M.Sc Student | Shukrun Ilan |
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Subject | Predictive Model of Wildland Fire for Managing Rescue Resources in Changing Conditions |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Shlomo Bekhor |

Full Thesis text |

**This study addresses the joint
problem of finding (1) the best cutline(s) from a set of possible cutlines to
which firefighting resources will be allocated and (2) the optimal allocation
of firefighting resources to the chosen cutline(s). A cutline is defined as a
physical separation of a moving fire from the fuel ahead of it with a line that
has been cleared down to the earth. **

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**The fire spread is modeled in a
similar fashion to other studies in fire propagation, by modeling a stochastic
process of a fire on a grid of spatial locations. The cutline is then modeled
as a contour around the fire. The first problem to solve is to find the best
position of the cutline, assuming that the fire spreads over time and the
direction and rate of spread are known only stochastically. The second problem
is to find the best allocation of the fire resources for this cutline. Few
models in the literature consider the more general case of both fire
propagation and resource allocation, and these models introduce simple
restrictive assumptions to model the cutline over a plane.**

** **

**This thesis accounts for multiple
fire sources and therefore the possibility of multiple cutlines. The complexity
of the problem increases rapidly with the number of possible cutlines and
resources. This problem is shown to be NP-hard, and the thesis develops a
heuristic to overcome issues pertaining to an exponentially growing number of
feasible solutions with increasing problem size. The heuristic can be used to
solve large problem instances arising in the real-world.**

** **

**The heuristic is based on a
two-step approach in which a tree is constructed that represents the feasible
cutlines at a given time. In the first step, the resource allocation problem is
solved for a given set of of feasible cutlines at a given point in time. This
problem is a type of generalized assignment problem. The second step exploits
the tree characterization that employs a reduced number of possible cutline
combinations. Solutions are guaranteed to meet resource limitations. **

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