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

Book Contribution - Book Abstract Conference Contribution

Inspired by the production and planning process of coreboard of ourindustry partner, a Fortune 1000 player in packaging, we present amixed-integer linear programming model that can jointly optimizelot sizes, production sequences and safety stocks in the presenceof sequence-dependent changeovers. First, we formulate a nonlinear (MINLP) model that can handle both the stochasticity and thesequence-dependency of the stochastic dynamic capacitated lotsizingproblem, based on the stochastic sequence-independent (Tempelmeieret 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 publishedby van Pelt and Fransoo 2018 and Tempelmeier et al. 2018. We usethe derivatives of the inventory on hand and backorder functions todevelop 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 equidistantlinearization strategy recommend by the aforementioned articles. As athird and last contribution, we develop a Relax-and-Fix with Fix-andOptimize heuristic and show in an extensive numerical study that itimproved the objective value by 20% on average and realized an average run time reduction of 60% over a state-of-the-art solver.
Book: 30th European Conference on Operational Research (EURO2019) : meeting abstracts
Pages: 266 - 266
Publication year:2019