Optimal procurement and pricing policies for inventory models with price and time dependent seasonal demand

In day to day life, one observes that many commodities have a seasonal demand pattern, where demand rate depends upon both price and time. A common observation is that in the event of shortage, the proportion of customers who will wait to purchase the item decreases as the waiting time increases. In this paper, we consider a deterministic inventory model that incorporates these aspects when the product under consideration has general price and time dependent seasonal demand rate. Inventory once ordered can be used for more than one season. Order for replenishment is placed at the end of the season in which inventory depletes completely. The period of shortage cannot exceed one season. Backlog of shortages is time dependent. Conditions for optimality of the net profit function for pricing and procurement decisions are discussed. The solution procedure, numerical examples and sensitivity analysis are presented.