<p>The parameter(s) of practically all real-world optimization problems involving decision-making are complicated due to uncertainty. For that reason, it is essential for solving optimization problem when dealing with unknown optimization problems. In this study, a production inventory model with interval uncertainty is proposed for manufacturing green products.Once more, the demand from customers is regarded as interval-valued and is dependent on the green level. The objective of this work is to address an interval optimization problem, focusing on an interval-valued objective function (average profit) associated with a production inventory model that determines the optimal green level and business period. To achieve this, a simple yet powerful differential evolution algorithm is hybridized with a tournamenting process, aided by interval ranking, to solve the inventory problems within an interval environment. This hybrid approach is termed as tournament differential evolution (TDE) algorithm. The first two variants of TDE technique are employed to obtain the best-found solutions for optimizing the interval-valued average profit. The results from these two TDE variants are then compared with those from several other well-known metaheuristic algorithms. Following this, statistical comparisons and a statistical test are performed on the centre value of the average profit to assess the effectiveness and performance of the proposed hybrid algorithm. Finally, a sensitivity analysis is conducted on the centre value of the average profit, the product's green level, the production run time and the cycle length by varying one model parameter at a time while keeping the others constant. Also, a managerial implications related to proposed work is discussed along with future direction of research.</p>