Newsvendor problem with discrete demand and constrained first moment under ambiguity

IF 1.4 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS Decisions in Economics and Finance Pub Date : 2024-08-30 DOI:10.1007/s10203-024-00477-7
Andrea Cinfrignini, Davide Petturiti, Gabriele Stabile
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Abstract

We study a single period newsvendor problem under ambiguity in the presence of a discrete random demand. Ambiguity is introduced in the model by \(\epsilon \)-contaminating the newsvendor’s prior probability measure with respect to two suitable classes of probability measures, assuring that the lower expected demand and the upper expected demand are both equal to the prior expected demand. Assuming that the newsvendor has a pessimistic attitude towards ambiguity, we characterize the order quantity that either maximizes the lower expected profit or minimizes the upper expected loss. Since the two contamination classes are cores of two distinct belief functions, we show that the maximin and minimax problems translate in the maximization and minimization of two distinct Choquet integrals.

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模糊条件下具有离散需求和受限第一矩的新闻供应商问题
我们研究的是在离散随机需求存在的情况下,模糊性条件下的单期新闻供应商问题。模糊性是通过(\epsilon \)污染新闻销售商的先验概率度量来引入模型的,它涉及两类合适的概率度量,确保下限预期需求和上限预期需求都等于先验预期需求。假定新闻销售商对模糊性持悲观态度,我们就能确定下限预期利润最大化或上限预期损失最小化的订货量。由于两个污染类别是两个不同信念函数的核心,我们证明最大化和最小化问题转化为两个不同 Choquet 积分的最大化和最小化。
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来源期刊
Decisions in Economics and Finance
Decisions in Economics and Finance SOCIAL SCIENCES, MATHEMATICAL METHODS-
CiteScore
2.50
自引率
9.10%
发文量
10
期刊介绍: Decisions in Economics and Finance: A Journal of Applied Mathematics is the official publication of the Association for Mathematics Applied to Social and Economic Sciences (AMASES). It provides a specialised forum for the publication of research in all areas of mathematics as applied to economics, finance, insurance, management and social sciences. Primary emphasis is placed on original research concerning topics in mathematics or computational techniques which are explicitly motivated by or contribute to the analysis of economic or financial problems.
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