A novel stochastic approach to buffer stock problem

Abstract

In this paper, the stochastic fluctuation of buffer stock level at time t is investigated. Therefore, random walk processes X(t) and Y (t) with two specific barriers have been defined to describe the stochastic fluctuation of the product level. Here X(t) equivalent to Y (t) - a and the parameter a specifies half capacity of the buffer stock warehouse. Next, the one-dimensional distribution of the process X(t) has calculated. Moreover, the ergodicity of the process X(t) has been proven and the exact formula for the characteristic function has been found. Then, the weak convergence theorem has been proven for the standardized process W(t) equivalent to X(t)/a, as a -> infinity . Additionally, exact and asymptotic expressions for the ergodic moments of the processes X(t) and Y (t) are obtained.