A NOVEL STOCHASTIC APPROACH TO BUFFER STOCK PROBLEM

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...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 14; no. 2; p. 644
Main Authors Hanalioglu, Z, Poladova, A, Gever, B, Khaniyev, T
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.04.2024
Subjects
Stocks
Warehouse stores
Warehouses
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ISSN2146-1147

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Summary: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) = X(t)/a, as a [right arrow] [infinity]. 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, buffer stock problem, stationary distribution, weak convergence, asymptotic expansion. AMS Subject Classification: 60G50, 60K15.
ISSN:2146-1147