A DYNAMIC PROGRAMMING APPROACH TO THE FIRE BLOCKING PROBLEM

This short note is concerned with a dynamic blocking problem for a model of fire propagation. The region burned by the fire is described as the set reached by trajectories of a differential inclusion, and can be reduced by constructing barriers, in real time. Optimal strategies are sought, which minimize the area destroyed by the fire together with the cost of the barriers. A dynamic programming approach is developed, providing necessary conditions for optimal strategies. In this general setting, we also introduce a notion of “instantaneous value of time”, and prove that it is non-increasing along optimal strategies. The paper is concluded by a discussion of various open problems.