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Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization

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  • Josef Kallrath

Abstract

This contribution gives an overview on the state-of-the-art and recent advances in mixed integer optimization to solve planning and design problems in the process industry. In some case studies specific aspects are stressed and the typical difficulties of real world problems are addressed. Mixed integer linear optimization is widely used to solve supply chain planning problems. Some of the complicating features such as origin tracing and shelf life constraints are discussed in more detail. If properly done the planning models can also be used to do product and customer portfolio analysis. We also stress the importance of multi-criteria optimization and correct modeling for optimization under uncertainty. Stochastic programming for continuous LP problems is now part of most optimization packages, and there is encouraging progress in the field of stochastic MILP and robust MILP. Process and network design problems often lead to nonconvex mixed integer nonlinear programming models. If the time to compute the solution is not bounded, there are already a commercial solvers available which can compute the global optima of such problems within hours. If time is more restricted, then tailored solution techniques are required. Copyright Springer Science + Business Media, Inc. 2005

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  • Josef Kallrath, 2005. "Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization," Annals of Operations Research, Springer, vol. 140(1), pages 339-373, November.
    • Handle: RePEc:spr:annopr:v:140:y:2005:i:1:p:339-373:10.1007/s10479-005-3976-2
    DOI: 10.1007/s10479-005-3976-2
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    Cited by:

    1. Steffen Rebennack & Josef Kallrath, 2015. "Continuous Piecewise Linear Delta-Approximations for Bivariate and Multivariate Functions," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 102-117, October.
    2. Akshay Gupte & Shabbir Ahmed & Santanu S. Dey & Myun Seok Cheon, 2017. "Relaxations and discretizations for the pooling problem," Journal of Global Optimization, Springer, vol. 67(3), pages 631-669, March.
    3. Wang, X. & Li, D. & O'brien, C. & Li, Y., 2010. "A production planning model to reduce risk and improve operations management," International Journal of Production Economics, Elsevier, vol. 124(2), pages 463-474, April.
    4. Flapper, Simme Douwe P. & González-Velarde, José Luis & Smith, Neale R. & Escobar-Saldívar, Luis Jacob, 2010. "On the optimal product assortment: Comparing product and customer based strategies," International Journal of Production Economics, Elsevier, vol. 125(1), pages 167-172, May.
    5. Steffen Rebennack & Josef Kallrath, 2012. "Continuous Piecewise Linear δ-Approximations for MINLP Problems. II. Bivariate and Multivariate Functions," Working Papers 2012-13, Colorado School of Mines, Division of Economics and Business.
    6. Minner, Stefan, 2009. "A comparison of simple heuristics for multi-product dynamic demand lot-sizing with limited warehouse capacity," International Journal of Production Economics, Elsevier, vol. 118(1), pages 305-310, March.
    7. Waldemarsson, Martin & Lidestam, Helene & Karlsson, Magnus, 2017. "How energy price changes can affect production- and supply chain planning – A case study at a pulp company," Applied Energy, Elsevier, vol. 203(C), pages 333-347.
    8. Timo Berthold & Jakob Witzig, 2021. "Conflict Analysis for MINLP," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 421-435, May.
    9. Dag Haugland & Eligius M. T. Hendrix, 2016. "Pooling Problems with Polynomial-Time Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 591-615, August.
    10. Dirk Briskorn & Philipp Zeise, 2019. "A cyclic production scheme for the synchronized and integrated two-level lot-sizing and scheduling problem with no-wait restrictions and stochastic demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(4), pages 895-942, December.
    11. Reza Roozbahani & Babak Abbasi & Sergei Schreider & Zahra Hosseinifard, 2020. "A basin-wide approach for water allocation and dams location-allocation," Annals of Operations Research, Springer, vol. 287(1), pages 323-349, April.

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