Multi-product newsvendor problem with value-at-risk considerations

We consider the single period stochastic inventory (newsvendor) problem with downside risk constraints. The aim in the classical newsvendor problem is maximizing the expected profit. This formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand. We utilize Value at Risk (VaR) as the risk measure in a newsvendor framework and investigate the multi-product newsvendor problem under a VaR constraint. To this end, we first derive the exact distribution function for the two-product newsvendor problem and develop an approximation method for the profit distribution of the N-product case (N>2). A mathematical programming approach is used to determine the solution of the newsvendor problem with a VaR constraint. This approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights. The accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically.