Journal of Scheduling

, Volume 18, Issue 2, pp 131–145 | Cite as

Scheduling multi-colour print jobs with sequence-dependent setup times

  • A. P. Burger
  • C. G. Jacobs
  • J. H. van VuurenEmail author
  • S. E. Visagie


In this paper, a scheduling problem is considered which arises in the packaging industry. Plastic and foil wrappers used for packaging candy bars, crisps and other snacks typically require overlay printing with multiple colours. Printing machines used for this purpose usually accommodate a small number of colours which are loaded into a magazine simultaneously. If two consecutively scheduled print jobs require significantly different colour overlays, then substantial down times are incurred during the transition from the former magazine colour configuration to the latter, because ink cartridges corresponding to colours not required for the latter job have to be cleaned after completion of the former job. The durations of these down times are therefore sequence dependent (the washing and refilling time is a function of the number of colours in which two consecutive printing jobs differ). It is consequently desirable to schedule print jobs so that the accumulated down times associated with all magazine colour transitions are as short as possible for each printing machine. We show that an instance of this scheduling problem can be modelled as the well-known tool switching problem, which is tractable for small instances only. The problem can, however, be solved rather effectively in heuristic fashion by decomposing it into two subproblems: a job grouping problem (which can be modelled as a unicost set covering problem) and a group sequencing problem (which is a generalisation of the celebrated travelling salesman problem). We solve the colour print scheduling problem both exactly and heuristically for small, randomly generated test problem instances, studying the trade-off between the time efficiency and solution quality of the two approaches. Finally, we apply both solution approaches to real problem data obtained from a printing company in the South African Western Cape as a special case study.


Job grouping Job scheduling Job sequencing Tool switching 

Mathematics Subject Classification

90B35 05A18 05C15 



Work towards this paper was supported financially by the South African National Research Foundation under Grant GUN 2072999.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • A. P. Burger
    • 1
  • C. G. Jacobs
    • 1
  • J. H. van Vuuren
    • 2
    Email author
  • S. E. Visagie
    • 1
  1. 1.Department of LogisticsStellenbosch UniversityMatielandSouth Africa
  2. 2.Department of Industrial EngineeringStellenbosch UniversityMatielandSouth Africa

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