可替代产品库存模型的研究  

Inventory Model with Substitution

作　　者：李小申[1] 张宏建 夏尊铨[3] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003 [2]许昌技术经济学校机电系,河南许昌461000 [3]大连理工大学数学科学学院,辽宁大连116024

出　　处：《数学的实践与认识》2011年第18期150-160,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471015)

摘　　要：以零售商的角度,讨论了在允许进货的情况下可替代产品的库存问题,建立了这类问题利润最大化的库存模型,讨论了各参数对利润和库存的影响.然后证明了问题的解是存在的,利润函数是子模的,并给出了最优解的一阶必要性条件,同时探讨了目标函数的凹性问题.通过理论分析和数值试验证明了在一定条件下替代和重新进货都能提高利润,并能降低总的库存水平.In market,many same or similar-characteristic products can substitute for each other,excess demand for product can be met not only by substitution but also by reorder. Our purpose is to find how substitution and reorder influence inventory policy from retailer's viewpoint.For this kind of problems with stochastic demands and proportional costs and revenues,we develop the profits maximization model.We show that the objective function is bounded and submodular,and therefore the optimal policy exists.We present the first-order necessary conditions for the optimal order quantities.We discuss the effects of the parameters on profits and stocks.We adress the concavity of the objectie function and the influence of substitution and reorder on profits and general stock level.

关 键 词：运筹学 库存理论 模型 替代 重新进货 

分 类 号：F224[经济管理—国民经济] F253.4