
18

19. 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
19

20. 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 20

21. Dispatching models
21

22. Optimal dispatching policies
using Markov decision process models
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
Determine which
ambulance to send based
on classified priority
Classified
priority
(H or L)
True
priority
HT or LT
22
Information changes over the course of a call
Decisions made based on classified priority.
Performance metrics based on true priority.
Classified customer risk
Map Priority 1, 2, 3 call types to high-priority (𝐻𝐻) or low-priority (𝐿𝐿)
Calls of the same type treated the same
True customer risk
Map all call types to high-priority (𝐻𝐻𝑇𝑇) or low-priority (𝐿𝐿𝑇𝑇)

23. 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
• 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 (random).
• 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

24. Under- or over-prioritize
• Assumption:
No priority 3 calls are truly high-priority
Case 1: Under-prioritize with different classification accuracy
Case 2: Over-prioritize
Pr1 Pr2 Pr3
Pr1 Pr2 Pr3
HT
HT
Pr1 Pr2 Pr3
HT
Pr1 Pr2 Pr3
HT
Informational
accuracy captured by:
𝛼𝛼 =
𝑃𝑃 𝐻𝐻𝑇𝑇 𝐻𝐻
𝑃𝑃(𝐻𝐻𝑇𝑇|𝐿𝐿)
24
Classified high-priority
Classified low-priority
Improved accuracy

25. 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.

26. Coverage
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
26
Better accuracy

27. Low and high priority calls
Conditional probability that the closest unit is dispatched given
initial classification
High-priority calls Low-priority calls0 10 20 30 40 50
0.98
0.985
0.99
0.995
1
1.005
α
Proportionclosestambulanceisdispatched
Closest Ambulance
Optimal Policy, Case 1
Optimal Policy, Case 2
0 10 20 30 40 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
α
Proportionclosestambulanceisdispatched
Closest Ambulance
Optimal Policy, Case 1
Optimal Policy, Case 2
Classified high-priority Classified low-priority
27

28. Case 1 (𝛼𝛼 = ∞), Case 2 policies
High-priority calls
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
Service can be improved via optimization of backup service and response to low-priority patients
Rationed for
high-priority calls
Rationed for low-
priority calls
28

29. Districting and location models
29

30. Ambulance response districts
How should we locate ambulances?
How should we design response districts around each ambulance?
• Multiple ambulances per station
• Ambulance unavailability (spatial queueing)
• Uncertain travel times / Fractional coverage
• Workload balancing: all ambulances do the same amount of work
30Ansari, S., McLay, L.A., Mayorga, M.E., 2016. A maximum expected covering problem for locating and dispatching servers.
Transportation Science, published online in Articles in Advance.
Spatial
queueing
model
Mixed integer
programming
model

31. Districting model
Mixed Integer Linear Program
max ∑𝑤𝑤∈𝑊𝑊 ∑𝑗𝑗∈𝐽𝐽 ∑𝑝𝑝=1
𝑠𝑠 ∑ 𝑚𝑚=1
min(𝑐𝑐 𝑤𝑤,𝑠𝑠−𝑝𝑝+1)
𝑞𝑞𝑗𝑗𝑗𝑗𝑗𝑗 1 − 𝑟𝑟 𝑚𝑚
𝑟𝑟 𝑝𝑝−1
𝜆𝜆𝑗𝑗
𝐻𝐻
𝑅𝑅𝑤𝑤𝑤𝑤 𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤
subject to
∑𝑝𝑝=1
𝑠𝑠 ∑ 𝑚𝑚=1
𝜅𝜅 𝑤𝑤𝑤𝑤
𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 ≤ 1, 𝑗𝑗 ∈ 𝐽𝐽, 𝑤𝑤 ∈ 𝑊𝑊
∑𝑝𝑝=1
𝑠𝑠 ∑ 𝑚𝑚=1
𝜅𝜅 𝑤𝑤𝑤𝑤
𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 ≤ 𝑦𝑦𝑤𝑤, 𝑗𝑗 ∈ 𝐽𝐽, 𝑤𝑤 ∈ 𝑊𝑊
∑𝑤𝑤∈𝑊𝑊 𝑥𝑥𝑤𝑤𝑤𝑤𝑤𝑤 = 1, 𝑗𝑗 ∈ 𝐽𝐽, 𝑝𝑝 = 1, … , 𝑠𝑠
∑𝑝𝑝=1
𝑠𝑠
𝑥𝑥𝑤𝑤𝑤𝑤𝑤𝑤 = 𝑦𝑦𝑤𝑤 , 𝑗𝑗 ∈ 𝐽𝐽, 𝑤𝑤 ∈ 𝑊𝑊
𝑥𝑥𝑤𝑤𝑤𝑤𝑤𝑤𝑤 = ∑𝑝𝑝=max 1,𝑝𝑝′−𝑐𝑐 𝑤𝑤+1
𝑝𝑝𝑝
∑ 𝑚𝑚=𝑝𝑝′−𝑝𝑝+1
𝜅𝜅 𝑤𝑤𝑤𝑤
𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 ,
𝑗𝑗 ∈ 𝐽𝐽, 𝑤𝑤 ∈ 𝑊𝑊, 𝑝𝑝′
= 1, … , 𝑠𝑠
∑𝑤𝑤∈𝑊𝑊 𝑦𝑦𝑤𝑤 = 𝑠𝑠
𝑦𝑦𝑤𝑤 ≤ 𝑐𝑐𝑤𝑤, 𝑤𝑤 ∈ 𝑊𝑊
𝑟𝑟 − 𝛿𝛿 𝑦𝑦𝑤𝑤 ≤
∑𝑗𝑗∈𝐽𝐽 ∑𝑝𝑝=1
𝑠𝑠 ∑ 𝑚𝑚=1
𝜅𝜅 𝑤𝑤𝑤𝑤
𝜆𝜆𝑗𝑗
𝐻𝐻
+ 𝜆𝜆𝑗𝑗
𝐿𝐿
𝑞𝑞𝑗𝑗𝑗𝑗𝑗𝑗 1 − 𝑟𝑟 𝑚𝑚
𝑟𝑟 𝑝𝑝−1
𝜏𝜏𝑤𝑤𝑤𝑤 𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤
≤ 𝑟𝑟 + 𝛿𝛿 𝑦𝑦𝑤𝑤, 𝑤𝑤 ∈ 𝑊𝑊
𝑥𝑥𝑤𝑤𝑤𝑤𝑤𝑤 ≥ 𝑥𝑥𝑤𝑤𝑤𝑤𝑤, 𝑗𝑗 ∈ 𝐽𝐽, 𝑤𝑤 ∈ 𝑊𝑊, 𝑗𝑗′
∈ 𝑁𝑁𝑤𝑤𝑤𝑤
𝑦𝑦𝑤𝑤 ∈ 𝑍𝑍0
+
, 𝑤𝑤 ∈ 𝑊𝑊
𝑥𝑥𝑤𝑤𝑤𝑤𝑤𝑤 ∈ 0,1 , 𝑤𝑤 ∈ 𝑊𝑊, 𝑗𝑗 ∈ 𝐽𝐽, 𝑝𝑝 = 1, … , 𝑠𝑠
𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 ∈ 0,1 , 𝑤𝑤 ∈ 𝑊𝑊, 𝑗𝑗 ∈ 𝐽𝐽, 𝑝𝑝 = 1, … , 𝑠𝑠, 𝑚𝑚 = 1, … , 𝑐𝑐𝑤𝑤
31
Every customer has all the priorities and the
number of assignments to a station is equal to
the number of servers located at that station
A customer location is not assigned to
a station more than once and no call
location is assigned to a closed station
Linking constraints
Balance the load amongst
the servers
Locate 𝑠𝑠 servers with no more than 𝑐𝑐𝑤𝑤 per
station
Expected coverage
Contiguous first priority districts
Binary and integrality
constraints on the variables

32. Parameters
• 𝐽𝐽: set of all customer (demand) nodes
• 𝑊𝑊: set of all potential station locations
• 𝑠𝑠: total number of servers in the system
• 𝜆𝜆𝑗𝑗
𝐻𝐻
(𝜆𝜆𝑗𝑗
𝐿𝐿
): mean high-priority (low-priority)
call arrival rates from node 𝑗𝑗
• 𝜆𝜆: system-wide total call arrival rate
• 𝜏𝜏𝑤𝑤𝑤𝑤: mean service time for calls originated
from node 𝑗𝑗 and served by a server from a
potential station 𝑤𝑤.
• 𝜏𝜏: system-wide mean service time
• 𝑐𝑐𝑤𝑤: capacity of station 𝑤𝑤
32
• 𝑟𝑟: system-wide average server utilization
• 𝑃𝑃𝑠𝑠: loss probability (probability that all 𝑠𝑠
servers are busy)
• 𝑅𝑅𝑤𝑤𝑤𝑤: expected proportion of calls from 𝑗𝑗
that are reached by servers from station 𝑤𝑤
in nine minutes
• 𝑞𝑞𝑗𝑗𝑗𝑗𝑗𝑗: correction factor for customer 𝑗𝑗's 𝑝𝑝th
priority server at which there are 𝑚𝑚 servers
located.
• 𝑁𝑁𝑤𝑤𝑤𝑤: set of demand nodes that are
neighbors to 𝑗𝑗 and are closer to station 𝑤𝑤
than 𝑗𝑗.
Decision variables
• 𝑦𝑦𝑤𝑤 = number of servers located at station 𝑤𝑤, 𝑤𝑤 ∈ 𝑊𝑊.
• 𝑧𝑧𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤= 1 if there are 𝑝𝑝 − 1 servers located at stations that node 𝑗𝑗 prefers over 𝑤𝑤 and there
are 𝑚𝑚 servers located at station 𝑤𝑤, 𝑤𝑤 ∈ 𝑊𝑊, 𝑗𝑗 ∈ 𝐽𝐽, 𝑝𝑝 = 1, … , 𝑠𝑠, 𝑚𝑚 = 1, … , 𝑐𝑐𝑤𝑤 and 0 otherwise.
• 𝑥𝑥𝑤𝑤𝑤𝑤𝑤𝑤= 1 if 𝑝𝑝′
< 𝑝𝑝 < 𝑠𝑠 − 𝑝𝑝𝑝𝑝 where are 𝑝𝑝′
is the number of servers located at stations that
node 𝑗𝑗 prefers over 𝑤𝑤, and 𝑝𝑝′′
is the number of servers located at stations that node 𝑗𝑗 prefers
less than 𝑤𝑤, 𝑤𝑤 ∈ 𝑊𝑊, 𝑗𝑗 ∈ 𝐽𝐽, 𝑝𝑝 = 1, … , 𝑠𝑠, and 0 otherwise.

33. Results
RESULT
The Base model that does not maintain contiguity or a balanced
load amongst the ambulances is NP-complete.
• reduction from k-median
RESULT
The first priority response districts for the Base model are
contiguous if there is no more than one ambulance per station.
RESULT
Identifying districts that balance the workload is NP-complete.
• reduction from bin packing
RESULT
Reduced model to assign only the top 𝑠𝑠′ ≤ 𝑠𝑠 ambulances
• Not trivial, allows model to scale up to have many ambulances
33

34. Hanover County: example

35. First priority districts for the base model
• Base Model: no workload balancing or contiguity constraints

36. Model with workload balancing but no
contiguity constraints
• First Priority Districts for one time period

37. First priority districts may be different if we
balance the workload
• Workload balancing
• Contiguous first priority districts
Two ambulances

38. Coordinating multiple types of vehicles is not
intuitive due to double response
• Not intuitive how to use multiple types of vehicles
• ALS ambulances / BLS ambulances (2 EMTp/EMT)
• ALS quick response vehicles (QRVs) (1 EMTp)
• Double response = both ALS and BLS units dispatched
• Downgrades / upgrades for Priority 1 / 2 calls
• Who transports the patient to the hospital?
• Research goal: operationalize guidelines for sending vehicle
types to prioritized patients
• (Linear) integer programming model for a two vehicle-type
system: ALS Non-transport QRVs and BLS ambulances
38

39. The more ALS QRVs in use, the better the
coverage
39

40. Application in a real setting: the results were
better than anticipated
40
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.

41. Where do EMS systems need to go?
41

42. EMS = Prehospital care
Operations Research
• Efficiency
• Optimality
• Utilization
• System-wide performance
Healthcare
• Efficacy
• Access
• Resources/costs
• “Patient centered outcomes”
42
Healthcare
Transportation
Public sector
Common ground?

43. More thoughts on patient centered outcomes
Operational measures used to
evaluate emergency departments
• Length of stay
• Throughput
Increasing push for more health
metrics
• Disease progression
• Recidivism
Many challenges for EMS modeling
• Health metrics needed
• Information collected at scene
• Equity models a good vehicle for
examining health measures
(access, cost, efficacy)
43
Healthcare
Transportation
Public sector

44. Patient centered outcomes
44

45. EMS response during/after extreme events
depends on critical infrastructure
45
EMS service largely dependent on other
interdependent systems and networks
Decisions may be very different during
disasters
• Ask patients to wait for service
• Patient priorities may be dynamic
• Evacuate patients from hospitals
• Massive coordination with other
agencies (mutual aid)
Two main research streams exist:
1. Normal operations
2. Disaster operations
More guidance needed for “typical”
emergencies and mass casualty
events
E.g., Health risks during/after
hurricanes:
• Increased mortality, traumatic
injuries, low-priority calls
• Carbon monoxide poisoning,
Electronic health devices
* Caused by power failures

46. Thank you!
46
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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
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Manufacturing & Service Operations Management, doi:10.1287/msom.1120.0411
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“Applications with Societal Impact,” John Wiley & Sons, Inc., Hoboken, NJ (published online: DOI: 10.1002/9780470400531.eorms0296)
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