Optimization of inventory system with defects, rework failure and two types of errors under crisp and fuzzy approach

<p style='text-indent:20px;'>In this paper, a new approach was applied to single-item single-source (<inline-formula><tex-math id="M1">\begin{document}$ SISS $\end{document}</tex-math></inline-formula>) system at the "<inline-formula><tex-math id="M2">\begin{document}$ EOQ-type $\end{document}</tex-math></inline-formula>" mode considering imperfect items and uncertainty environment. The mentioned method intended produce an optimum order/production quantity as well taking care of processes. proportion received lot size described by inspection process. That is, two-way errors may be committed inspector separate items. Thus, survey aimed maximize benefit in traditional inventory systems. incorporation both defects defective classifications (Type-<inline-formula><tex-math id="M3">\begin{document}$ I\&II $\end{document}</tex-math></inline-formula> errors) illustrated, way that were returned consumers. Moreover, model had extra step scope inspection; which occurred after rework process with no error. To get closer practical circumstances consider uncertainty, formulated fuzzy demand, rework, rates considered triangular numbers where output factors obtained via nonlinear parametric programming Zadeh's extension principle. Finally, scenario illustrated through mathematical model. concavity objective function also calculated total profit presented clarify solution procedure numerical examples.</p>