一类最优EOQ模型的进一步扩展

The Furhter Generalization of a Kind of Optimal EOQ Model

对一类经济批量订购模型作如下进一步扩展:第一,允许短缺,短缺量部分拖后供给,且短缺期间损失率与实际缺货量成正比;第二,订购费用是可变的,且线性依赖于订购量.在此假定下,研究了有限计划时间水平及常数变质率下,部分短缺量拖后的变质性物品多阶段库存问题,给出了寻找最优订购策略的算法,证明了所给最优策略的存在唯一性及在该策略下费用函数取得最小值.最后给出应用实例.

This paper generalizes a kind of economic order quantity model as follows： First, shortages are allowed to occur and are backlogged partially, the lost rate during the shortage period is proportional to the quantities of actual backorder; Second, the order cost is flexible and depends linearly on the order lot-size. Under such assumptions, we discuss the inventory problems with multiple periods and partial backlogging over a finite planning period for a deteriorating item that decays at constant rate. A proposed solution procedure is presented for finding the optimal replenishment policy. We prove the existence and uniqueness of this optimal ordering policy and also point out that the cost function acquires the minimum under such policy. Two practical examples are shown to illustrate the model and solution procedure.