Optimal Inventory Policy and Optimal Price Discount on Backorders under Ramp Type Demand Environment

In classical inventory models, the demand rate is assumed to be constant. In reality, time plays an
important role in the inventory system. In the case of ramp type demand rate, the demand increases
with time up to certain limit and then ultimately stabilizes and becomes constant. In this paper, an
inventory model is studied with ramp type demand rate where holding cost is expressed as linearly
increasing function of time. The study includes some features that are likely to be associated with
certain types of inventory, like inventory of seasonal fruits and vegetables, newly launched fashion
items, electronic goods etc. When stock on hand is zero, the inventory manager offers a price
discount to customers who are willing to backorder their demand. The optimum ordering policy and
the optimum discount offered for each backorder are determined by minimizing the total cost in a
replenishment interval. Through numerical study, it is observed that for low backorder cost, it is
beneficial to the inventory manager to offer the customers high discount on backorders.