Inventory and sales decisions in a vendor-buyer system with imperfect items and learning in inspection

In this study, we propose a joint economic lot-sizing model to include learning process along with errors in inspection and full backordering system. We aim to study pricing and inventory decisions in a two-level supply chain involving a single vendor and a single buyer in which the demand is sensitive to price and company's advertisement efforts. The mathematical inventory model is developed analytically and solved using a proposed algorithm. The objective of the model is to maximise joint total profit by simultaneously determining optimal shipment size, number of deliveries, backorder quantity and product selling price. A numerical example is provided to show the application of the model and to investigate the impact of key parameter's changes on model behaviour. By comparing the integrated/centralised model to the independent/decentralised model, we note that the integrated/centralised model provides better profit to the system, along with lower selling price and smaller amount of backorder.