A NOVEL STOCHASTIC APPROACH TO BUFFER STOCK PROBLEM

A NOVEL STOCHASTIC APPROACH TO BUFFER STOCK PROBLEM

Z. Hanalioglu, A. Poladova, B. Gever, T. Khaniyev

[PDF]

Abstract

In this paper, the stochastic uctuation of bu er stock level at time t is investigated. Therefore, random walk processes X(t) and Y (t) with two speci c barriers have been de ned to describe the stochastic uctuation of the product level. Here X(t)   Y (t) / a and the parameter a speci es half capacity of the bu er 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)   X(t)=a, as a ! 1. Additionally, exact and asymptotic expressions for the ergodic moments of the processes X(t) and Y (t) are obtained.

Keywords

Random walk with two barriers, bu er stock problem, stationary distribution, weak convergence, asymptotic expansion.