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In the field of applied mathematics, optimization techniques formulate to the maximizing and minimizing for an objective function. The purpose of the optimization problems plays a vital role in the field of inventory management. The aim is to minimize the total cost, which comprises many fluctuating costs such as shortage, ordering, and holding cost. In this paper, the defective items were under the classification synchronous and asynchronous under a rework strategy process. The rework strategy is separating and accumulating the imperfect items at the time of completion of the process. This study considered asynchronous defective items and tried to minimize the total cost incurred. The optimality of the non-linear programming was achieved by the Hessian matrix, which results in the minimization of the total cost incurred. Furthermore, the usage of hexagonal fuzzy numbers formulates many real-life problems that arise due to flawed knowledge. There might be several situations in decision-making problems where optimization techniques require six parameters or more. The inclusion of Python coding has further made numerical working simpler. Furthermore, sensitivity analysis is carried out. [ABSTRACT FROM AUTHOR]