Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.10735 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912482700820480 |
|---|---|
| author | Li, Jonathan Yu-Meng Mao, Tiantian Valimoradi, Reza |
| author_facet | Li, Jonathan Yu-Meng Mao, Tiantian Valimoradi, Reza |
| contents | How should a risk-averse newsvendor order optimally under distributional ambiguity? Attempts to extend Scarf's celebrated distribution-free ordering rule using risk measures have led to conflicting prescriptions: CVaR-based models invariably recommend ordering less as risk aversion increases, while mean-standard deviation models -- paradoxically -- suggest ordering more, particularly when ordering costs are high. We resolve this behavioral paradox through a coherent generalization of Scarf's distribution-free framework, modeling risk aversion via distortion functionals from dual utility theory. Despite the generality of this class, we derive closed-form optimal ordering rules for any coherent risk preference. These rules uncover a consistent behavioral principle: a more risk-averse newsvendor may rationally order more when overstocking is inexpensive (i.e., when the cost-to-price ratio is low), but will always order less when ordering is costly. Our framework offers a more nuanced, managerially intuitive, and behaviorally coherent understanding of risk-averse inventory decisions. It exposes the limitations of non-coherent models, delivers interpretable and easy-to-compute ordering rules grounded in coherent preferences, and unifies prior work under a single, tractable approach. We further extend the results to multi-product settings with arbitrary demand dependencies, showing that optimal order quantities remain separable and can be obtained by solving single-product problems independently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconciling Risk-Aversion Paradoxes in the Distribution-Free Newsvendor Problem: Scarf's Rule Meets Dual Utility Li, Jonathan Yu-Meng Mao, Tiantian Valimoradi, Reza Optimization and Control How should a risk-averse newsvendor order optimally under distributional ambiguity? Attempts to extend Scarf's celebrated distribution-free ordering rule using risk measures have led to conflicting prescriptions: CVaR-based models invariably recommend ordering less as risk aversion increases, while mean-standard deviation models -- paradoxically -- suggest ordering more, particularly when ordering costs are high. We resolve this behavioral paradox through a coherent generalization of Scarf's distribution-free framework, modeling risk aversion via distortion functionals from dual utility theory. Despite the generality of this class, we derive closed-form optimal ordering rules for any coherent risk preference. These rules uncover a consistent behavioral principle: a more risk-averse newsvendor may rationally order more when overstocking is inexpensive (i.e., when the cost-to-price ratio is low), but will always order less when ordering is costly. Our framework offers a more nuanced, managerially intuitive, and behaviorally coherent understanding of risk-averse inventory decisions. It exposes the limitations of non-coherent models, delivers interpretable and easy-to-compute ordering rules grounded in coherent preferences, and unifies prior work under a single, tractable approach. We further extend the results to multi-product settings with arbitrary demand dependencies, showing that optimal order quantities remain separable and can be obtained by solving single-product problems independently. |
| title | Reconciling Risk-Aversion Paradoxes in the Distribution-Free Newsvendor Problem: Scarf's Rule Meets Dual Utility |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.10735 |