Influence of Correlation Coefficient of Lead Time on Bullwhip Effect: Establishing a New Era of Modelling in Correlated Time for Supply Chain

Few decades ago, the star of Supply chain management took birth in horizon of business. This characteristically mean management of supply chain. But today\´s world of exactitude and accuracy enforce a need of word which we can think of as Management of Supply chain management! There is race in more and more real time development of business mathematical model. To inherit meaning to quote "Management of Supply chain management", we propose more specific and novel approach to model demand process. "Bullwhip Effect", which means intensification of variance moving upwards, has attracted the apprehension of many researchers. Many past research take demand as AR(1) process with constant lead time. A step ahead, model with demand as AR(1) process with stochastic lead time is being proposed. Giving height to this series of modeling, for the first time in 2007, Lee et al. gave paper on demand with generalize AR (p) process with deterministic lead time. Since then nowhere, it is accentuate that even lead time can follow AR(1) process, in addition to being stochastic! ; which is most imperative void to analyze real life problem. So hereby, to fill this gap, we propose new realm where lead time will be AR(1) process to give more reality to complex supply chain problem analysis. We worked on theory by Riezebos, J. et al. (2006) for lead time following dynamic process with sub category of being stochastic, and propose the new equation for bullwhip effect in environment where both demand as well as lead time is following AR (1) process. In addition we analyze the bullwhip effect as a function of: lead time, lead time autocorrelation coefficient, demand autocorrelation coefficient and hence drawn out the remarkable results. This undeniably will assist researchers in more real time problem analysis more accurately.