IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v57y2010i3p237-251.html
   My bibliography  Save this article

Optimal job splitting on a multi‐slot machine with applications in the printing industry

Author

Listed:
  • Ali Ekici
  • Özlem Ergun
  • Pınar Keskinocak
  • Michail G. Lagoudakis

Abstract

In this article, we define a scheduling/packing problem called the Job Splitting Problem, motivated by the practices in the printing industry. There are n types of items to be produced on an m‐slot machine. A particular assignment of the types to the slots is called a “run” configuration and requires a setup cost. Once a run begins, the production continues according to that configuration and the “length” of the run represents the quantity produced in each slot during that run. For each unit of production in excess of demand, there is a waste cost. Our goal is to construct a production plan, i.e., a set of runs, such that the total setup and waste cost is minimized. We show that the problem is strongly NP‐hard and propose two integer programming formulations, several preprocessing steps, and two heuristics. We also provide a worst‐case bound for one of the heuristics. Extensive tests on real‐world and randomly generated instances show that the heuristics are both fast and effective, finding near‐optimal solutions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • Ali Ekici & Özlem Ergun & Pınar Keskinocak & Michail G. Lagoudakis, 2010. "Optimal job splitting on a multi‐slot machine with applications in the printing industry," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(3), pages 237-251, April.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:3:p:237-251
    DOI: 10.1002/nav.20396
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20396
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20396?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    3. François Vanderbeck, 2000. "Exact Algorithm for Minimising the Number of Setups in the One-Dimensional Cutting Stock Problem," Operations Research, INFORMS, vol. 48(6), pages 915-926, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Herbert Meyr & Mirko Kiel, 2022. "Minimizing setups and waste when printing labels of consumer goods," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 733-761, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    2. Kallrath, Julia & Rebennack, Steffen & Kallrath, Josef & Kusche, Rüdiger, 2014. "Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges," European Journal of Operational Research, Elsevier, vol. 238(1), pages 374-389.
    3. Hajizadeh, Iman & Lee, Chi-Guhn, 2007. "Alternative configurations for cutting machines in a tube cutting mill," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1385-1396, December.
    4. Wang, Danni & Xiao, Fan & Zhou, Lei & Liang, Zhe, 2020. "Two-dimensional skiving and cutting stock problem with setup cost based on column-and-row generation," European Journal of Operational Research, Elsevier, vol. 286(2), pages 547-563.
    5. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    6. Letchford, Adam N. & Amaral, Andre, 2001. "Analysis of upper bounds for the Pallet Loading Problem," European Journal of Operational Research, Elsevier, vol. 132(3), pages 582-593, August.
    7. Mhand Hifi & Rym M'Hallah, 2005. "An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems," Operations Research, INFORMS, vol. 53(1), pages 140-150, February.
    8. B. S. C. Campello & C. T. L. S. Ghidini & A. O. C. Ayres & W. A. Oliveira, 2022. "A residual recombination heuristic for one-dimensional cutting stock problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 194-220, April.
    9. C Alves & J M Valério de Carvalho, 2008. "New integer programming formulations and an exact algorithm for the ordered cutting stock problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(11), pages 1520-1531, November.
    10. Dell’Amico, Mauro & Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2019. "Mathematical models and decomposition methods for the multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(3), pages 886-899.
    11. Morabito, Reinaldo & Belluzzo, Luciano, 2007. "Optimising the cutting of wood fibre plates in the hardboard industry," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1405-1420, December.
    12. Mateus Martin & Horacio Hideki Yanasse & Luiz Leduíno Salles-Neto, 2022. "Pattern-based ILP models for the one-dimensional cutting stock problem with setup cost," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 557-582, August.
    13. Adejuyigbe O. Fajemisin & Steven D. Prestwich & Laura Climent, 2023. "Cutting uncertain stock and vehicle routing in a sustainability forestry harvesting problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 139-164, April.
    14. Daniel Adelman & George L. Nemhauser, 1999. "Price-Directed Control of Remnant Inventory Systems," Operations Research, INFORMS, vol. 47(6), pages 889-898, December.
    15. Gradisar, Miro & Kljajic, Miroljub & Resinovic, Gortan & Jesenko, Joze, 1999. "A sequential heuristic procedure for one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 114(3), pages 557-568, May.
    16. Mhand Hifi & Toufik Saadi, 2012. "A parallel algorithm for two-staged two-dimensional fixed-orientation cutting problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 783-807, March.
    17. Tao Wu & Kerem Akartunal? & Raf Jans & Zhe Liang, 2017. "Progressive Selection Method for the Coupled Lot-Sizing and Cutting-Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 523-543, August.
    18. Belov, G. & Scheithauer, G., 2006. "A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting," European Journal of Operational Research, Elsevier, vol. 171(1), pages 85-106, May.
    19. Kelly Poldi & Silvio Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    20. Gradisar, Miro & Resinovic, Gortan & Kljajic, Miroljub, 1999. "A hybrid approach for optimization of one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 119(3), pages 719-728, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:57:y:2010:i:3:p:237-251. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.