AIChE Letter: Process Systems Engineering

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An efficient reformulation of the multiechelon stochastic inventory system with uncertain demands

  1. Axel Nyberg1,
  2. Ignacio E. Grossmann2,*,
  3. Tapio Westerlund3

Article first published online: 29 NOV 2012

DOI: 10.1002/aic.13977

Issue

AIChE Journal

AIChE Journal

Volume 59, Issue 1, pages 23–28, January 2013

Additional Information

How to Cite

Nyberg, A., Grossmann, I. E. and Westerlund, T. (2013), An efficient reformulation of the multiechelon stochastic inventory system with uncertain demands. AIChE J., 59: 23–28. doi: 10.1002/aic.13977

Author Information

  1. 1

    Dept. of Chemical Engineering, Process Design and Systems Engineering Laboratory, Åbo Akademi University, Turku, Finland

  2. 2

    Dept. of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA

  3. 3

    Process Design and Systems Engineering Laboratory, Åbo Akademi University, Turku, Finland

*Correspondence concerning this article should be addressed to I. E. Grossmann at grossmann@cmu.edu.

Publication History

  1. Issue published online: 21 DEC 2012
  2. Article first published online: 29 NOV 2012
  3. Accepted manuscript online: 15 NOV 2012 04:01PM EST
  4. Manuscript Revised: 27 SEP 2012
  5. Manuscript Received: 21 JUL 2012

Funded by

  • Academy of Finland. Grant Number: 127992
  • Foundation of Åbo Akademi University
  • Center of Excellence in Optimization and Systems Engineering
  • Center of Advanced Process Decision-making (CAPD)

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Keywords:

  • optimization;
  • mixed-integer linear programming;
  • exact linearization;
  • supply-chains

Significance

It is shown that by reformulating the three-stage multiechelon inventory system with specific exact linearizations, larger problems can be solved directly with mixed-integer linear programming (MILP) without decomposition. The new formulation is significantly smaller in the number of continuous variables and constraints. An MILP underestimation of the problem can be solved as part of a sequential piecewise approximation scheme to solve the problem within a desired optimality gap.

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