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Discrete and continuous time representations and mathematical models for large production scheduling problems: A case study from the pharmaceutical industry

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  • Stefansson, Hlynur
  • Sigmarsdottir, Sigrun
  • Jensson, Pall
  • Shah, Nilay

Abstract

The underlying time framework used is one of the major differences in the basic structure of mathematical programming formulations used for production scheduling problems. The models are either based on continuous or discrete time representations. In the literature there is no general agreement on which is better or more suitable for different types of production or business environments. In this paper we study a large real-world scheduling problem from a pharmaceutical company. The problem is at least NP-hard and cannot be solved with standard solution methods. We therefore decompose the problem into two parts and compare discrete and continuous time representations for solving the individual parts. Our results show pros and cons of each model. The continuous formulation can be used to solve larger test cases and it is also more accurate for the problem under consideration.

Suggested Citation

  • Stefansson, Hlynur & Sigmarsdottir, Sigrun & Jensson, Pall & Shah, Nilay, 2011. "Discrete and continuous time representations and mathematical models for large production scheduling problems: A case study from the pharmaceutical industry," European Journal of Operational Research, Elsevier, vol. 215(2), pages 383-392, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:2:p:383-392
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    References listed on IDEAS

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    1. Josef Kallrath, 1999. "Mixed-Integer Nonlinear Programming Applications," Palgrave Macmillan Books, in: Tito A. Ciriani & Stefano Gliozzi & Ellis L. Johnson & Roberto Tadei (ed.), Operational Research in Industry, chapter 3, pages 42-76, Palgrave Macmillan.
    2. Christodoulos Floudas & Xiaoxia Lin, 2005. "Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications," Annals of Operations Research, Springer, vol. 139(1), pages 131-162, October.
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    Cited by:

    1. Mustafa, Faizan E & Ahmed, Ijaz & Basit, Abdul & Alvi, Um-E-Habiba & Malik, Saddam Hussain & Mahmood, Atif & Ali, Paghunda Roheela, 2023. "A review on effective alarm management systems for industrial process control: Barriers and opportunities," International Journal of Critical Infrastructure Protection, Elsevier, vol. 41(C).
    2. Voll, Philip & Jennings, Mark & Hennen, Maike & Shah, Nilay & Bardow, André, 2015. "The optimum is not enough: A near-optimal solution paradigm for energy systems synthesis," Energy, Elsevier, vol. 82(C), pages 446-456.
    3. Seyed Ahmad Hosseini, 2013. "A Model-Based Approach and Analysis for Multi-Period Networks," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 486-512, May.
    4. Silvente, Javier & Aguirre, Adrián M. & Zamarripa, Miguel A. & Méndez, Carlos A. & Graells, Moisès & Espuña, Antonio, 2015. "Improved time representation model for the simultaneous energy supply and demand management in microgrids," Energy, Elsevier, vol. 87(C), pages 615-627.
    5. Sahling, Florian & Hahn, Gerd J., 2019. "Dynamic lot sizing in biopharmaceutical manufacturing," International Journal of Production Economics, Elsevier, vol. 207(C), pages 96-106.
    6. Taho Yang & Shin-Yi Lin & Yu-Hsiu Hung & Chung-Chien Hong, 2022. "A Study on the Optimization of In-Process Inspection Procedure for Active Pharmaceutical Ingredients Manufacturing Process," Sustainability, MDPI, vol. 14(6), pages 1-20, March.
    7. Baumann, Philipp & Trautmann, Norbert, 2014. "A hybrid method for large-scale short-term scheduling of make-and-pack production processes," European Journal of Operational Research, Elsevier, vol. 236(2), pages 718-735.
    8. Pulluru, Sai Jishna & Akkerman, Renzo, 2018. "Water-integrated scheduling of batch process plants: Modelling approach and application in technology selection," European Journal of Operational Research, Elsevier, vol. 269(1), pages 227-243.
    9. Tom Rihm & Norbert Trautmann & Adrian Zimmermann, 2018. "MIP formulations for an application of project scheduling in human resource management," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 609-639, December.
    10. Leachman, Robert C. & Johnston, Lenrick & Li, Shan & Shen, Zuo-Jun, 2014. "An automated planning engine for biopharmaceutical production," European Journal of Operational Research, Elsevier, vol. 238(1), pages 327-338.

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