Note—On the Minimum of a Nonconvex Inventory Function
处理Hadley和Whitin启发式库存模型中的非凸双变量最小化问题，提出一种方法，即使不满足标准二阶条件也能确定解的存在性和唯一性，并指出当提前期需求分布为单峰或J形时，局部最小值即为全局最小值。
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.