Carbon emissions in a multi-echelon production-inventory model with lead time constraints

We develop a deterministic optimization model that incorporates carbon emissions in a multi-echelon production-inventory model with lead time constraints. We impose that each customer order must be delivered within the due date fixed by the customer. The quantity that cannot be delivered on time is a lost sale. We consider a multi-echelon supply chain with different external suppliers, different manufacturing facilities, and different distribution centers. We adopt a general inventory policy. Indeed, we do not impose any constraints on the stock level that must be kept for each product in each facility in each period and on the procurement order quantities in the different facilities. Carbon emissions are associated with the decisions of manufacturing of intermediate and final products, ordering (transportation) from external and internal suppliers, and inventory positioning of the different products in the different stages of the supply chain. We first deal with the case of carbon emissions tax and then turn to the case of carbon emissions cap.