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Multi-level single machine lot-sizing and scheduling with zero lead times

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  • Stadtler, Hartmut

Abstract

A pharmaceutical company raised the question whether an increased product portfolio could still be manufactured on the existing machinery. The proportional lot-sizing and scheduling problem (PLSP) seemed to be most appropriate to answer this question. However, although there are papers dealing with a multi-level PLSP none allows a zero lead time offset which is a prerequisite for the case considered here. In this paper we will extend and modify an existing mixed integer linear programming (MIP) model formulation in two ways: first, we will extend the single-level single machine PLSP to a multi-level single machine PLSP (PLSP-ML-SM) with a zero lead time offset. Second, we will describe a new and more compact model formulation incorporating period overlapping setup times and batch size constraints. Based on the real-world application several test instances have been generated to provide insights into those characteristics which make instances of the PLSP-ML-SM difficult to solve by a standard MIP solver.

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  • Stadtler, Hartmut, 2011. "Multi-level single machine lot-sizing and scheduling with zero lead times," European Journal of Operational Research, Elsevier, vol. 209(3), pages 241-252, March.
    • Handle: RePEc:eee:ejores:v:209:y:2011:i:3:p:241-252
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    References listed on IDEAS

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    1. Meyr, H., 2000. "Simultaneous Lotsizing and Scheduling by combining Local Search with Dual Reoptimization," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 39380, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    Cited by:

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    2. Almeder, Christian & Klabjan, Diego & Traxler, Renate & Almada-Lobo, Bernardo, 2015. "Lead time considerations for the multi-level capacitated lot-sizing problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 727-738.
    3. Alexandre Checoli Choueiri & Eduardo Alves Portela Santos, 2021. "Multi-product scheduling through process mining: bridging optimization and machine process intelligence," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1649-1667, August.
    4. Wei, Mingyuan & Qi, Mingyao & Wu, Tao & Zhang, Canrong, 2019. "Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials," European Journal of Operational Research, Elsevier, vol. 277(2), pages 521-541.
    5. Tobias Kreiter & Ulrich Pferschy, 2020. "Integer programming models versus advanced planning business software for a multi-level mixed-model assembly line problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1141-1177, September.
    6. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    7. Karina Copil & Martin Wörbelauer & Herbert Meyr & Horst Tempelmeier, 2017. "Simultaneous lotsizing and scheduling problems: a classification and review of models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 1-64, January.
    8. Kaczmarczyk, Waldemar, 2020. "Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods," International Journal of Production Economics, Elsevier, vol. 219(C), pages 236-247.
    9. Sahling, Florian & Hahn, Gerd J., 2019. "Dynamic lot sizing in biopharmaceutical manufacturing," International Journal of Production Economics, Elsevier, vol. 207(C), pages 96-106.
    10. Stadtler, Hartmut & Sahling, Florian, 2013. "A lot-sizing and scheduling model for multi-stage flow lines with zero lead times," European Journal of Operational Research, Elsevier, vol. 225(3), pages 404-419.
    11. Ríos-Solís, Yasmín Á & Ibarra-Rojas, Omar J. & Cabo, Marta & Possani, Edgar, 2020. "A heuristic based on mathematical programming for a lot-sizing and scheduling problem in mold-injection production," European Journal of Operational Research, Elsevier, vol. 284(3), pages 861-873.
    12. Matthias Gerhard Wichmann & Christoph Johannes & Thomas Stefan Spengler, 2019. "An extension of the general lot-sizing and scheduling problem (GLSP) with time-dependent energy prices," Journal of Business Economics, Springer, vol. 89(5), pages 481-514, July.
    13. Ferreira, Deisemara & Clark, Alistair R. & Almada-Lobo, Bernardo & Morabito, Reinaldo, 2012. "Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production," International Journal of Production Economics, Elsevier, vol. 136(2), pages 255-265.

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