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Production-inventory systems in stochastic environment and stochastic lead times

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Abstract

We consider a production-inventory system where the production and demand rates are modulated by a finite state Continuous Time Markov Chain (CTMC). When the inventory position (inventory on hand – backorders+inventory on order) falls to a reorder point r, we place an order of size q from an external supplier. We consider the case of stochastic leadtimes, where the leadtimes are i.i.d. exponential(μ) random variables, and orders may or may not be allowed to cross. We derive the distribution of the inventory level, and analyze the long run holding, backlogging, and ordering cost rate per unit time. We use simulation to study the sensitivity of the system to the distribution of the lead times.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC, 27599, USA

    Vidyadhar Kulkarni

  2. SAS Institute, Inc., Cary, NC, 27511, USA

    Keqi Yan

Authors
  1. Vidyadhar Kulkarni
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  2. Keqi Yan
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Correspondence to Vidyadhar Kulkarni.

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Kulkarni, V., Yan, K. Production-inventory systems in stochastic environment and stochastic lead times. Queueing Syst 70, 207–231 (2012). https://doi.org/10.1007/s11134-011-9272-8

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