final capstone presentation
TRANSCRIPT
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