Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale

Perishable products constitute a sizable component of inventories. Common questions in a production and selling situation involving a perishable (or a non-perishable) product are: What should be the price and what should be the size of the replenishment? When demand for the product is price sensitive, pricing and lot sizing decisions are interdependent. Similarly, when a product is highly perishable, the demand may need to be backlogged to avoid costs due to deterioration, i.e., perishability and backlogging are complementary conditions. In this paper we consider the pricing and lot sizing problem for a perishable good under finite production, exponential decay and partial backordering and lost sale. The backlogging phenomenon in the literature is often modeled using backordering and lost sale costs. These cost parameters however are not easy to estimate in practice. In this paper, we use a new approach to model backlogging of demand. In this approach, customers are viewed to be impatient. The backlogging option gets used only when it is economic to do so. We extend the analysis presented for a perishable product to the case in which the product is non-perishable.