A newsvendor model with service and loss constraints

Actual performance measurement systems do not only consider financial measures like costs and profits but also non-financial indicators with respect customer service, quality and flexibility. Using the newsvendor model we explore the influence of possibly conflicting performance measures on important operations decisions like the order quantity and the selling price of a product. For price-independent as well as price-dependent demand distribution like in the classical newsvendor model the objective is to maximise the expected profit. But the optimal decisions are computed with respect to a service constraint - a lower bound for the level of product availability - and to a loss constraint - an upper bound for the probability of resulting in loss. For the price-independent model a condition for the existence of an optimal order quantity and its structure is presented. For the price-setting newsvendor the admissible region of the order quantity and the selling price is characterised for the additive and the multiplicative model. Furthermore, it is shown that higher variability of demand leads to a smaller admissible region of the decision variables thereby easing the computation of the optimal decisions.Constrained Newsvendor Model, Price-Setting Newsvendor

Performance Measurement for Inventory Models with Risk Preferences

In financial economics in general the objective function expresses the risk preferences of the decision maker, see for example the mean variance approach in portfolio theory. Only recently in inventory management instead of maximizing expected profit or minimizing expected cost risk-averse objective functions have been used for determining the optimal order quantity. Examples are the exponential utility function and the conditional value at risk criterion. We use the well-known newsvendor model to determine the optimal performance measures for an objective function with two risk parameters, which can describe risk neutral, risk averse as well as risk taking behaviour of the inventory manager. We provide for this approach a complete characterization with respect to the performance measures expected profit and service level. We show that a risk averse inventory manager can not dominate a risk neutral or a risk taking inventory manager. Finally, we provide a managerial guideline for selecting the appropriate risk parameters of the objective function.Performance Measurement, Risk Preferences, Newsvendor Model

Einige Anmerkungen zur Verwendung des Erwartungswertes

Der Erwartungswert spielt in den Wirtschaftswissenschaften bei vielen Problemen, in denen stochastische Einflüsse berücksichtigt werden, eine zentrale Rolle. Dies kann unmittelbar der Fall sein, indem der Erwartungswert einer monetären Zielgröße optimiert wird, dies kann z. B. auch im Zusammenhang mit einem Risikomaß (mean-deviation-rules) oder auch in Form des Erwartungsnutzens, d. h. des Erwartungswerts des Nutzens, der Fall sein. In dieser Arbeit werden teilweise bekannte Einwendungen gegen die Verwendung des Erwartungswerts beschrieben und Möglichkeiten aufgezeigt, diesen Rechnung zu tragen. Im Rahmen eines in der Betriebswirtschaftslehre weit verbreiteten Entscheidungsszenarios (Newsvendor-Modell) werden weitere grundlegende Einwendungen gegen die Verwendung des Erwartungswerts aufgezeigt.Erwartungswert, Gesetz der großen Zahlen, Newsvendor-Modell