1 Introduction

One of the most used paradigm in the area of the supply chain management is the newsboy model. This model has an elegant analytical solution if one assumes the knowledge of the probability distribution of the future demand. But, in all practical cases, only a limited knowledge upon this distribution can be assumed and the newsboy is no more playing against a given distribution, but rather against a family of distributions. This question is usually addressed by a max-min method.

When playing against all the distributions sharing given values of $\mu , \sigma$, the Scarf's theorem holds (Gallego and Moon, 1993; Yue et al., 2006; Scarf, 1958). In Douillet and Rabenasolo (2005), we have introduced another measure of the dispersion (the inter-means parameter $\delta$) and have proven that assuming an exact knowledge of $\mu , \delta$ leads to very different conclusions.

The present paper, which is a continuation of Douillet and Rabenasolo 2006, is organized as follows. Section Min-max and newsboy model gives a more precise description of the problem, fixes the notations and recalls the requested former results.

Section Information value of assumptions examines how these results can be used when only historical data are available. It will be shown that obtaining $\left(\mu , \sigma\right)$ or $\left(\mu , \delta \right)$ is neither 'distribution free' nor 'cost free'. Different assumptions lead to different families of models, leading to different results. Comparing these results highlights the information value of the assumptions.

In Section Information value of parameters, we examine the influence of the uncertainties related to the confidence intervals surrounding the parameters.

The paper ends by some concluding remarks and a bibliography.