Optimal replenishment and sales team initiatives for pharmaceutical products – A mathematical model

The paper addresses an inventory model of pharmaceutical products where the demand rate of the customers increases with the volume of the initiatives of the sales team. In this model, the deterioration of the product varies depending on on-hand inventory. The volume of sales team initiatives is a control variable. It is dependent on on-hand inventory and vice versa. The profit function of the farm is formulated by the trading of inventory costs, purchasing costs, losses due to deterioration and sales team initiative costs, considering inflation and the time value of the monetary cost and profit parameters. Finally, the profit function is maximized by a variation of the calculus method. A numerical example is given to justify our model.