广义均值保持变换的随机单调性及其在库存系统中的应用

doi:10.12005/orms.2018.0057

运筹与管理 ›› 2018, Vol. 27 ›› Issue (3): 32-40.DOI: 10.12005/orms.2018.0057

广义均值保持变换的随机单调性及其在库存系统中的应用

禹海波, 李媛

北京工业大学经济与管理学院,北京 100124

收稿日期:2017-06-18 出版日期:2018-03-25
作者简介:禹海波(1965-),男,河南人,教授,博士,研究方向:随机库存与供应链管理、不确定性理论与方法;李媛(1995-),女,山西人,硕士研究生,研究方向:供应链管理、风险管理。
基金资助:
北京社会科学基金研究基地重点项目(16JDGLA004);国家自然科学基金(71672004);国家自然科学基金应急管理项目(11541006)

Stochastic Comparison of the Generalized Mean-preserving Transformations and Its Applications to Inventory Decisions and Optimization

YU Hai-bo, LI Yuan

School of Economics and Management, Beijing University of Technology, Beijing 100124, China

Received:2017-06-18 Online:2018-03-25

摘要/Abstract

摘要： 本文提出一类非线性且均值可能不等的广义均值保持变换,研究实现其变换前后随机变量比较的充分条件或充分必要条件,并用此变换来定量刻画需求不确定性对库存系统决策和利润的影响。首先给出变换前后或不同参数下分布函数的关系及其满足一阶随机占优和割准则序的充分条件,特征刻画此变换与广义TTT变换之间的关系。进一步,用三类特殊的广义均值保持变换进行验证。最后,将此变换应用到报童模型中,得出该变换对包含最小化成本及最大化利润的一致化报童问题的随机单调性。

关键词: 广义均值保持变换, 可变性, 随机占优, 报童模型

Abstract: In this paper, we provide a generalized mean-preserving transformation which has non-linear and mean inequality conversions, to study the sufficient conditions or sufficient and necessary conditions which can achieve its stochastic comparison. We also characterize the effect of demand uncertainty in decision and profit in inventory system. First, we get the relationship between the distribution function and the random monotonicity before and after the conversion. We also get the connection between the generalized mean-preserving transformation and generalized TTT transformation. In addition, three special generalized mean-preserving transformations are used for validation. Finally, the transition is applied to the newsvendor model which has both minimize cost newsvendor problem and maximize profit newsvendor problem, and the random monotonicity of the unified newspaper problem transformation is obtained.

Key words: generalized mean-preserving transformation, variability, stochastic dominance, newsvendor problem

中图分类号:

F224
C934

禹海波, 李媛. 广义均值保持变换的随机单调性及其在库存系统中的应用[J]. 运筹与管理, 2018, 27(3): 32-40.

YU Hai-bo, LI Yuan. Stochastic Comparison of the Generalized Mean-preserving Transformations and Its Applications to Inventory Decisions and Optimization[J]. Operations Research and Management Science, 2018, 27(3): 32-40.

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广义均值保持变换的随机单调性及其在库存系统中的应用

Stochastic Comparison of the Generalized Mean-preserving Transformations and Its Applications to Inventory Decisions and Optimization

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