Um estudo sobre o problema do carteiro rural: aplicações na colheita da cana-de-açúcar
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Data
2022-01-25
Autores
Carvalho, Drielly Alves de
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Universidade Estadual Paulista (Unesp)
Resumo
Dentre as principais atividades do agronegócio brasileiro, encontra-se a produção da cana-de-açúcar, sendo o Brasil o principal produtor mundial. A cadeia produtiva da cana se encontra em constante desenvolvimento, buscando sempre novas tecnologias e ferramentas que possam contribuir para um planejamento eficaz de toda a cadeia produtiva. O processo de colheita da cana-de-açúcar representa umas das etapas mais importantes e mais caras da cadeia produtiva, sendo de grande importância que ela seja planejada e realizada da melhor forma. Dentre as ferramentas disponíveis para auxiliar no processo de tomada de decisões, os problemas e modelos matemáticos de otimização têm se mostrado úteis para representar e resolver o problema da colheita. O Problema do Carteiro Rural (PCR) é um clássico problema da otimização combinatória e muito usado para representar problemas logísticos. O problema da colheita da cana pode ser representado pelo PCR, onde as arestas requeridas representam as linhas de cana-de-açúcar, e as demais arestas representam os espaços livres para a locomoção da colhedora. Além disso, o problema pode ser estendido para múltiplos carteiros (K-PCR). A partir do problema do carteiro rural são propostas 4 versões para o problema da colheita da cana: PCR clássico, K-PCR utilizando um modelo Min-Max, PCR e K-PCR com um problema de designação utilizando também um modelo Min-Max. Foram utilizadas instâncias da literatura para a validação dos modelos, os quais se mostraram eficientes para instâncias de até 50 vértices. Os modelos foram propostos com os objetivos de minimizar o tempo de colheita e gerar rotas equilibradas entres as máquinas disponíveis, sendo que ambos os objetivos foram alcançados na maior parte das instâncias.
Brazil is the world's largest producer of sugarcane, which is the main activity of Brazilian agribusiness. The sugarcane production chain is in constant development, always looking for new technologies and tools that can contribute to an effective planning of the whole production chain. As the sugarcane harvesting process is one of the most important and expensive stage of the sugarcane production chain, it should be planned and carried out in the best way. Among the tools available to help the decision making process, mathematical optimization problems and models have proven to be useful to represent and solve the harvesting problem. The Rural Postman Problem (RPP) is a classic combinatorial optimization problem and is widely used to represent logistic problems. The sugarcane harvesting problem can be represented by the RPP, where the required edges represent the sugarcane plantations, and the other edges represent the free spaces for the harvester to move. Furthermore, the problem can be extended to Multiple Rural Postman (K-RPP). From the Rural Postman Problem, 4 mathematical models are proposed for the sugarcane harvesting problem: classic RPP, K-RPP with a min-max model, and the RPP and the K-RPP, both with a designation problem using a Min-Max model. Instances from the literature were used to validate the models, which proved to be efficient for instances up to 50 nodes. The models were proposed with the goals of minimizing the harvesting time and generating balanced routes among the available machines, and both goals were achieved in most instances.
Brazil is the world's largest producer of sugarcane, which is the main activity of Brazilian agribusiness. The sugarcane production chain is in constant development, always looking for new technologies and tools that can contribute to an effective planning of the whole production chain. As the sugarcane harvesting process is one of the most important and expensive stage of the sugarcane production chain, it should be planned and carried out in the best way. Among the tools available to help the decision making process, mathematical optimization problems and models have proven to be useful to represent and solve the harvesting problem. The Rural Postman Problem (RPP) is a classic combinatorial optimization problem and is widely used to represent logistic problems. The sugarcane harvesting problem can be represented by the RPP, where the required edges represent the sugarcane plantations, and the other edges represent the free spaces for the harvester to move. Furthermore, the problem can be extended to Multiple Rural Postman (K-RPP). From the Rural Postman Problem, 4 mathematical models are proposed for the sugarcane harvesting problem: classic RPP, K-RPP with a min-max model, and the RPP and the K-RPP, both with a designation problem using a Min-Max model. Instances from the literature were used to validate the models, which proved to be efficient for instances up to 50 nodes. The models were proposed with the goals of minimizing the harvesting time and generating balanced routes among the available machines, and both goals were achieved in most instances.
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Palavras-chave
Problema do carteiro rural, Colheita da cana-de-açúcar, Modelos matemáticos, Modelos Min-Max, Rural postman problem, Sugarcane harvest, Mathematical models, Min-Max models