Distributionally Robust Newsvendor with Moment Constraints

TL;DR

This paper extends distributionally robust newsvendor models by incorporating moment constraints and uses Wasserstein distance to analyze how ambiguity impacts order decisions and profits, supported by theoretical development and a case study.

Contribution

It introduces a novel framework combining moment constraints with Wasserstein ambiguity sets in the newsvendor problem, deriving a finite-dimensional dual problem for practical analysis.

Findings

Distributional ambiguity influences optimal order quantities.

The dual problem simplifies analysis of robust newsvendor models.

Case study demonstrates practical implications in auto sales.

Abstract

This paper expands the work on distributionally robust newsvendor to incorporate moment constraints. The use of Wasserstein distance as the ambiguity measure is preserved. The infinite dimensional primal problem is formulated; problem of moments duality is invoked to derive the simpler finite dimensional dual problem. An important research question is: How does distributional ambiguity affect the optimal order quantity and the corresponding profits/costs? To investigate this, some theory is developed and a case study in auto sales is performed. We conclude with some comments on directions for further research.