Stochastic Simulations of Storage and Inventory Systems

This article aims to present the applications of Levy processes for the stochastic modeling of storage resources. Two cases were considered. In the first one, the volume of supplies to the storehouse is described by a random process (Levy process), while issuing the products is described by a deterministic and linear function. The second case is reversed: the delivery to the storehouse is described by a linear function (variable: time), while issuing the goods is described by a Levy process. For both cases the form of the stock level process and examples of its trajectories, when the net supply is a Levy process, are given. We investigated the following net supply processes: gamma process, α-stable Levy process with α = 0.5, Cauchy process, Wiener process.

[1]  竹中 茂夫.  G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance , 1996 .

[2]  Roberto Musmanno,et al.  Introduction to Logistics Systems Planning and Control (Wiley Interscience Series in Systems and Optimization) , 2004 .

[3]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[4]  A. Weron,et al.  Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes , 1993 .

[5]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[6]  Z. Michna,et al.  Lévy processes in storage and inventory problems , 2013, 1303.5964.

[7]  J. L. Nolan,et al.  Numerical calculation of stable densities and distribution functions: Heavy tails and highly volatil , 1997 .

[8]  Joachim H. Ahrens,et al.  Generating gamma variates by a modified rejection technique , 1982, CACM.

[9]  F. Dufresne,et al.  Risk Theory with the Gamma Process , 1991, ASTIN Bulletin.

[10]  W. R. Schucany,et al.  Generating Random Variates Using Transformations with Multiple Roots , 1976 .

[11]  R. Weron.  Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables" , 1996 .

[12]  Edward A. Silver,et al.  Inventory Management: An Overview, Canadian Publications, Practical Applications and Suggestions for Future Research , 2008, INFOR Inf. Syst. Oper. Res..

[13]  Howard R. Waters,et al.  Gamma Processes and Finite Time Survival Probabilities , 1993, ASTIN Bulletin.

[14]  Ken-iti Sato.  Lévy Processes and Infinitely Divisible Distributions , 1999 .