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2012 | nr 8(15) | 17--28
Tytuł artykułu

Stochastic Simulations of Storage and Inventory Systems

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article aims to present the applications of Lévy 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 (Lévy 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 Lévy process. For both cases the form of the stock level process and examples of its trajectories, when the net supply is a Lévy process, are given. We investigated the following net supply processes: gamma process, α-stable Lévy process with α = 0.5, Cauchy process, Wiener process.(original abstract)
Rocznik
Numer
Strony
17--28
Opis fizyczny
Twórcy
  • Uniwersytet Ekonomiczny we Wrocławiu
  • Uniwersytet Ekonomiczny we Wrocławiu
Bibliografia
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  • Dickson D.C.M., Waters H.R. (1993). Gamma process and finite time survival probabilities. ASTIN Bulletin. Vol. 23. Pp. 259-272.
  • Dufresne F., Gerber H.U., Shiu E.S.W. (1991). Risk theory with the gamma Process. ASTIN Bulletin. Vol. 21. Pp. 177-192.
  • Ghiani G., Laporte G., Musmanno R. (2004). Introduction to Logistics Systems Planning and Control. John Wiley and Sons. Chichester.
  • Janicki A., Weron A. (1994). Simulation and Chaotic Behavior of  -Stable Stochastic Processes. Marcel Dekker. New York.
  • Krawczyk S. (2011). Logistyka. Teoria i praktyka. Tom 1-2. Difin.
  • Michael J., Schucany W., Haas R. (1976). Generating random variates using transformations with multiple roots. American Statistician. Vol. 30. No. 2. Pp. 88-90.
  • Michna Z., Bombała, W., Nielsen P. (2013). Lévy processes in storage and inventory models. arXiv preprint. arXiv:1303.5964, 2013 - arxiv.org.
  • Nolan J.P. (1997). Numerical calculation of stable densities and distribution functions. Stochastic Models. Vol. 13. Pp. 759-774.
  • Prabhu N.U. (1998). Stochastic Storage Processes. Springer, New York.
  • Samorodnitsky G., Taqqu M. (1994). Non-Gaussian Stable Processes: Stochastic Models with Infinite Variance. Chapman and Hall. London.
  • Sato K. (1999). Lévy processes and infinitely divisible distributions. Cambridge University Press. Cambridge.
  • Silver E.A. (2008). Inventory Management: An Overview, Canadian Publications, Practical Applications and Suggestions for Future Research. INFOR 46. Pp. 15-28.
  • Silver E.A., Pyke D.F., Peterson R. (1998). Inventory Management and Production Planning and Scheduling. John Wiley & Sons.
  • Weron R. (1996). On the Chambers-Mallows-Stuck method for simulating skewed stable random variables. Statistics and Probability Letters. Vol. 28. Pp. 165-171.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171373371

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