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Simultaneous lotsizing and scheduling considering secondary resources: a general model, literature review and classification

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Abstract

Typical simultaneous lotsizing and scheduling models consider the limited capacity of the production system by respecting a maximum time the respective machines or production lines can be available. Further limitations of the production quantities can arise by the scarce availability of, e.g., setup tools, setup operators or raw materials which thus cannot be neglected in optimization models. In the literature on simultaneous lotsizing and scheduling, these production factors are called “secondary resources”. This paper provides a structured overview of the literature on simultaneous lotsizing and scheduling involving secondary resources. The proposed classification yields for the first time a unified view of scarce production factors. The insights about different types of secondary resources help to develop a new model formulation generalizing and extending the currently used approaches that are specific for some settings. Some illustrative examples demonstrate the functional principle and flexibility of this new formulation which can thus be used for a wide range of applications.

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Notes

  1. This denomination has only later been introduced by Fleischmann (1990).

  2. See also Copil (2016).

  3. Using the same index sequence ji three times for \(z^{c}_{lji,s-1}\), \(z^{c}_{ljis}\) and \(z_{ljis}\) allows (10) to carry the information, which product had been produced last, over all microperiods of a continued setup.

  4. We omit the index l of the production lines for ease of readability.

  5. If a property o does only refer to some ingredient of the SRs, as for example the sugar content of orange and pineapple concentrate, a corresponding factor \(a_{on}\) can be introduced and (24) can be changed to \(\sum _{n \in \Xi _o} a_{on} x^{p}_{lns} \ge f^{p}_{jo}x_{ljs}\).

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Acknowledgements

We thank the anonymous reviewers and area editor for their helpful comments. The third author was partially funded by ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme, and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project SAICTPAC/0034/2015-POCI-01- 0145-FEDER-016418.

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Authors and Affiliations

  1. Department of Supply Chain Management, University of Hohenheim, Stuttgart, Germany

    Martin Wörbelauer & Herbert Meyr

  2. INESC-TEC, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

    Bernardo Almada-Lobo

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  1. Martin Wörbelauer
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  2. Herbert Meyr
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  3. Bernardo Almada-Lobo
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Correspondence to Martin Wörbelauer.

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Wörbelauer, M., Meyr, H. & Almada-Lobo, B. Simultaneous lotsizing and scheduling considering secondary resources: a general model, literature review and classification. OR Spectrum 41, 1–43 (2019). https://doi.org/10.1007/s00291-018-0536-0

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