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

  • Ulrich Tüshaus
  • Christoph Wahl
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 460)


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.


Lead Time Customer Demand Demand Process Customer Order Safety Stock 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Ulrich Tüshaus
    • 1
  • Christoph Wahl
    • 2
  1. 1.Universität der Bundeswehr HamburgHamburgGermany
  2. 2.Universität St. GallenSt. GallenSwitzerland

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