Promotional effort and quality sensitive two echelon production inventory model with partial backlogging

This study deals with the modelling aspect of a two echelon imperfect production system in the presence of the promotional effort of the retailer. The production cost of the system varies with both the ordering lot size and quality of product, and the demand of the product depends on the quality of the product. The inventory level for the manufacturer starts with shortages and new production and the inventory level for the retailer also begin with shortages and new product lot. The cycle ends for both the players with also backlogged inventory. The backlogging rate for each of the player is dependent on waiting time. The behaviour of the model under integrated system is analysed. In the decentralised structure, retailer Stackelberg model are also discussed. The sensitivity of the key parameters is examined to test feasibility of the model. Finally, a numerical example is provided to investigate the proposed model.