VaR as a risk measure for multiperiod static inventory models

This paper explores the possibility to use value-at-risk (VaR) in the context ofinventory management. VaR is being used more and more in financial management as a natural measure ofthe risk taken with a given position. In the framework of inventory management it can work as well. After having built a decision model, where the choice concerns the quantity to be ordered to face a random demand, in order to optimize the expected result (an expected cost to be minimized or an expected profit to be maximized) the model explores the probability distribution ofthe result, both via analytical methods and via simulation methods. The analytical exploration ofthis problem has originated a general method to deduce from inequalities for distribution functions, which are based on the expected value, related tail inequalities, which are particularly useful for VaR problems, where only one tail is involved.