Scheduling and Routing with Degradation-Triggered Job Arrivals: An Application to Forest Firefighting with an Unmanned Aerial Vehicle Fleet

Abstract

We define an intertwined scheduling and routing problem where new jobs appear due to the degradation of the existing jobs. Specifically, once a job arrives at a potential job location, a time window begins during which the demand of the job can be fulfilled. The demand degrades within the time window, and once it surpasses a particular threshold, it triggers the arrival of new jobs. Each job location inherently possesses an initial default reward, and the presence of an unprocessed job at a location gradually reduces this default value. The overall objective is to maximize the total remaining reward. The underlying motivation of this problem aligns with the proverb ``a stitch in time saves nine," and the problem itself carries practical implications. We focus on the problem in the context of aerial forest firefighting. Each ignited area has a designated action window; delaying intervention causes the fire to grow, diminishing the area's value and causing it to spread to adjacent areas. We develop a mixed-integer programming model that maximizes value retention in wildfire-threatened regions, and a hybrid model based on dynamic constraint generation to enhance the scalability of the model. We evaluate the performance and practicality of our models through computational experiments and a case study. Additionally, we ensure the study's reproducibility and encourage further research by providing open access to the codebase of our model.