In this model, the manufacturer needs to inspect and rework defective items due to the flawed manufacturing process. When checking for defective products, two types of errors, namely Type 1 error and Type 2 error, may occur at the inspection stage. If a lot of defective materials are rejected during the inspection, a non-destructive screening process separates the material into reworkable and non-defective categories. This study includes inspection rate insufficiency (IRI) and inspection rate sufficiency (IRS) based on the relationship between inspection and production rates. Rework Priority Policy (RPP) is followed in every scenario. This paper aims to minimize the inspection error and optimize the total profit. Numerical examples help demonstrate the value of this well-established model. A sensitivity analysis of this study was carried out to check its accuracy.

This paper presents an inventory model with a price‐dependent stochastic demand and finite replenishment rate mode. It establishes a production‐inventory system with a controllable deterioration rate, preservation technology, different types of rework process, promotional effort, and carbon emission reduction. This study finds the optimal solution and determines the most efficient production and safety technology investments to maximize the manufacturer’s total profit over the planning horizon. Also, this inventory model balances sustainability and profitability to maximize the profit and to determine the optimal cycle length. In addition, the research highlights the most advantageous investments in production and preservation technology, emphasizing their critical role in increasing profitability and identifying the most effective duration of the production cycle. The study presents a comprehensive approach to inventory optimization that tackles practical and strategic challenges in manufacturing contexts. This research refers to cases and numerical examples, providing management insights and sensitivity analysis to determine the optimal course of action to change the parameters of the model.