Resource Allocation Policies for Minimizing Mortality inMass Casualty Events

Dr. Izack Cohen

izik68@Technion.ac.il

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