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In this paper, we consider an imperfect production-inventory system which consists of a single manufacturer and a single retailer. The manufacturer delivers the order quantity to the retailer in some unequal-sized batches. To separate the defective items, the retailer performs an error-free screening process after receiving each delivery from the manufacturer. Shortage in retailer's inventory is allowed and completely backlogged. The customer demand is influenced by the retail price, advertisement frequency and greening level of the product. The centralized model and the decentralized model based on a Stackelberg gaming approach are developed to determine optimal pricing, advertising and inventory decisions. A cost-sharing contract between the manufacturer and the retailer is implemented, which enhances the environmental performance, advertisement frequency and profitability of the supply chain significantly. The proposed model is illustrated with a numerical example. Sensitivity analysis for some key parameters is carried out and several managerial insights are also highlighted.

Optimal batch shipment policy for an imperfect production system under price-, advertisement- and green-sensitive demand