Inventory resonances in multi-echelon supply chains

The authors consider multi-echelon supply chains, typically consisting of retailer, manufacturer, supplier, etc., in which each actor chooses its own inventory replenishment strategy, and is subject to its own replenishment delay. The authors model the chain with a system of linear differential delay equations. In matrix form the system of equations is triangular and the authors derive an exact, algorithmic solution, which allows the determination of inventory behaviour over time for each echelon. The solution is characterised by a set of Lambert modes, obtained from the solution to a set of transcendental equations. For a complete set of solutions the modes must be independent. When the modes are not independent, the authors find that additional solutions exist, and these exhibit a transient surge in inventory. In analogy with ordinary differential equations, the authors refer to this as a 'resonance' in the inventory. The authors discuss the practical import of this theoretical prediction.

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  • Supplemental Notes:
    • Abstract reprinted with permission from Taylor & Francis
  • Authors:
    • Hodgson, J P E
    • Warburton, R D H
  • Publication Date: 2009-8


  • English

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  • Accession Number: 01140830
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Sep 21 2009 10:56AM