A two-echelon supply chain inventory model for perishable products with a shifting production rate, stock-dependent demand rate, and imperfect quality raw material

Abstract

This model extends the classical economic production quantity (EPQ) model to address the complexities within a two-echelon supply chain system. The model integrates the cost of raw materials necessary for production and takes into account the presence of imperfect quality items within the acquired raw materials. Upon receipt of the raw material, a thorough screening process is conducted to identify imperfect quality items. Combining imperfect raw material and the concept of shifting production rate, two different inventory models for deteriorating products are formulated under imperfect production with demand dependent on the stock level. In the first model, the imperfect raw materials are sold at a discounted price at the end of the screening period, whereas in the second one, imperfect items are kept in stock until the end of the inventory cycle and then returned to the supplier. Numerical analysis reveals that selling imperfect raw materials yields a favourable financial outcome, with an optimal inventory level 𝐼1 = 11,774 units, optimal cycle time 𝑇=2140 h, and a total profit per hour of USD 183, while keeping the imperfect raw materials to return them to the supplier results in a negative profit of USD −4.44×103 per hour, indicating an unfavourable financial outcome with the optimal inventory level 𝐼1 and optimal cycle time T of 26,349 units and 4702.6 h, respectively. The findings show the importance of selling imperfect raw materials rather than returning them and provide valuable insights for inventory management in systems with deteriorating products and imperfect production processes. Sensitivity analysis further demonstrates the robustness of the model. This study contributes to satisfying the need for inventory models that consider both the procurement of imperfect raw materials, stock-dependent demand, and deteriorating products, along with shifts in production rates in a multi-echelon supply chain.