A Novel Model for Economic Recycle Quantity with Two-Level Piecewise Constant Demand and Shortages

This paper focuses on the production systems that may produce a proportion of recyclable defective products. The developed model is called an Economic Recycle Quantity (ERQ) model with the assumption of a full recovery of defective items. The defective parts are collected during the production-off time and can be used during the next production cycle of the same category. The demand rate of the non-defective items is a two-level piecewise factor—one during the production-run time and another during the production-off time. The developed model aims to optimize the total inventory cost, the order quantity, and the amount of recyclable defective items that represent the ERQ. The mathematical formulations of the model are deduced theoretically. The model was solved analytically, and the optimal results are illustrated. Sensitivity analysis is carried out to investigate the effect of varying system parameters and validate the proposed model. Results of the sensitivity analysis show that the consideration of defective part recycling reduces the total inventory cost where the raw material is reduced. The cost reduction is about 1%; of course, the environmental impact is more appreciated. Furthermore, the managerial implications are described, and the future perspectives are discussed.