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Resource Allocation Policies for Minimizing Mortality inMass Casualty Events
Dr. Izack Cohen
Prof. Avishai Mandelbaum, Noa Zychlinski MSc.
The Faculty of Industrial Engineering and Management
The Technion – Israel institution of Technology
Oklahoma City, 1995
Madrid, 2004
Argentina, 1994
NYC, 2001
London, 2005
Turkey, 2011
2
Rio De Janeiro, 2011
Indian Ocean, 2004
Japan, 2011
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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4
Flow of Casualties through an ED during an MCE
5
Casualties Flow in a Two-Station Network
To immediate operation
Arriving Immediates
Mortality
To admission and ICU
(1)Shock Rooms
(2)Operation
RoomsTo admission
and ICU
Mortality
Optimization Problem
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1 2
1 1 2 2( ), ( ) 0
[ ( ) ( )] MinT
N NQ t Q t dt
1 1 1 1 1 1
2 12 1 1 1 2 2 2 2 2
1 2
such that for all 0, :
( ) ( ) ( ( ) ( )) ( )
( ) ( ( ) ( )) ( ( ) ( )) ( )
( ) ( )
t T
Q t t Q t N t Q t
Q t p Q t N t Q t N t Q t
N t N t N
1 2 1 2
1 2
( ), ( ), ( ), ( ) 0 , and
(0) 0, (0) 0.
N t N t Q t Q t
Q Q
Mortality Rate
Casualties at Station
Minimizing Mortality
Arrival Rate
Treatment Rate Surgeons
at Station
Change in Casualties
Casualties at Station
Balance Equation for Station 1
Balance Equation for Station 2
Resource Constraint
From Solutions to Policies
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Conditions
Station 1 or 2 –
equal performance
(Case 1)
Station 1
(Case 4)
Station 2
(Case 7)
Station 1
(Case 2)
Station 1
(Case 5)
Prioritize Station 1 and switch
priorities at some t
(Case 8)
Station 2
(Case 3)
Prioritize Station 2 and
switch priorities at some t
(Case 6)
Station 2
(Case 9)
1 2q q= 1 2q q>1 2q q<
1 12 21 p
1 12 21 p
1 12 21 p
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Policies Application
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.
(a) (b)
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Optimal resource allocation solutions for different time points 0, 60, 120, 180
MCE Real-Time Management
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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 real-
time management of MCEs.
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Acknowledgements• 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
