Safety stock planning under causal demand forecasting

Mainstream inventory management approaches typically assume a given theoretical demand distribution and estimate the required parameters from historical data. A time series based framework uses a forecast (and a measure of forecast error) to parameterize the demand model. However, demand might depend on many other factors rather than just time and demand history. Inspired by a retail inventory management application where customer demand, among other factors, highly depends on sales prices, price changes, weather conditions, this paper presents two data-driven frameworks to set safety stock levels when demand depends on several exogenous variables. The first approach uses regression models to forecast demand and illustrates how estimation errors in this framework can be utilized to set required safety stocks. The second approach uses Linear Programming under different objectives and service level constraints to optimize a (linear) target inventory function of the exogenous variables. We illustrate the approaches using a case example and compare two methods with respect to their ability to achieve target service levels and the impact on inventory levels in a numerical study. We show that considerable improvements of the overly simplifying method of moments are possible and that the ordinary least squares approach yields a better performance than the LP-method, especially when the data sample for estimation is small and the objective is to satisfy a non-stockout probability constraint. However, if some of the standard assumptions of ordinary least squares regression are violated, the LP approach provides more robust inventory levels.