Economic Production Quantity Model Considering Rework of Imperfect Goods under Stock, Advertisement, Selling Price and Replacement Period-Dependent Demand

Abstract

An economic production quantity (EPQ) system with an imperfect production model in which demand is affected by advertisement frequency, selling price, stock level and product replacement time is discussed in this paper. It is unavoidable to produce only perfect quality goods in a manufacturing operation due to real-life issues like labor problems, machinery faults, etc. Therefore, we consider the production system imperfect and manufacture a fraction of imperfect goods that depend on the production rate. All produced goods are continuously shifted to the screening center, where perfect goods are directly sold to the consumers. After the screening period, the imperfect goods are transferred to the reworking center, where some imperfect goods are reworked at a price. The remaining defective products are sold as a single lot. A profit function is developed for this proposed production inventory model, which is highly nonlinear. The total profit is maximized using the graphical method to get the optimal production quantity and total business time. The profit function’s concavity is shown graphically by using the Mathematica software. To demonstrate the model’s feasibility, numerical examples are provided. Sensitivity analysis is carried out to highlight the findings of the suggested production inventory system and depict the managerial insights.