{"ID":2895029,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.10735","arxiv_id":"2507.10735","title":"Reconciling Risk-Aversion Paradoxes in the Distribution-Free Newsvendor Problem: Scarf's Rule Meets Dual Utility","abstract":"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.","short_abstract":"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 deviat...","url_abs":"https://arxiv.org/abs/2507.10735","url_pdf":"https://arxiv.org/pdf/2507.10735v1","authors":"[\"Jonathan Yu-Meng Li\",\"Tiantian Mao\",\"Reza Valimoradi\"]","published":"2025-07-14T18:58:53Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}