Stock control analytics: a data-driven approach to compute the fill rate considering undershoots

One of the most frequently used inventory policies is the order-point, order-up-to-level (s, S) system. In this system, the inventory is continuously reviewed and a replenishment request is placed whenever the inventory position drops to or below the order point, s. The variable replenishment order quantity and the variable replenishment cycle characterize the system by the use of complex mathematical computations. Different methodological approaches diminish the mathematical complexity by neglecting the undershoots, i.e., the quantity that the inventory position is below the order point when it is reached. In this paper, we conceptually and empirically analyse the bias that neglecting the undershoots introduces into the estimation of the fill rate. After that, we suggest a new methodology developed under a data-driven perspective that uses a state-dependent parameter algorithm to correct such a bias. As a result, we propose two new methods, one parametric and the other nonparametric, to enhance the fill rate estimate. Both methods, named analytics fill rate methods, remove the bias that neglecting the undershoots introduces and are used to illustrate the practical implications of this hypothesis on the performance and design of the (s, S) system. This research is developed in a lost sales context with simulated stochastic and i.i.d. discrete demands as well as actual sales data.