可替代产品库存模型的研究(英文)  

Single-Period Two-Product Inventory Model with Reorder and Substitution

作　　者：李小申[1] 夏尊铨[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《运筹学学报》2008年第3期23-34,共12页Operations Research Transactions

基　　金：National Natural Science Foundation of China(10471015).

摘　　要：市场上,很多产品之间可相互替代,商家为了获得的更多的利润,经常会用一种产品替代另一种产品.不仅如此,某种产品缺货时,也可以重新进货以满足顾客的需求.我们从销售商的角度,讨论这两个因素对库存策略的影响,建立了这类问题有两个产品的单周期的利润最大化模型,证明了目标函数是凹的和子模的,从而问题的解是存在的,给出了最优订货量(原始库存)的必要条件,讨论了各参数对库存的影响.通过比较,证明了商家采取替代策略和允许再订货可以提高利润并且可减少库存总量.In market, many same or similar-characteristic products can substitute for each other, retailers usually adopt substitution strategy for more benefits, and excess demand for product can also be met by reorder. For single-period two-product inventory problem of this kind, we develop the profits maximization model with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal stock policy exists. We present the optimal conditions for stock quantities, and provide some properties of the optimal stock quantities. We explore the impacts of parameters on the profits and the optimal stock quantities. By comparison we prove that reorder , and adoption of the substitution strategy for special cases, can raise the profits and reduce the general stock level.

关 键 词：运筹学 库存模型 最优订货量 替代 重新进货 

分 类 号：O227[理学—运筹学与控制论] TS108.61[理学—数学]