The impact of stochastic lead times on the bullwhip effect
  In this article we want to review the research state on the bullwhip effect in supply chains with stochastic lead times and give a contribution to quantifying the bullwhip effect. We analyze the models quantifying the bullwhip effect in supply chains with stochastic lead times and find advantages and disadvantages of their approaches to the bullwhip problem. Using real data we confirm that real lead times are stochastic and can be modeled by a sequence of independent identically distributed random variables. Moreover we modify a model where stochastic lead times and lead time demand forecasting are considered and give an analytical expression for the bullwhip effect measure which indicates that the distribution of a lead time and the delay parameter of the lead time demand prediction are the main factors of the bullwhip phenomenon. Moreover we analyze a recent paper of Michna and Nielsen adding simulation results. 
Zbigniew Michna, Peter Nielsen, Izabela Ewa Nielsen
stat.AP