Use of Uncertain Additional Information in Newsvendor Models

TL;DR

This paper explores how incorporating uncertain additional information can improve the estimation of optimal inventory levels in the newsvendor problem, leading to better profit maximization.

Contribution

It introduces methods for minimum variance and mean squared error estimation that leverage uncertain additional information to enhance inventory level predictions.

Findings

Incorporating additional information reduces estimation variance.

Enhanced estimators improve expected profit over traditional methods.

The approach outperforms standard quantile estimation techniques.

Abstract

The newsvendor problem is a popular inventory management problem in supply chain management and logistics. Solutions to the newsvendor problem determine optimal inventory levels. This model is typically fully determined by a purchase and sale prices and a distribution of random market demand. From a statistical point of view, this problem is often considered as a quantile estimation of a critical fractile which maximizes anticipated profit. The distribution of demand is a random variable and is often estimated on historic data. In an ideal situation, when the probability distribution of the demand is known, one can determine the quantile of a critical fractile minimizing a particular loss function. Since maximum likelihood estimation is asymptotically efficient, under certain regularity assumptions, the maximum likelihood estimators are used for the quantile estimation problem. Then, the Cramer-Rao lower bound determines the lowest possible asymptotic variance. Can one find a quantile estimate with a smaller variance then the Cramer-Rao lower bound? If a relevant additional information is available then the answer is yes. Additional information may be available in different forms. This manuscript considers minimum variance and minimum mean squared error estimation for incorporating additional information for estimating optimal inventory levels. By a more precise assessment of optimal inventory levels, we maximize expected profit