TWO-PHASE MULTI-NOMENCLATURE PRODUCTION/STORAGE MODEL WITH RANDOM INPUT
Abstract
Introduction. Recently, much attention in applications of stochastic models to real production/transportation systems modeling and control have been paid. It is explained by necessity to take into account the uncertainty and risks when projecting/operating such kind of systems. Purpose. To formulate and solve the problem of optimal values of products removal rates finding. Results. The mathematical model of a manufacturing system with several kinds of final product and one kind of raw materials is under consideration. This production system is interpreted as two-phase storage system with random input flow of raw materials which is described by Levy process with nondecreasing sample paths and zero drift. The first phase consists of one warehouse for raw materials storage and second one consists of industrial equipment and several parallel warehouses for final products storage. The production rates and rates of products removal from warehouses are constant. Conclusions. The joint distribution of storage levels of raw materials and any kind of final product at warehouses is found in closed form (in the terms of Laplace-Stieltjes transform). The problem of optimal values of products removal rates finding is formulated and solved.
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References
2. Neuts, M.F. (1995). Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Boston, 2nd Ed. Dover Publ.
3. Kulkarni, V.G. (1995). Modeling and Analysis of Stochastic Systems. London, Chapmen & Hall.
4. Prabhu, N.U. (1998). Stochastic Storage Processes: Queues, Insurance Risk, Dams, and Data Communication. New York, 2nd Ed. Springer Verlag.
5. Ost, A. (2001). Performance of Communication Systems – A Model-Based Approach with Matrix-Geometric Methods. Berlin, Springer Verlag.
6. Ryzhikov, Yu.I. (2001). Queueing Theory and Inventory Control [Teoriya ocheredej i upravlenie zapasami]. St.-Petersburg [in Russian], 384 p.
7. Voevudskiy, E.N., & Postan, M.Ya. (1991). Stochastic Model of Multi-Phase Storage System. Communications of Academy of Science of USSR. 318(1), 5156.
8. Postan, M.Ya. (1995). On Application of Stochastic Processes of the Stock Theory to Modeling Computerized Information Networks. Prob. Inform. Transm., 31(3), 262–283.
9. Postan, M.Ya. (2000). Theory of Stochastic Storage Networks: Present State and Perspectives. In: Proc. of 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics, and Simulation, CD, File CP 216-5. Lausanne.
10. Postan, M.Ya. (2006). Economic-Mathematical Models of Multimodal Transport [Ekonomiko-matematicheskie modeli smeshannyh perevozok]. Odessa, Astroprint [in Russian], 376 p.
