Sensitivity of the EOQ Model to Parameter Estimates

The Economic Order Quantity (EOQ) model for independent demand is well known to be somewhat insensitive to the choice of order quantity. The cost goes up as the square root of the ratio of the actual order quantity to that of the optimal order quantity. The question arises as to how sensitive this cost is to parameter estimates. This paper extends the work by T. J. Lowe and L. B. Schwarz to show that under minimax and expected value criteria, the sensitivity of the cost to the parameters of the model grows as the fourth root of the uncertainty in the values of the parameters. Furthermore, for a wide class of distributions, including the beta (hence, uniform) and the gamma (hence, exponentials), a tight bound exists for the expected error.