A note on the stochastic nature of lead times in multi-echelon supply chains

Recent supply chain research has concluded that stochastic lead times are a significant source of bullwhip effect in reorder-based supply chains. Despite this, the study of lead times and their nature has received remarkably little attention in literature. In this research we prove there exists an interdependency between lead time and service level measure, and thus the magnitude of the bullwhip effect. In a multi-echelon supply chain setting, the decision maker can experience disproportionate bullwhip effect. One cause of this is the fact that lead time distribution may likely stem from skewed and peaked distributions. As a member of a multi-echelon supply chain, a firm can experience an order variance that depend on the total number of echelon and information about their lead-time dependencies. These results correspond well with the few contributions found in literature showing actual lead times.