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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.
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
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
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
Collaborators
Maria Mayorga
North Carolina State University
Students / Former students
Sardar Ansari
Soovin Yoon
Suzan Afacan
Eric Dubois
5
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
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
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
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
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
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
Response times vs. cardiac arrest survival
12
CDF of
calls for
service
covered
Response time (minutes) 9
80%
Response times vs. cardiac arrest survival
13
CDF of
calls for
service
covered
Response time (minutes) 9
80%
What is the best response time threshold?
• Guidelines suggest 9 minutes
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
15
Responses
no longer
“count”
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
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
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
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
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
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
Dispatching models
22
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
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
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
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
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.
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
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
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)
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
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
What about natural disasters and severe
weather events?
33
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
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
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
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
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
How can we optimally restore a network
while providing service?
39
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
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
𝑡𝑡 = 0
42
𝑡𝑡 = 5
43
𝑡𝑡 = 10
44
𝑡𝑡 = ∞
45
Objective function versus time
46
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
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

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Designing emergency medical service systems to enhance community resilience

  • 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
  • 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
  • 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