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      An inventory problem with two randomly available suppliers

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      Author(s)
      Gürler, Ü.
      Parlar, M.
      Date
      1997
      Source Title
      Operations Research
      Print ISSN
      0030-364X
      Publisher
      Institute for Operations Research and the Management Sciences
      Volume
      45
      Issue
      6
      Pages
      904 - 918
      Language
      English
      Type
      Article
      Item Usage Stats
      206
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      331
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      Abstract
      This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is modeled as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a general distribution. In analogy with queuing notation, we call this an Es1[Es2]/G1[G2] system. Since the resulting stochastic process is non-Markovian, we employ the "method of stages" to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition functions for the semi-Markov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detailed numerical example is presented for the E2[E2]/M[M] case. Analytic solutions are obtained for the particular case of "large" (asymptotic) order quantity, in which case the objective function assumes a very simple form that can be used to analyze the optimality conditions. The paper concludes with the discussion of an alternative inventory policy for modeling the random supply availability problem.
      Keywords
      Availability
      Functions
      Integral equations
      Mathematical models
      Mathematical transformations
      Numerical methods
      Queueing theory
      Random processes
      State space methods
      Erlang random variables
      Inventory
      Random supply availability
      Renewal reward theorem
      Stages method
      Inventory control
      Permalink
      http://hdl.handle.net/11693/25551
      Published Version (Please cite this version)
      https://doi.org/10.1287/opre.45.6.904
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      • Department of Management 639
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