Non-parametric generalised newsvendor model

TL;DR

This paper introduces a non-parametric approach to the newsvendor model with piece-wise polynomial costs and unknown demand distribution, providing a robust estimator for optimal order quantity.

Contribution

It generalizes the classical newsvendor model to handle non-linear costs and develops a consistent non-parametric estimator for the optimal order quantity.

Findings

Estimator is strongly consistent when the optimal order quantity is unique.

Method performs robustly and efficiently in simulations.

Extended to cases with multiple optimal solutions.

Abstract

In classical newsvendor model, piece-wise linear shortage and excess costs are balanced out to determine the optimal order quantity. However, for critical perishable commodities, severity of the costs may be much more than linear. In this paper we discuss a generalisation of the newsvendor model with piece-wise polynomial cost functions to accommodate their severity. In addition, the stochastic demand has been assumed to follow a completely unknown probability distribution. Subsequently, non-parametric estimator of the optimal order quantity has been developed from a random polynomial type estimating equation using a random sample on demand. Strong consistency of the estimator has been proven when the true optimal order quantity is unique. The result has been extended to the case where multiple solutions for optimal order quantity are available. Probability of existence of the estimated optimal order quantity has been studied through extensive simulation experiments. Simulation results indicate that the non-parametric method provides robust yet efficient estimator of the optimal order quantity in terms of mean square error.