Relatively Robust Economic Order Quantity with Optimal Laplacian Confidence Intervals

The parameters for determining the economic order quantity (EOQ) are often not well known or may change between order cycles in an unpredictable manner. We propose a distribution-free method to determine a relatively robust EOQ that guarantees optimal cost performance relative to the ex-post optimal cost that could have been achieved with perfect information about the unknown parameter values. Furthermore, we determine optimal Laplacian confidence intervals for the parameters which lead to a guaranteed in-model robustness of about 37.8% of the optimum when demand, holding cost, and order cost are unknown, and 81.6% when only one of these parameters, such as demand, is unknown. Accordingly, when all parameters are unknown, the optimal Laplacian confidence intervals vary by 79.5% around the respective central values, and when only one parameter is unknown, the remaining confidence interval varies by 86.6% around its central value.