Replenishment Planning for Stochastic Inventory Systems with Shortage Cost

  • Roberto Rossi
  • S. Armagan Tarim
  • Brahim Hnich
  • Steven Prestwich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4510)

Abstract

One of the most important policies adopted in inventory control is the (R,S) policy (also known as the “replenishment cycle” policy). Under the non-stationary demand assumption the (R,S) policy takes the form (Rn,Sn) where Rn denotes the length of the nth replenishment cycle, and Sn the corresponding order-up-to-level. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a CP approach able to compute optimal (Rn,Sn) policy parameters under stochastic demand, ordering, holding and shortage costs. The convexity of the cost-function is exploited during the search to compute bounds. We use the optimal solutions to analyze the quality of the solutions provided by an approximate MIP approach that exploits a piecewise linear approximation for the cost function.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Roberto Rossi
    • 1
  • S. Armagan Tarim
    • 2
  • Brahim Hnich
    • 3
  • Steven Prestwich
    • 1
  1. 1.Cork Constraint Computation Centre, University College, CorkIreland
  2. 2.Department of Management, Hacettepe UniversityTurkey
  3. 3.Faculty of Computer Science, Izmir University of EconomicsTurkey

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