Revisiting rescheduling: MRP nervousness and the bullwhip effect

Abstract

We study the material requirements planning (MRP) system nervousness problem from a dynamic, stochastic and economic perspective in a two-echelon supply chain under first-order auto-regressive demand. MRP nervousness is an effect where the future order forecasts, given to suppliers so that they may plan production and organise their affairs, exhibits extreme period-to-period variability. We develop a measure of nervousness that weights future forecast errors geometrically over time. Near-term forecast errors are weighted higher than distant forecast errors. Focusing on replenishment policies for high volume items, we investigate two methods of generating order call-offs and two methods of creating order forecasts. For order call-offs, we consider the traditional order-up-to (OUT) policy and the proportional OUT policy (POUT). For order forecasts, we study both minimum mean square error (MMSE) forecasts of the demand process and MMSE forecasts coupled with a procedure that accounts for the known future influence of the POUT policy. We show that when retailers use the POUT policy and account for its predictable future behaviour, they can reduce the bullwhip effect, supply chain inventory costs and the manufacturer’s MRP nervousness.

Keywords:

• bullwhip effect
• inventory management
• material requirements planning (MRP)
• supply chain management
• nervousness

Notes

1. This stream of research has used the moniker order uncertainty to describe the nervousness effect. We have elected not do this to avoid confusion with the risk/uncertainty framework. Furthermore, using the nervousness term draws attention to the established literature in the MRP field.

2. It is widely accepted in the literature that rescheduling an open order in the near future is more costly than one in the distant future. It was reflected in the change cost procedure by Carlson, Jucker, and Kropp (1979). The methods to evaluate nervousness from Kimms (1998), Pujawan (2004) and Kabak and Ornek (2009) also considered that there is either no consequences of distant change, an equal weight, or a proportional weight. These measures are only amenable to numerical analysis. However, our geometrically weighted forecast error results in a closed form solution, a desirable property in a mathematical modelling study.

3. Extensive numerical investigations suggest that only one minimum exists, but we remain unable to formally prove this.

4. Without this normality assumption, we would have to resort to a simulation-based analysis as the required convolution of the pdf’s involved quickly becomes intractable.