Creating an evacuation plan for livestock during emergency disasters: The case of

Fukushima, JapanBy:

Chrysafis Vogiatzis, Ruriko Yoshida, Ines Aviles-Spadoni, and Shigeki Imamoto

March 11, 2011• Magnitude 9.0 - 70 km east of Oshika Peninsula

– 15,790 deaths, 5,933 injured 4,056 missing across 18 prefectures, 125,000 buildings damaged or destroyed

• Most powerful earthquake to ever hit Japan - one of five most powerful in the world

• 40 m high tsunami - 10 km inland.

• Meltdown at three reactors in Fukushima Nuclear Power Plant complex

• 20 km radius evacuation zone

Why we decided to get to work on a plan?

• Economic implications to region, farmers

• Loss of lively hood

• Public health implications

• Humane implications

What kind of assistance is out there?

•After Hurricane Katrina in 2005, the Pets Evacuation and Transportation Standards Act (PETS Act, Pub. Law No. 109–308) was passed into law in 2006

•The Federal Emergency Management Agency does have information for dealing with livestock in a variety of disasters but none formulated mathematically

•And, no specific evacuation plans for livestock in areas where nuclear power plants are located

So we set our sights on…• Providing the livestock industry a tool to protect their animals

and farm, in this case, those located near nuclear power plants

• IFAW Report states “It is essential to devise a plan to save the greatest number of animals possible in the shortest amount of time through the work of these specialized teams.”

• Our efforts• Completely altruistic• Non-funded

What does this mean for the U.S.?• Total of 104

reactors• 20% electricity• Eastern half of U.S.• 52 are 40-years-old• Beef, 32,834,801 • Dairy, 9,266,574

Prior to civilian evacuation, the Japanese Ministry of Economy, Trade and Industry reported that, 9300head of cattle were in the Fukushima Prefecture including 30,000 pigs and 440,000 chickens

Our Research

• We came up with two new models for livestock evacuation

• We present also an algorithm based on the augmented Lagrange relaxation

• Computational results and comparisons are also given to depict the success of our approach.

Why use OR?• What is Operations Research?

– A discipline that employs mathematical formulations and techniques to model and solve real life problems.

• Why use it?– Provides us with the best possible solution

– Makes planning and management to problems more efficient

– Has had an impact on social welfare (aviations, logistics, scheduling)

Evacuation Management

• It is a special, large scale optimization problem

• Techniques suitable for smaller instances might prove to be computationally costly

– Evacuation modeling is a special case of a network design problem

– NP-hard; i.e. difficult to solve

– Approximation schemes are used to reduce running time

Models• Mathematical formulations need to be tight

and rigorous

• Different models assess different measures and approach other solutions

• We show two models:

– Origin-destination problem

– Network design evacuation problem

O-D Evacuation ProblemAssumptions:

– Time horizon until end of evacuation phase

– Simulation results for danger progress

– Accurate livestock numbers

maximizing total outflow

flow preservation

capacity

standard success probability

nonnegativity

O-D Evacuation Model• Time Dynamic model, which implies a time

extended network

• Flow preservation constraints for time dynamic models make our LP solution non integral (loss of total unimodularity)

• Stochastic optimization involved

A closer look

Network Design Evacuation• NP-hard

• VRP-based formulation

– |K| vehicles that have to evacuate animals

minimize total cost

percentage constraint

all percentages sum <=1

vehicle capacity

0 <= each percentage <= 1

VRP-based formulation

Lagrange Relaxation

• Barrier method: exterior point sequences

• This implies our solution might be non integral in the end

• However,

– easier problem to solve (getting rid of the coupling constraint)

– in the time given we can solve it to approximate an integral solution

Lagrange RelaxationOverall,

Approximation Scheme

Computational Results

Computational Results

Computational Results

• O-D Formulation:– Maximum optimality gap noted: 2.9%

• Average gap of 1.4%, which can be practically ignored!

– Speedup achieved up to 180%

• Network Design Formulation:– Maximum optimality gap noted: 22.8%

• Average gap of just 5.6%!

– Speedup achieved up to 600%

Future work

• Create and test more models

• Come up with a better algorithm, i.e. a decomposition scheme

• Working with prefectures, counties to compare with actual real life plans (technology transfer)

QUESTIONS?

Future Work