An analysis of a three echelon supply chain model with minimum mean squared error forecasting


Lee, So, and Tang (2000) analysed a model of a supply chain both with and without information sharing in order to identify the benefit of supply chain collaboration. Here, first-order autoregressive end consumer demand was shared (and not shared) with the manufacturer (supplier) in a dyadic two echelon supply chain. Inspired by Lee, So, and Tang (2000)’s model structure, we obtain exact analytical expressions for bullwhip and inventory variance in a three echelon supply chain. Our model contains three supply chain participants employing the order-up-to policy with minimum mean square error forecast scheme. In this paper, after demonstrating that the character of the stochastic ordering process observed at each level of the supply chain is mathematically tractable, we quantify the bullwhip produced by the system, together with the variance amplification ratios of the inventory levels. Our analysis reveals that the level of supply chain has no impact upon bullwhip effect, rather bullwhip is determined by the accumulated lead-time from the customer. We also find that the conditional variance of forecast error over the lead-time is identical to the variance of inventory, and that the inventory variance is determined by local replenishment lead-times.

Second World Conference on Production and Operations Management, 30th April-3rd May, Cancun, Mexico, 24 pages