Relatively Robust Inventory Optimization under Parameter Uncertainty

The study revisits the classical Economic Order Quantity (EOQ) model and extends it to situations where model inputs are not precisely known. Instead of relying on stochastic assumptions or full distributional knowledge, the proposed method guarantees cost efficiency relative to the best decision that could have been made with perfect information. Importantly, the paper distinguishes between in-model performance and out-of-model performance, allowing for parameter realizations outside the prespecified ambiguity domain. This leads to the definition of an optimal ambiguity domain based on simple Laplacian considerations.

Prof. Weber’s paper [1] introduces a relatively robust EOQ—an order quantity that minimizes worst-case cost inefficiency across a plausible range of parameter values. Based on a Laplacian principle of insufficient reason, the method also derives optimal confidence intervals for the unknown parameters. These intervals lead to explicit performance guarantees under minimal informational assumptions. When all three core parameters—demand, holding cost, and order cost—are uncertain, the robust EOQ guarantees at least 37.8 percent of the ex-post optimal performance. This increases to 81.6 percent when only one parameter is unknown.

The findings have practical relevance for firms that operate with incomplete data or in volatile environments. By allowing decisions to be based on confidence intervals rather than precise forecasts, the method supports robust lot-sizing even under significant uncertainty. The resulting robust EOQ can be calculated in closed form, using the geometric mean of the best- and worst-case EOQs, and is thus easy to implement.

This study builds on prior work at the Chair of Operations, Economics and Strategy on decision-making under uncertainty, monopoly pricing, and operational robustness in energy systems [2–5].

Abstract

The parameters for determining the economic order quantity (EOQ) are often uncertain and variable. This paper develops a distribution-free method to compute a relatively robust EOQ that guarantees optimal performance relative to ex-post costs under perfect information. The model further derives optimal Laplacian confidence intervals for the uncertain parameters, yielding explicit robustness guarantees depending on how many parameters are unknown. The resulting robust EOQ can be implemented using only sample averages and yields provable in-model performance.