It is well known that longer and more uncertain lead-times in a distribution system increase the need for safety stock and/or reduce the service level at lower levels. It is also well known that ordering decisions at higher level of the supply chain have an impact on the lead-time. Yet not much research has been devoted to increasing the knowledge of how exactly these decisions do influence the lead-time and there is a lack of simple methods to estimate the expected value and variance of the lead-time. Recent research that strongly indicates that it is optimal to provide a low service level at the earlier stages only emphasizes the importance of shedding a light on this issue. This as lower service levels leads to prolonged and more frequent stock outs and hence longer and more uncertain lead-time

In this paper we provide a large simulation study of a two-level distribution system where different decision parameters as well as external parameters influence the lead-time are investigated. Not surprisingly, the study shows that the service level at a higher, not surprisingly, has a positive effect on both the length and variability of the lead time, i.e. they decrease with an increasing service-level. More interestingly though, is that of the other parameters it is only the order quantities that has a significant impact on the lead-time. Both the expected value and variance of the lead-time increase with the retailer’s as well as the central warehouse’s order quantity. This can be describe as an inverted bullwhip effect as the lead-time variability increase as one moves down the supply chain towards the end customer.

In the paper we also develop simple methods to estimate the mean value and variance of the lead-time. The methods are based on replacing a stochastic lead-time demand at the central warehouse with a stochastic demand rate. For a given inventory position and demand rate it is shown how to compute the delay at the central warehouse due to stock-outs in a straight forward manner. These delays are then weighted together based on the probability for each combination of inventory position and demand rate to attain the estimates. The difference between the developed methods lay in how the stochastic demand rate is estimated. The above mentioned simulation study shows that the estimates exhibit a good accuracy and constitutes an improvement compared to existing methods with similar computational complexity.