Delivery delay variation in multi-echelon inventory problems

Mathematical models for controlling multi-echelon inventory and production levels have been developed for entire interconnected systems rather than myopically for each point in the inventory or production system. With such models comes the additional burden of considering the lead times and delays associated with the movement of items through the network. The delays develop when a backorder state occurs and are often considered in models by approximating the mean delay by an application of Little's Law and without consideration of the delay variation. In this article a general methodology for incorporating the variation of the delay is derived and incorporated into a backorders optimisation model. The result of incorporating delay variation into the model is a tolerance interval for order quantities that may be utilised for tighter inventory control.