The economic lot scheduling problem: a content analysis

Abstract

The paper at hand addresses the Economic Lot Scheduling Problem (ELSP), which is concerned with finding a feasible and cost-minimal production schedule for multiple items produced in lots on a single machine. The ELSP started to attract the attention of researchers in the 1950s, where the focus was primarily on the development of simple heuristics for solving the problem. Over the subsequent decades, this topic has frequently been addressed in the literature, with the subject of research being the development of new scheduling policies or solution procedures or extensions of the scope of the original model. To date, a large number of journal articles has been published on the ELSP and its model variants. To identify key research themes, publication patterns and opportunities for future research, the paper at hand applies a content analysis to a sample of 242 papers published on the Economic Lot Scheduling Problem. The results of the content analysis indicate that prior research on this topic had a strong focus on the development of solution methodologies, and that several aspects that are directly connected to lot sizing and scheduling have not attracted much attention in research on the ELSP yet, such as, for example, energy cost and sustainability.

Keywords:

• economic lot scheduling problem
• ELSP
• content analysis
• scheduling
• lot sizing
• literature review

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article can be accessed http://doi.org/10.1080/00207543.2019.1668071.

ORCID

Christoph H. Glock http://orcid.org/0000-0001-6006-0070

Notes

1 All abbreviations used in this paper are summarised in the list of abbreviations (Appendix C in supplementary material).

2 A problem is strongly NP-hard if it is NP-hard even when any numbers appearing in the input are bounded by some polynomial in the length of the input (Atallah 1998).

3 To avoid that certain recording units are counted more than once, all recording units that are contained in other recording units and that have not been subtracted from the number of hits yet, such as ‘unrelated parallel machine’ that is already contained in the recording unit ‘parallel machine’, are not considered for this calculation. All recording units where this criterion applies are highlighted with an asterisk in Table A1 (see supplementary material).

4 The number of recording units contained in a group could, however, be seen as an indicator of the relative importance of that group as well.

5 We excluded the recording units ‘Economic Lot Scheduling Problem’ and ‘ELSP’ from this analysis, as it is not surprising that these recording units led to an enormous number of hits in our final sample given the topic of the paper.

6 We subtract the number of recording unit hits for ‘setup cost’ and excluded the recording units ‘setup cost’ and ‘setup time’ from this analysis.

7 We again excluded the recording units ‘Economic Lot Scheduling Problem’ and ‘ELSP’.

8 Uncertainty in the ELSP has also inspired a dedicated review on this topic, see Winands, Adan, and van Houtum (2011).

9 To avoid that certain recording units are counted more than once, all recording units that are contained in other recording units and that have not been subtracted from the number of hits yet, such as ‘integer linear programming’ that is already contained in the recording unit ‘linear programming’, are not considered for this calculation. All recording units where this criterion applies are highlighted with an asterisk in Table A1 (see supplementary material).

10 To avoid that certain recording units are counted more than once, all recording units that are contained in other recording units and that have not been subtracted from the number of hits yet, such as ‘integer linear programming’ that is already contained in the recording unit ‘linear programming’, are not considered for this calculation. All recording units where this criterion applies are highlighted with an asterisk in Table A1 (see supplementary material).

11 We again excluded the recording units ‘Economic Lot Scheduling Problem’ and ‘ELSP’.