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

Authors

  • Axel Nyberg,

    1. Dept. of Chemical Engineering, Process Design and Systems Engineering Laboratory, Åbo Akademi University, Turku, Finland
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  • Ignacio E. Grossmann,

    Corresponding author
    1. Dept. of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA
    • Dept. of Chemical Engineering, Process Design and Systems Engineering Laboratory, Åbo Akademi University, Turku, Finland
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  • Tapio Westerlund

    1. Process Design and Systems Engineering Laboratory, Åbo Akademi University, Turku, Finland
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Correspondence concerning this article should be addressed to I. E. Grossmann at grossmann@cmu.edu.

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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