Stock diffusion theory: a dynamic model for inventory control |
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| Authors: | Marcello Braglia Francesco Zammori |
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| Affiliation: | 1. Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione , Università di Pisa , via Bonanno Pisano 25/b, Pisa, 56126 , Italy Phone: Phone: +39–050-2218129 Fax: Phone: +39–050-2218129;2. Dipartimento di Ingegneria Industriale , Università degli Studi di Parma , via G.P. Usberti 181/A, Parma, 43124 , Italy Phone: Phone: +39–0521-905887 |
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| Abstract: | This paper proposes a dynamic approach for inventory management, which can be used for a definitely non stationary demand whose rate evolves both in mean and in variance. Specifically, the stock consumption is modelled as a Markov process with a slow diffusion term and the Fokker Planck equation is used to derive the probability distribution of the stock consumption and that of the reorder time. The knowledge of these distributions makes it possible to manage the inventory in a dynamical way and to keep the safety stock to a minimum level. To test the model, some typical demand patterns are used: results demonstrate its ability to capture both the evolution of the mean and that of the variance of the demand. |
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| Keywords: | diffusion theory Fokker-Planck equation inventory management |
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