# On the existence of unique minimum for the cost function in a (Q,R) inventory model with backorders George E. Halkos, Ilias S. Kevork? and Christos N. Tziourtzioumis

On the existence of unique minimum for the cost function in a (Q,R) inventory model with backorders. *IMA Journal of Management Mathematics* doi: 10.1093/imaman/dpw010. In common with I.S. Kevork and C.N. Tziourtzioumis (2016).

For a continuous reviewinventory model with non-negative reorder point and fixed lead-time, we investigate the minimization process of the Hadley–Whitin’s cost function. Assuming that the lead-time demand is described by unimodal distributions satisfying specific assumptions, an algorithm has been developed to obtain the minimum of this approximate cost function. The added value of this algorithm is illustrated through some new comparative results produced for normal and log-normal lead-time demands. These comparative results refer to target inventory measures taken by minimizing first the approximate and then the corresponding exact cost function. Contrary to what is believed we show that under certain combinations of parameters values valid approximations using the approximate cost function occur even when the stock-out probability is sufficiently large.