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Resource Allocation Policies for
Minimizing Mortality in
Mass Casualty Events
Dr. Izack Cohen
[email protected]
Prof. Avishai Mandelbaum, Noa Zychlinski MSc.
The Faculty of Industrial Engineering and Management
The Technion – Israel institution of Technology
Indian Ocean, 2004
NYC, 2001
Madrid, 2004
Turkey, 2011
Japan, 2011
Rio De Janeiro, 2011
Argentina, 1994
London, 2005
Oklahoma City, 1995
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The Main Results
• A general, fluid-model based approach, for modeling
MCEs.
• An MCE classification scheme ,wherein a resource
allocation policy is suggested for each class.
• A real-time management approach.
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Flow of Casualties through an ED during an MCE
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Casualties Flow in a Two-Station Network
Mortality
Mortality
Arriving
Immediates
(1)
Shock
Rooms
To immediate
operation
(2)
Operation
Rooms
To admission
and ICU
To admission
and ICU
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Optimization Problem
Casualties
at Station
Mortality
Rate
T
Min
Q1 (t )   2Q2 (t )] dt
 [1Treatment
Arrival
0
Rate
Rate
such that for all t   0, T  :
N1 ( ), N 2 ( )
Casualties
at Station

Q1 (t )   (t )   1 (Q1 (t )  N1 (t ))  1  Q1 (t )

Minimizing Mortality
Surgeons
at Station
Balance Equation for
Station 1
Q 2 (t )  p12   1 (Q1 (t )  N1 (t ))   2 (Q2 (t )  N 2 (t ))   2  Q2 (t )
Change in
N1 (t )  N 2 (t )  N
Casualties
Resource Constraint
Balance Equation for
Station 2
N1 (t ), N 2 (t ), Q1 (t ), Q2 (t )  0 , and
Q1 (0)  0, Q2 (0)  0.
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From Solutions to Policies
Conditions
1 1  p12   2
q1 = q2
q1 > q2
q1 < q2
Station 1 or 2 –
Station 1
Station 2
equal performance
(Case 4)
(Case 7)
Station 1
Station 1
Prioritize Station 1 and switch
(Case 2)
(Case 5)
priorities at some t
(Case 1)
1 1  p12   2
(Case 8)
1 1  p12   2
Station 2
Prioritize Station 2 and
Station 2
(Case 3)
switch priorities at some t
(Case 9)
(Case 6)
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Policies Application
(a)
(b)
A dynamic allocation of surgeons to two treatment stations, life-saving
followed by operating, so as to minimize mortality during an MCE. (a)
Represents an event that took place far from the hospital, hence the
arrival waves are 60 minutes apart and (b) represents an event at closer
proximity where the arrival waves are 15 minutes apart.
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MCE Real-Time Management
Optimal resource allocation solutions for different time points 0, 60,
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120, 180
Summary
•
Traditional MCE models are based on simulation
experiments.
•
We used fluid models to formulate the problem and
then gained structural results.
• The suggested optimal allocation policies can be easily
applied to prepare an emergency plan for reference
scenarios.
• A developed rolling horizon approach allows for realtime management of MCEs.
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• Prof. Avishai Mandelbaum, Mrs. Noa Zychlinski – co-authors
• Dr. Michalson Moshe, Medical Director of Trauma teaching center,
Rambam Hospital
• Dr. Israelit Shlomi, Chief of ED, Rambam Hospital
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