Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially backlogged shortages

Due to the highly competitive marketing economy, for different kinds of products’ related suppliers confer various incentives to their respective retailers with certain terms and conditions. Even though suppliers may require advance payments before delivering their products, they incentivize the scheme by offering instant price-discounts, maybe with some other additional benefits and we have constructed an inventory-model consisting of two-warehouses mathematically with deteriorating products. In this proposed model, the suppliers offer some price-discounts for advance payments made by their retailers. As advance payments put a constraint on the capital position of the retailers, the retailers meanwhile, enjoy some delay in the final payment of the rest amount which acts as a booster for their business. A partially backlogged shortage is allowed and its rate is considered to be dependent on the duration of waiting time from the replenishment of a lot to the arrival of the next lot. Finally, a numerical example is performed for validation of the suggested model