A new generalized newsvendor model with random demand

TL;DR

This paper extends the newsvendor model to account for critical goods with higher costs for shortages or excess inventory, considering unknown demand distributions and proposing estimators based on sample data.

Contribution

It introduces a generalized newsvendor model for critical commodities with higher loss costs and develops estimators for optimal order quantity under unknown demand distribution parameters.

Findings

Proposes a generalized newsvendor model for critical goods.

Develops estimators based on full and broken sample data.

Compares estimators using simulated bias and MSE.

Abstract

Newsvendor problem is an extensively researched topic in inventory management. In this class of inventory problems, shortage and excess costs are considered to be proportional to the quantity lost. But, for critical goods or commodities, inventory decision is a typical example where, excess or shortage may lead to greater losses than merely the total cost. Such a problem has not been discussed much in the literature. Moreover, majority of the existing literature assumes the demand distribution to be completely known. In this paper, we propose a generalization of the newsvendor problem for critical goods or commodities with higher shortage or excess losses but of same degree. We also assume that, the parameters of the demand distribution are unknown. We also discuss different estimators of the optimal order quantity based on a random sample of demand. In particular, we provide different estimators based on (i) full sample and (ii) broken sample data (i.e with single order statistic). We also report comparison of the estimators using simulated bias and mean square error (MSE).