6 Conclusion

We have discussed about the limitation of the standard hypothesis of the knowledge of the uncertain demand modeled in the form of an exact probability distribution function. Such a model has been largely used in the literature to solve the problem of the optimal purchasing policy, a decision problem which is currently met in the supply chain. We propose to identify some characteristics of the future demand which are practically determinable, and following Scarf's method, to analyze the optimal decision obtained from the defined family of demand models.

• With the knowledge of the only mean demand , the order quantity is obviously . The model is limited since there is no possibility to analyze any uncertainties. The risk for the company manager is, in that case, to rely on a fictitious ideal revenue which does not take into account the cost of uncertainties.
• With a knowledge on and or the coefficient of variation , the robust decision is . This decision takes into account any general form of the demand probability function, leading to a conservative result. The gain correspond to the knowledge of the expected (minimal) guaranteed revenue. Any additional knowledge can improve this decision since the set of demand models is reduced.
• We have investigated the triangular models which have three parameters for the probability function : the minimum possible demand, the maximum possible, and the most probable demand. These parameters can certainly be identified without too much imprecision by sales managers.

The immediate perspective is to extend this result to the case of more variable demand . Another perspective is the extension of these results to the multi-period purchasing strategy where the next order quantities can make some corrections on the previous decisions by observing the inventory at hand. This discussion can also be used to investigate how prices are fixed by the market for risky products: in the long run, the sellers will reorient their activity if they don't obtain in the average at least the average remuneration for their capital. Thus the final price must contain not only the costs and the usual remuneration, but also (at least) an insurance for the risks .