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A linearization approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers

(2019)
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Abstract
Inspired by the production and planning process of coreboard of our industry partner, a Fortune 1000 player in packaging, we present a mixed-integer linear programming model that can jointly optimize lot sizes, production sequences and safety stocks in the presence of sequence-dependent changeovers. First, we formulate a nonlinear (MINLP) model that can handle both the stochasticity and the sequence-dependency of the stochastic dynamic capacitated lotsizing problem, based on the stochastic sequence-independent (Tempelmeier et al. 2018) and deterministic sequence-dependent (Guimaraes et al. 2014) version of the problem. Then, we develop a piecewise linearization approach for the non-linear inventory on hand and backorder curves that builds on and challenges earlier research published by van Pelt and Fransoo 2018 and Tempelmeier et al. 2018. We use the derivatives of the inventory on hand and backorder functions to develop a tailored breakpoint selection strategy that reduces the maximum approximation error between the linearized and non-linear objective function from 20.3% to 0.5% in comparison to the equidistant linearization strategy recommend by the aforementioned articles. As a third and last contribution, we develop a Relax-and-Fix with Fix-andOptimize heuristic and show in an extensive numerical study that it improved the objective value by 20% on average and realized an average run time reduction of 60% over a state-of-the-art solver.
Keywords
Production planning, Lotsizing and scheduling, Random demand, Mixed-integer linear programming, Sequence-dependent changeovers

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Citation

Please use this url to cite or link to this publication:

Chicago
De Smet, Niels, Stefan Minner, El-Houssaine Aghezzaf, and Bram Desmet. 2019. “A Linearization Approach to the Stochastic Dynamic Capacitated Lotsizing Problem with Sequence-dependent Changeovers.” In Dublin.
APA
De Smet, N., Minner, S., Aghezzaf, E.-H., & Desmet, B. (2019). A linearization approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers. Presented at the 30th European Conference on Operational Research, Dublin.
Vancouver
1.
De Smet N, Minner S, Aghezzaf E-H, Desmet B. A linearization approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers. Dublin; 2019.
MLA
De Smet, Niels et al. “A Linearization Approach to the Stochastic Dynamic Capacitated Lotsizing Problem with Sequence-dependent Changeovers.” Dublin, 2019. Print.
@inproceedings{8624512,
  abstract     = {Inspired by the production and planning process of coreboard of our
industry partner, a Fortune 1000 player in packaging, we present a
mixed-integer linear programming model that can jointly optimize
lot sizes, production sequences and safety stocks in the presence
of sequence-dependent changeovers. First, we formulate a nonlinear (MINLP) model that can handle both the stochasticity and the
sequence-dependency of the stochastic dynamic capacitated lotsizing
problem, based on the stochastic sequence-independent (Tempelmeier
et al. 2018) and deterministic sequence-dependent (Guimaraes et al.
2014) version of the problem. Then, we develop a piecewise linearization approach for the non-linear inventory on hand and backorder curves that builds on and challenges earlier research published
by van Pelt and Fransoo 2018 and Tempelmeier et al. 2018. We use
the derivatives of the inventory on hand and backorder functions to
develop a tailored breakpoint selection strategy that reduces the maximum approximation error between the linearized and non-linear objective function from 20.3% to 0.5% in comparison to the equidistant
linearization strategy recommend by the aforementioned articles. As a
third and last contribution, we develop a Relax-and-Fix with Fix-andOptimize heuristic and show in an extensive numerical study that it
improved the objective value by 20% on average and realized an average run time reduction of 60% over a state-of-the-art solver.},
  author       = {De Smet, Niels and Minner, Stefan and Aghezzaf, El-Houssaine and Desmet, Bram},
  keywords     = {Production planning,Lotsizing and scheduling,Random demand,Mixed-integer linear programming,Sequence-dependent changeovers},
  language     = {eng},
  location     = {Dublin},
  title        = {A linearization approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers},
  url          = {https://www.euro2019dublin.com/},
  year         = {2019},
}