Inventory policies for deteriorating items with time-price backlog dependent demand

The effect of stock-out plays a major role in customer's decision-making. This article consists of an inventory model with an assumption of customer's demand, which is affected by shortages; that is for the period of shortages, the demand rate declines in proportion to the existing backlogging. Also, the customer's demand is expressed as a function of time and price, which is appropriate for the products for which demand increases initially and after sometime it starts to decrease. Furthermore, for computing the total profit, the backlogged demand rate is approximated by a piecewise constant function. Depending on the cycle length T, total six models are derived with/without utilisation of preservation technology. Finally, in order to validate the derived models, numerical examples along with sensitivity analysis is undertaken, which extracts some fruitful managerial insights.