Proceedings of the 2014 Industrial and Systems Engineering Research Conference Y. Guan and H. Liao, eds. Robust Analysis of the Basic Economic Order Quantity Model Sang Jin Kweon, Seong Wook Hwang, and José A. Ventura 1 Harold and Inge Marcus Department of Industrial & Manufacturing Engineering The Pennsylvania State University University Park, PA 16802, USA Emails: svk5333@psu.edu, soh5223@psu.edu, and jav1@psu.edu Abstract This paper considers the basic economic order quantity (EOQ) model when all parameters, such as the demand rate, the ordering cost, and the inventory holding cost, are uncertain, and furthermore, their probability information is also unknown. To address the uncertainty, we adopt a robustness-based approach. In this approach, each unknown parameter is described as a continuous value restricted to be in a prespecified interval. The objective of this paper is to build a robust inventory policy in closed-form under input data uncertainty. In order to predict the set of all possible optimal inventory scenarios when all parameters are unknown, we develop closed-form expressions that characterize the set of all possible EOQ’s and corresponding minimum average costs. In addition, this paper considers a minimax approach to derive the optimal inventory policy in closed-form that minimizes the worst-error ratio. Keywords Operations Research, EOQ, Uncertainty, Robust analysis, Minimax approach 1. Introduction Since Harris [3] proposed the Economic Order Quantity (EOQ) model in order to approach inventory management mathematically, many studies have been performed to manage various inventory systems. The three main parameters in the basic EOQ model are the demand per unit time (D), the ordering cost (K), and the inventory holding cost per unit per unit time (h). In Harris’s model, all parameters are assumed to be known and deterministic. This assumption makes it easy to calculate an analytically closed-form solution that minimizes the total cost. The problem of this assumption is that it may be almost impossible to know the exact value for each parameter in a real life inventory environment, and furthermore, these values change frequently due to numerous unexpected factors [1]. Thus, it may be an optimal solution to the wrong problem if parameters are unknown. Many studies release this unrealistic assumption and suggest methodologies to manage inventory systems under input data uncertainty [11]. In particular, the stochastic inventory problems have successfully used to describe the uncertainty in parameters [9]. The stochastic approach relies on the assumption that the probability information for each parameter is easily obtainable, but it may be difficult to collect or analyze data to obtain probability information in a real inventory environment. On the other hand, the robust optimization version of the problem, which is the other approach to express input data uncertainty, does not require probability information about each parameter. Instead, in this approach, each parameter is just regarded as being restricted to be in some continuous, prespecified interval. Lowe and Schwarz [7] use the robustness-based approach in the basic EOQ model. Since error occurs when estimating values for the uncertain parameters, measuring and minimizing error is an important issue in robust optimization. For this, they suggest two criteria. For their first criterion, error is defined as the mathematical difference between the feasible average cost rate the company faces, denoted by   , and the minimum average cost rate the company would face if there were no error in estimation, denoted by   . For their second criterion, they define error as the ratio of    to   . They propose methodologies to minimize the worst possible error and the expected error, respectively. Dobson [2] provides properties about the EOQ model under input data uncertainty and proves the insensitivity of the EOQ under the two cr iteria suggested by Lowe and Schwarz’s work 1 Corresponding author