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


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


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

    1. 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. 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.
    2. repec:eee:ejores:v:269:y:2018:i:1:p:227-243 is not listed on IDEAS
    3. 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.
    4. repec:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0183-6 is not listed on IDEAS
    5. 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.
    6. 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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