An inventory system with demand dependent on both time and price assuming backlogged shortages

In this work we analyze an inventory model for items whose demand is a bivariate function of price and time. It is supposed that the demand rate multiplicatively combines the effects of a time-power function and a price-logit function. The aim is to maximize the profit per time unit, assuming that the inventory cost per time unit is the sum of the holding, shortage, ordering and purchasing costs. An algorithm is developed to find the optimal price, the optimal lot size and the optimal replenishment cycle. Several numerical examples are introduced to illustrate the solution procedure.