Abstract
Karmarkar’s model is well recognized in production management and inventory theory: Using the (M/M/1) queueing model, the relation between lot-sizes and mean time in the system is derived for a stochastic inventory model.
In this paper, a short description of Karmarkar’s model is given and fundamental inconsistancies between implicit assumptions of this and the (M/M/1) queueing model are demonstrated. Using well known results of queueing theory, these inconsistencies can be removed. It turns out, however, that — due to the law of large numbers — the model tends to a deterministic one for sufficiently large lot-sizes. Hence, Karmarkar’s approach cannot be used to describe the behaviour of stochastic production systems.
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© 1999 Springer-Verlag Berlin Heidelberg
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Kistner, KP. (1999). Lot Sizing and Queueing Models Some Remarks on Karmarkar’s Model. In: Leopold-Wildburger, U., Feichtinger, G., Kistner, KP. (eds) Modelling and Decisions in Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12519-9_11
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DOI: https://doi.org/10.1007/978-3-662-12519-9_11
Publisher Name: Physica, Heidelberg
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