An inventory model for deteriorating items with imperfect quality under advance payment policy

In the business world, it is generally observed that the supplier gives a cash discount due to advance payment. The buyer may either pay off the total purchase cost or a fraction of the total purchase cost before receiving the products. If the buyer makes full payment then he receives a cash discount instantly. If the buyer pays a fraction of the total purchase cost, then (s)he receives the cash discount while paying the remaining amount at the time of receiving the lot. Moreover, in most of the inventory models, it is generally assumed that the delivered lot contains only perfect items. But in reality, the presence of imperfect items in the received lot cannot be overlooked as it will affect the total profit of the system. Thus, the study of inventory models considering the presence of imperfect items in the lot makes the model more realistic and it has received much attention from inventory managers. This paper develops a model that jointly considers imperfect quality items and the concept of an advance payment scheme (full and partial). The objective is to determine optimal ordering quantity to maximise the total profit of the system. The necessary theoretical results showing the existence of global maximum is derived. The model is illustrated with the help of numerical examples, and sensitivity analysis is carried out on some important system parameters to see the effects on the total profit of the system. The study shows that a full advance payment scheme is beneficial for the buyer.