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Inventory Positioning in a Two-Stage Distribution System with Service Level Constraints

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Advances in Distribution Logistics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 460))

Abstract

A 1-warehouse, n-retailer system is considered in which periodic customer demand only occurs at the lower echelon. Inventory may be stored at both echelons. Transshipments between stockpoints are excluded. All stockpoints replenish inventory by means of local (T, S)-policies which are assumed to share a simple nested schedule. An approximate mathematical representation of the considered distribution system is introduced which lends itself to a use in performance measurement or optimization.

Numerically attractive expressions for stock on hand and backlog are based on a cycle-oriented approach which allows an easy handling of the complexity arising from stochastic customer demands. Besides, other performance measures like the well-known fill rate, a γ-service and the so-called lead time index are approximated. The analytical link between system states at the upper and lower echelons is achieved by modeling customer waiting times as coupling variables.

Numerical studies show a high correspondance between simulated and analytical quantities. Moreover, numerical results underline the appropriateness of including average waiting time estimates as an additional time factor in formulas for stock on hand and backlog at an arbitary retailer.

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Author information

Authors and Affiliations

  1. Universität der Bundeswehr Hamburg, 22039, Hamburg, Germany

    Ulrich Tüshaus

  2. Universität St. Gallen, 9000, St. Gallen, Switzerland

    Christoph Wahl

Authors
  1. Ulrich Tüshaus
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  2. Christoph Wahl
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Editor information

Editors and Affiliations

  1. Institute for Production and Logistics, University of Augsburg, Universitätsstraße 16, D-86135, Augsburg, Germany

    Bernhard Fleischmann

  2. Rotterdam School of Management, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands

    Jo A. E. E. van Nunen

  3. Department of Quantitative Methods, University of Brescia, C. da S. Chiara 48b, I-25122, Brescia, Italy

    M. Grazia Speranza

  4. Institute for Operations Research, University of St. Gallen, Bodanstraße 6, CH-900, St. Gallen, Switzerland

    Paul Stähly

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© 1998 Springer-Verlag Berlin Heidelberg

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Tüshaus, U., Wahl, C. (1998). Inventory Positioning in a Two-Stage Distribution System with Service Level Constraints. In: Fleischmann, B., van Nunen, J.A.E.E., Speranza, M.G., Stähly, P. (eds) Advances in Distribution Logistics. Lecture Notes in Economics and Mathematical Systems, vol 460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46865-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-46865-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64288-6

  • Online ISBN: 978-3-642-46865-0

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