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      On the use of phase-type distributions for inventory management with supply disruptions

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      Author
      Balcıoǧlu, B.
      Gürler, Ü.
      Date
      2011
      Source Title
      Applied Stochastic Models in Business and Industry
      Print ISSN
      1524-1904
      Electronic ISSN
      1526-4025
      Publisher
      John Wiley & Sons
      Volume
      27
      Issue
      6
      Pages
      660 - 675
      Language
      English
      Type
      Article
      Item Usage Stats
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      98
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      Abstract
      Maintaining the continuity of operations becomes increasingly important for systems that are subject to disruptions due to various reasons. In this paper, we study an inventory system operating under a (q, r) policy, where the supply can become inaccessible for random durations. The availability of the supply is modeled by assuming a single supplier that goes through ON and OFF periods of stochastic duration, both of which are modeled by phase-type distributions (PTD). We provide two alternative representations of the state transition probabilities of the system, one with integral and the other employing Kolmogorov differential equations. We then use an efficient formulation for the analytical model that gives the optimal policy parameters and the long-run average cost. An extensive numerical study is conducted, which shows that OFF time characteristics have a bigger impact on optimal policy parameters. The ON time characteristics are also important for critical goods if disasters can happen.
      Keywords
      Phase-type distributions
      Stochastic inventory
      Supply disruptions
      Permalink
      http://hdl.handle.net/11693/21734
      Published Version (Please cite this version)
      http://dx.doi.org/10.1002/asmb.879
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      • Department of Industrial Engineering 677
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