A cooperative manufacturer-retailer inventory model with carbon tax regulation, imperfect production, and rework

In this paper, a mathematical inventory model is formulated for a supply chain system composed of single manufacturer and single retailer. Market demand is probabilistic in nature and replenishment lead time is formulated by addressing production time and shipment time. A hybrid system made of a regular production and a green production is used by the manufacturer to produce end products. The manufacturer’s production facility is imperfect and produces some defective items when it is in out of control state. The reworking process is operated to improve the quality of defective products. Tax regulation is imposed by the regulator to control the emissions resulting from some activities, namely transportation, storage, rework, and production. We consider a situation in which the emissions from the production and rework, and the number of defective items can be controlled by production rate adjustment. The objective of the proposed model is to minimize the joint total cost by simultaneously determining the number of shipments, shipment quantity, safety factor, production allocation factor, and production rate. An efficient procedure is proposed to obtain the optimal values of decision variables and a numerical example along with sensitivity analysis are presented to show the applicability of the model and to study the model’s behaviour. The results show that by allowing the production rate to be adjusted and setting the production factor appropriately, the emissions and the defects resulting from manufacturer’s activity can be controlled. In addition, the increasing of the carbon tax and regular’s production cost will lead to the increasing of production allocation to greener production.