# The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

## TL;DR

This paper analyzes how stochastic lead times and correlated demand influence the bullwhip effect, providing explicit formulas and insights into how forecasting parameters affect supply chain variability.

## Contribution

It derives an analytical expression quantifying the bullwhip effect considering random lead times and correlated demand using moving average forecasts, revealing key behavioral insights.

## Key findings

- Bullwhip effect increases with demand auto-correlation.
- Maximum bullwhip occurs at specific auto-correlation values.
- Forecasting more past data reduces variability.

## Abstract

We quantify the bullwhip effect (which measures how the variance in replenishment orders is amplified as the orders move up the supply chain) when random demands and random lead times are estimated using the industrially popular moving average forecasting method. We assume that the lead times constitute a sequence of independent identically distributed random variables and correlated demands are described by a first order autoregressive process. We obtain an expression that reveals the impact of demand and lead time forecasting on the bullwhip effect. We draw a number of conclusions on the behavior of the bullwhip effect with respect to the demand auto-correlation and the number of past lead times and demands used in the forecasts. Furthermore we find the maxima and minima of the bullwhip measure as a function of the demand auto-correlation.