The management of the man−machine interaction is essential to achieve a competitive advantage among production firms and is more highlighted in the processing of agricultural products. The agricultural industry is underdeveloped and requires a transformation in technology. Advances in processing agricultural products (agri-product) are essential to achieve a smart production rate with good quality and to control waste. This research deals with modelling of a controllable production rate by a combination of the workforce and machines to minimize the total cost of production. The optimization of the carbon emission variable and management of the imperfection in processing makes the model eco-efficient. The perishability factor in the model is ignored due to the selection of a single sugar processing firm in the supply chain with a single vendor for the pragmatic application of the proposed research. A non-linear production model is developed to provide an economic benefit to the firms in terms of the minimum total cost with variable cycle time, workforce, machines, and plant production rate. A numerical experiment is performed by utilizing the data set of the agri-processing firm. A derivative free approach, i.e., algebraic approach, is utilized to find the best solution. The sensitivity analysis is performed to support the managers for the development of agricultural product supply chain management (Agri-SCM).