In this paper, we study an inventory system for products where demand depends on time and
price. Shortages are allowed and are fully backordered. We suppose that the demand rate is
the product of a power time pattern and a three-parametric exponential price function. The
objective is to determine the economic lot size, the optimal shortage level and the best selling
price to maximize the total profit per unit time. We present an efficient procedure to determine
the optimal solution of the inventory problem for all possible scenarios. This procedure is
illustrated with several numerical examples. A sensitivity analysis of the optimal inventory
policy with respect to the parameters of the demand rate function is also given. Finally, the
main contributions of this paper are highlighted and future research directions are introduced.
