Otimização de custo da cadeia de movimentação interna de suco integral de laranja não concentrado utilizando programação linear inteira mista

Abstract

Currently, Brazil is one of the world’s largest producers and suppliers of orange juice, with its main export product being NFC (Not From Concentrate) juice. Orange juice exports generate annual revenues ranging from US$1.5 billion to US$2.5 billion for the country, with the primary markets being the European Union, the United States, and Asian countries. However, orange production has been impacted by Greening, considered the most destructive disease in global citrus farming, along with extreme weather conditions that negatively affect fruit development, leading to raw material shortages and affecting the quality and volume of the final product—orange juice. In light of the challenges in meeting demand and product specifications, and considering the current dynamics of the orange juice market, this study aims to develop a mathematical model in operations research to minimize the transportation costs of non-concentrated orange juice (NFC) from industrial plants to the Port Terminal using Mixed-Integer Linear Programming (MILP). The models were developed using the Pyomo library in Python and solved with the Gurobi® optimization package. The objective function was defined as the sum of logistics chain costs and pasteurizer expenses. The solution approach employed the Branch and Cut method, with variations applied to the system, including changes to the upper limit between the feasible solution found and the optimal limit (MIPGap - Mixed-Integer Programming Gap) and modifications to the fleet of trucks used. This approach enabled the achievement of optimized results, yielding savings of up to R$10.6 million and R$6.8 million when comparing scenarios with MIPGaps of 10% and 5%, respectively, to the 1% MIPGap scenario. Additionally, the scenario utilizing only company-owned trucks resulted in higher costs—around R$6.2 million—due to slower delivery rates. The simulator adhered to all system-imposed constraints, including capacity limits.