EES-EOQ model with uncertain acquisition quantity and market demand in dedicated or combined remanufacturing systems

The classical economic order quantity (EOQ) model assumes that market demand is deterministic and would be invalid without this premise. Thus far, available literature on the EOQ model do not consider any situation where both market demand and acquisition quantity are uncertain. Therefore, this work develops an evolved environmental sustainability EOQ (EES-EOQ) model to overcome the limitations of the classical EOQ model. Employing the remanufacture-up-to ratio to control the production quantity indirectly, we deduce three optimal strategies: (I) minimize the inventory cost, (II) maximize the overall environmental benefit in a dedicated remanufacturing model, and (III) coordinate forward logistics and reverse logistics to achieve environment optimization in the combined remanufacturing model. With stochastic analysis, we mathematically prove the existence and uniqueness of the optimal remanufacture-up-to ratio in each strategy. Validated by numerical experiments and sensitivity analysis, we demonstrate that the replenishment of new products in the combined model can effectively eliminate the risks of being out of stock and strike an optimal balance between uncertain supply and demand. This study provides the theoretical foundation for remanufacturers to develop optimal remanufacturing strategies for mitigating environmental issues caused by excessive carbon emissions.