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The (r,q) policy for the lost-sales inventory system when more than one order may be outstanding

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  • Johansen, Søren Glud

    ()
    (Department of Operations Research)

  • Thorstenson, Anders

    ()
    (Department of Business Studies)

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    Abstract

    We study the continuous-review (r; q) system in which un_lled demands are treated as lost sales. The reorder point r is allowed to be equal to or larger than the order quantity q. Hence, we do not restrict our attention to the well-known case with at most one replenishment order outstanding, but our modeling streamlines exact analysis of that case. The cost structure is standard. We assume that demand is Poisson, that lead times are Erlangian and that orders do not cross in time (lead times are sequential). We determine the equilibrium distribution of the inventory on hand at the delivery instants from the solution (obtained by the Gauss-Seidel method) of the equilibrium equations of a Markov chain. To optimize r and q we develop an adapted version of the algorithm suggested by Federgruen and Zheng for the backorders model (BO). The results obtained in our numerical study show that the suggested procedure dominates standard textbook approximations. In particular, the reductions in the average cost of a simple Economic Order Quantity policy are in the range of 3-14%. Except when lead times are long and variable or when the unit cost of shortage is low, the optimal BO policy provides a fair approximation to the average cost of the best policy.

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    Bibliographic Info

    Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series CORAL Working Papers with number L-2004-03.

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    Length: 28 pages
    Date of creation: 11 Oct 2004
    Date of revision:
    Handle: RePEc:hhb:aarbls:2004-003

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    Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
    Fax: + 45 86 15 19 43
    Web page: http://www.asb.dk/about/departments/bs.aspx
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    Related research

    Keywords: inventory/production; operating characteristics; policies; probability; Markov processes; Area of review; Manufacturing; Service; Supply Chain Operations;

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    1. Hill, Roger M., 1992. "Numerical analysis of a continuous-review lost-sales inventory model where two orders may be outstanding," European Journal of Operational Research, Elsevier, vol. 62(1), pages 11-26, October.
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