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. We use the well-known newsvendor model to determine the optimal order quantity 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. This approach can also be applied to situations in which the demand distribution cannot be specified uniquely. We consider robust optimization procedures—maximin and minimax regret—to determine optimal order quantities if the set of potential demand variables can be partially ordered by stochastic dominance rules.