A carbon-constrained EOQ model with uncertain demand for remanufactured products

The classical economic order quantity (EOQ) model is simple and practicable, but it would be invalid without the rigorous assumption that demand is constant. This work breaks through the limitation and develops an extended EOQ model under uncertain demand, in order to derive different optimal acquisition strategies. Under the carbon cap and trade mechanism, the optimal quantities in environmental and economic optimization are usually different, while we deduce the optimal acquisition strategies (III and IIII) to solve multi-objective optimization problems. We rigorously prove the uniqueness of optimal order quantity in each strategy and provide close-form expressions for possible holding and opportunity costs caused by the uncertain supply-demand relationship. Other than conducting an optimization analysis from the perspective of firms, we also analyze the effects of taxation policy on the optimal strategies from the perspective of the government. An interesting phenomenon is that increasing carbon tax will not only reduce profit margins, but will also change the optimal acquisition decisions. Consequently, remanufacturing enterprises can be guided in a sustainable direction, by adopting more energy-efficient strategies to enter the “profitable region”.