In the manufacturing sector, machine failures frequently disrupt the supply chain, leading to financial losses, particularly when downtime is prolonged. Various methods have been proposed to assess the impact of machine failures on profitability. However, the literature lacks a comprehensive approach that addresses machine failures in the context of maintaining a continuous supply chain through the implementation of an alternative production source during shortage. To bridge this gap, this study proposes an Economic Production Quantity (EPQ) model that incorporates machine failure and compares the manufacturer's profit under two scenarios: one with shortages and another with an alternative production unit compensating for the shortfall. The model aims to maximize profit by optimizing the decision variables. The proposed model is validated through numerical examples, with a detailed sensitivity analysis and managerial insights provided to support decision-making from a business perspective.

Traditional economic production quantity (EPQ) model assumes that the production products are perfect. However, this assumption does not hold for many real production systems due to several weaknesses. This paper considers production inventory model with defective items for deteriorating items. In this paper, production rate is considered to be greater than demand rate. Mathematical model is developed for finding optimal order quantity, cycle time and total profit. Moreover, a numerical example is provided to illustrate the proposed model. Next, sensitivity analysis is established to demonstrate the model developed. Finally, some conclusions and future research directions are proposed.