A simple mechanism for the disaster emergency unit scheduling problem

Abstract

In this paper, we study the optimization and mechanism design for the disaster emergency unit (DEU) scheduling problem motivated by the 2017 Chile wildfires, which is described as the worst in Chile’s modern history. We consider a DEU to control wildfires and n forestry companies. Each forestry company j is located in town j. We assume these companies do not satisfy all safety conditions in order to reduce the wildfires impact and then, an emergency induces a damage function to the town j, with the working time of DEU to control wildfires in town j. Each forestry company j has private information about the forest density, which in addition to the feedrate of wildfires determines its marginal waiting cost due to forest working area to be recovered. In practice, it generates a waiting cost for each forestry company j is the position of forestry company j in the sequence The goal is to determine a schedule defined by a sequence and the working time of DEU for minimizing of 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 DEU. We show that the centralized problem can be solve Karush-Kuhn-Tucker (KKT) conditions and design an easy-to-implement truthful mechanism for decentralized problem, charging in some way the damage to the forestry companies based on the optimal solution properties obtained from the centralized problem. A numerical example to illustrate the problem and the usefulness of our contributions is described.