A single-vendor single-buyer supply chain model with price and green sensitive demand under batch shipment policy and planned backorder

This paper considers a two-level supply chain which consists of a single-vendor and a single-buyer. The vendor produces a single product in lot and transfers the whole lot to the buyer in a combination of equal and unequal sized batches. All unequal sized batches are in a geometric progression with a fixed common ratio. Consumer's demand is sensitive to the retail price and greening improvement level of the product. At the buyer, planned shortages are allowed and are completely backlogged. Assuming that the buyer has higher decision power than the vendor, we develop non-coordinated decentralised model and coordinated model with cost sharing contract, and the integrated centralised model. The numerical results show that the cost sharing contract gives an impressive improvement in the profits of both the vendor and the buyer over their profits in the non-coordinated system. A sensitivity analysis is performed to explore how the changes in the key model-parameters effect the optimal profits of the vendor and the buyer and the whole supply chain.