TexFire IIITexas Wildfire Aerial Response Optimization

Applications of Operations ResearchSohum Daftary

Fire Intensity per County

• Keetch- Byrum Drought Index (KBDI)• Input– Fuel Dryness– Precipitation– Humidity

• Output– 0:800 Scale

Fire Rate of Spread per County• Output

– Stratified Rate as percent of county area– Expected Value for County Total– Chains per Hour

• Input– Weather– Topography– Fuel

Aerial Suppression:

Approach 1: Cost Minimization

Burn Time

Dam

age

Cost

of W

ildfir

e

Assumptions• Logistic growth of

Cost• County (j)• r(j) = rate of fire

spread • K(j) = CostScore• Use Empirics to

Calculate Constant

Approaches

CostScore

• What is the maximum monetary damage a wildfire can deal?

• Total Market Value of Taxable Property per County– Residences– Minerals– Agricultural Land– Commercial Sites

Mitigation vs Damage

Optimal Mitigation Cost

Desired Burn Time

• C = Mitigation Cost• NVC = Damage Cost

Problems

• Unrealistic– Too utilitarian– Costs and Benefits not realized on actor

• Model Set up– Complex– Difficult to isolate in a linear program with Cost

Score function

Approach 2: Damage Minimization

• Minimize Miles of Fire Burned • Minimize Time to “Stop” the Fire

Mitigation Plan Assumptions

Suppression v. Effectiveness

• Suppression – Max Fire Mitigation

• Effectiveness – Scalar on Suppression

Fire to County Assumptions

• 25 Counties (j)• Nearest Airfield (i)– Determined by TexFire II– Assume Helicopters and SEATs have same rate– Assume Helicopters and SEATs return to same base

Linear Programming

Skeletal structure of LPSimplex model using Excel Solver, GAMS, or AMPL

Model

Generalized Network

Flow 1

3

2

Rn

M

M

0

B = 1

Z = 1

Z = 1

3’

2’

1’-x(Rn), -(B)

(0,S)

(0,S)

(0,S)

-x(Rn), -(B)

-x(Rn), -(B)

ModelDECISION VARIABLES X (j) number of helicopters dispatched from AIRFIELD (i) to COUNTY (j) Y (j)number of SEATS dispatched from AIRFIELD (i) to COUNTY (j)

Model Summarized

Results

0 20 40 60 800

1

2

3

4

Count of Fire Burn Times

Frequency

Fire Burn Time (Hours)

Coun

t

Results

SUCCESS!

Next Steps

• Coverage of all 250 Counties• More accurate assumptions– Multiple county fire breakout– Variable aircraft rates and refuel locations

• Implementation of CostScore Model

Next Steps