Abstract
Approximate steady state probability distribution of the stock level for the single product production-inventory system when the demand is a Markov-modulated Poisson process (MMPP) with finite number of states under the on/off production rate control is obtained. The control causes the stock level to fluctuate around a given value by reducing the production rate when the stock exceeds this value. The asymptotic distributions of the stock-out and overproduction periods are also obtained. Exact steady state distribution of the stock level for MMPP demand arrivals with two states and exponential batch size distribution is compared with the approximate one.
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Livshits, K., Kitaeva, A., Ulyanova, E. (2018). Steady State Probabilistic Characteristics of the On/Off Production Rate Control Production-Inventory System with MMPP Demand Arrivals. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM WRQ 2018 2018. Communications in Computer and Information Science, vol 912. Springer, Cham. https://doi.org/10.1007/978-3-319-97595-5_20
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DOI: https://doi.org/10.1007/978-3-319-97595-5_20
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