The disaster emergency unit scheduling problem to control wildfires

In this paper, we study optimization and mechanism design relative to the disaster emergency unit (DEU) scheduling problem to control wildfires. We consider a single DEU and a set of forestry companies, in a scenario where the resources are constrained and an emergency induces damage to the nearby towns. Each forestry company has information about the forest density, which in addition to the feedrate of wildfires determines its marginal waiting cost. In practice, it generates a waiting cost for each forestry company according to its position in the sequence and the working time for the DEU. The goal is to determine a schedule and the working times of the DEU, so as to minimize the sum of the total damage and the total waiting cost of the forestry companies subject to constraints on the damage and use of the working time of the DEU. We show that the centralized problem can be solved by Karush-Kuhn-Tucker (KKT) conditions and design an easy-to-implement truthful mechanism for the decentralized problem. This design charges the damage to the forestry companies based on the optimal solution properties obtained from the centralized problem, with overcharging bounded by a constant. A numerical example to illustrate the problem and the usefulness of our contributions is described. Finally, we extend our results to similar problems for sequential use of a resource, in which strictly increasing convex isoelastic damage functions are considered.