Marcus Ritt

Gustavo Delazeri, Marcus Ritt

Wildfires cause major losses worldwide, and the frequency of fire-weather conditions is likely to increase in many regions. We study the allocation of suppression resources over time on a graph-based representation of a landscape to slow down fire propagation. Our contributions are theoretical and methodological. First, we prove that this problem and related variants in the literature are NP-complete, including cases without resource-timing constraints. Second, we propose a new mixed-integer programming (MIP) formulation that obtains state-of-the-art results, showing that MIP is a competitive approach contrary to earlier findings. Third, showing that existing benchmarks lack realism and difficulty, we introduce a physics-grounded instance generator based on Rothermel's surface fire spread model. We use these diverse instances to benchmark the literature, identifying the specific conditions where each algorithm succeeds or fails.

Leonardo Borba, Marcus Ritt

In traditional assembly lines, it is reasonable to assume that task execution times are the same for each worker. However, in sheltered work centres for disabled this assumption is not valid: some workers may execute some tasks considerably slower or even be incapable of executing them. Worker heterogeneity leads to a problem called the assembly line worker assignment and balancing problem (ALWABP). For a fixed number of workers the problem is to maximize the production rate of an assembly line by assigning workers to stations and tasks to workers, while satisfying precedence constraints between the tasks. This paper introduces new heuristic and exact methods to solve this problem. We present a new MIP model, propose a novel heuristic algorithm based on beam search, as well as a task-oriented branch-and-bound procedure which uses new reduction rules and lower bounds for solving the problem. Extensive computational tests on a large set of instances show that these methods are effective and improve over existing ones.