When does skewness matter in robust inventory management?

We investigate the impact of skewed demand on robust inventory management. Including skewness in calculations leads to cubic constraints that prevent a standard two-stage method from deriving an explicit and tractable objective function. To overcome this roadblock, we propose a joint optimization method to directly derive the robust solution in a closed form. The joint optimization method is widely applicable to various robust inventory models with different ambiguity sets. The notable advantage is that we can obtain the final solution without deriving the objective function, so many tedious intermediate steps are circumvented. We conduct numerical experiments on industry data to demonstrate that our moment-based policies deliver more consistent performance than divergence-based policies. After obtaining various closed-form solutions, we demonstrate that including skewness in the model improves the profit generated by the robust optimal order quantity if either demand is bounded or the cost-to-price ratio is low, even though the sample moments used may not equal the population moments. Furthermore, under these conditions in which skewness should be included in the calculations, the firm’s expected profit, under the most unfavorable distribution, increases with variance but decreases with skewness. This result stands in contrast to findings in the economics and finance literature, where distributional ambiguity is not considered.