Note—On the Minimum of a Nonconvex Inventory Function

The paper deals with a nonconvex, bivariate minimization problem arising in a heuristic inventory model of Hadley and Whitin (Hadley, G., T. M. Whitin. 1963. Analysis of Inventory Systems. Prentice-Hall, Inc., Englewood Cliffs, NJ.). An approach is suggested whereby the existence and uniqueness of the solution can be determined even though the model does not fulfill the standard second-order conditions. It is observed that the global minimum for this model can be identified by means of the first-order conditions and the shape of the lead time demand distribution. In particular, the local minimum is also the global minimum for this model when lead time demand distribution is either unimodal or J-shaped.