Risk preferences of a newsvendor with service and loss constraints

Using the newsvendor framework, we present an approach to determine an order quantity, which is relevant for the observed ordering behavior of an inventory manager. Whereas in literature just one constraint has been used, we suggest two conflicting constraints. The service constraint specified by a target value for the cycle service level is fulfilled by high order quantities, the loss constraint is characterized by a target resulting in losses is met by low order quantities. Choosing as objective function a mean-deviation rule where risk attitudes are measured by the conditional value at risk the optimal order quantity is determined depending on the risk parameters. If the newsvendor is not able to specify the risk preferences we use the constraints to describe the risk attitudes of the decision maker in dependence of the profitability of the product and its demand distribution including those products where no admissible order quantity exists. If there are admissible solutions we identify conditions such that the service constraint is dominating, i.e. the prescribed service level is high and necessarily risk taking behavior is implied. Contrary, if the loss constraint dominates, i.e. the probability of loss is low the decision maker in any case is a risk averter. But if both the service target and the loss target are not too challenging then for products with high profitability all risk preferences are possible.