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SILVICULTURAL TASKS SCHEDULING OPTIMIZATION: A CASE STUDY OF FUNCTIONS AND METHODS
SILVICULTURAL TASKS SCHEDULING OPTIMIZATION: A CASE STUDY OF FUNCTIONS AND METHODS
ABSTRACT Scheduling problems are tasks of the operational routine in companies, which demand an optimal solution to support the decision. However, these problems have not been frequently investigated in forestry science. Therefore, it was proposed to describe a mathematical formulation for silviculture optimization under scheduling restriction of the workforce /sequencing of tasks (SSRCMM). Seeking the most suitable method to solve this combinatorial problem, two strategies were compared: i) Integer Linear Programming (ILP) and ii) simulated annealing (SA). The main criteria to assess strategies’ performance were to provide feasible solutions at an acceptable processing time and final project cost. The instance approached is a real problem outlined in 32 stands and five silvicultural tasks scheduled within a 40-day deadline. Three objective functions were also tested, defining case studies (S) to attend to the recurring managers’ decisions by minimizing: S1 – project cost, S2 – makespan, and S3 – workforce usage. The results reveal a robust model to support the forest planner in operational-level tasks. The ILP achieved the optimal solution only for the minimization of the project cost (S1) due to the delay in processing time of the other case studies. Thus, the SA stands out as an efficient method to solve the SSRCMM by providing satisfactory solutions in a reduced time. All the objective functions fitted properly with their proposed goals. The makespan and workforce usage functions increased by US$1,820.29 (S2) and US$2,146.39 (S3) from the S1, respectively, to finish the project earlier and reduce the oscillation of workforce usage over the days. Facing these findings, it is suggested that future researchers incorporate other challenges in decision-making, involving a multi-objective formulation or methods to reveal new insights for forest management and planning. RESUMO Problemas de agendamento são tarefas da rotina operacional presentes nas empresas, que exigem uma solução ótima para apoiar a decisão. No entanto, esses problemas ainda não foram investigados com frequência na ciência florestal. Neste sentido, propôs-se descrever uma formulação matemática para a otimização da silvicultura sob restrição de agendamento da mão de obra/ sequenciamento das atividades (SSRRMM). Buscando o método mais adequado para solucionar este problema combinatório, comparou-se duas estratégias: i) Programação Linear Inteira (PLI) e ii) Simulated annealing (SA). Os principais critérios para avaliar o desempenho das estratégias foram fornecer soluções fáctiveis em tempo de processamento e custo final do projeto aceitáveis. A instância abordada é um problema real contendo 32 talhões e cinco atividades silviculturais programadas dentro de um prazo de 40 dias. Testou-se ainda três funções objetivo, definindo estudos de caso (S) para atender às decisões recorrentes dos gestores, minimizando: S1 - custo do projeto, S2 - makespan e S3 - utilização da mão de obra. Os resultados revelam um modelo robusto para apoiar o planejador florestal em tarefas a nível operacional. O PLI alcançou a solução ótima apenas para a minimização do custo do projeto (S1) devido à demora no tempo de processamento dos outros estudos de caso. Desta forma, destaca-se o SA como um método eficiente para solucionar o SSRRMM, fornecendo soluções satisfatórias em um tempo reduzido. Todas as funções objetivo se ajustaram adequadamente aos seus objetivos propostos. As funções de makespan e de uso da mão de obra aumentaram US$ 1.820,29 (S2) e US$ 2.146,39 (S3) em relação ao S1, respectivamente, para terminar o projeto mais cedo e reduzir a oscilação do uso da mão de obra ao longo dos dias. Diante dessas descobertas, sugere-se aos futuros pesquisadores incorporar outros desafios na tomada de decisão, envolvendo uma formulação multi-objetivo ou métodos para revelar novos insights dentro do manejo e planejamento florestal.
- Federal University of Lavras Brazil
- UNIVERSIDADE FEDERAL DE ALAGOAS Brazil
- Federal University of Alagoas Brazil
Integer linear programming, Pesquisa Operacional, Forestry, Programação linear inteira, SD1-669.5, Operational research, Simulated annealing
Integer linear programming, Pesquisa Operacional, Forestry, Programação linear inteira, SD1-669.5, Operational research, Simulated annealing
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citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average Powered byBIP!