Abstract
In this paper, we study the label printing problem (LPP) which has applications in the printing industry. In LPP, the demand for a set of labels is satisfied by printing the labels using templates with multiple slots. Given a fixed number of templates, the decisions in LPP are determining (i) the assignment of labels to the slots of the templates (which we call template designs), and (ii) the number of prints made using each template design. The objective is to satisfy the demand with minimum waste. We consider two variants of LPP where (i) each label can be assigned to the slot(s) of a single template, and (ii) each label can be assigned to the slot(s) of multiple templates. To address LPP, we propose a novel sampling-based construct-improve heuristic where we first generate “good” template designs and then choose the ones to be used and determine the number of prints made through a set covering-type mathematical model. Then, we improve the solution using some improvement ideas that utilize a strengthened linear integer model for the problem. Using the instances from the literature, we show that the proposed heuristic provides better results compared to the benchmark algorithm. We also find optimal solutions for some of the instances from the literature using the strengthened linear integer model. With the help of the optimal solutions found we identify some problems in the previously reported results in a related study. Finally, we observe that the proposed heuristic approach not only provides better solutions but also runs in less amount of time compared to the benchmark algorithm on the large instances.
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References
Alonso-Pecina F, Romero D (2018) A hybrid simulated annealing/linear programming approach for the cover printing problem. Math Probl Eng 2018. Article ID 6193649
Baumann P, Forrer S, Trautmann N (2015) Planning of a make-to-order production process in the printing industry. Flex Serv Manuf J 27(4):534–560
Ekici A, Ergun Ö, Keskinocak P, Lagoudakis M (2010) Optimal job splitting on a multi-slot machine with applications in the printing industry. Nav Res Logist 57(3):237–251
Elaoud S, Teghem J, Bouaziz B (2007) Genetic algorithms to solve the cover printing problem. Comput Oper Res 34(11):3346–3361
Groß D, Hamacher H, Horn S, Schobel A (2009) Stop location design in public transportation networks: covering and accessibility objectives. TOP 17:335–346
Hsieh Y, You P (2014) An immune evolutionary approach for the label printing problem. Int J Comput Intell Syst 7(3):515–523
Mohan S, Neogy S, Seth A, Garg N, Mittal S (2007) An optimization model to determine master designs and runs for advertisement printing. J Math Model Algorithms 6(2):259–271
Pusztai P (2008) An application of the greedy heuristic of set cover to traffic checks. Cent Eur J Oper Res 16(4):407–414
Romero D, Alonso-Pecina F (2012) Ad hoc heuristic for the cover printing problem. Discret Optim 9(1):17–28
Teghem J, Pirlot M, Antoniadis C (1995) Embedding of linear programming in a simulated annealing algorithm for solving a mixed integer production planning problem. J Comput Appl Math 64(1–2):91–102
The World Counts (2014) Paper waste facts. http://www.theworldcounts.com/stories/Paper-Waste-Facts. Accessed 09 Sep 2019
Tuyttens D, Vandaele A (2010) Using a greedy random adaptative search procedure to solve the cover printing problem. Comput Oper Res 37(4):640–648
Tuyttens D, Vandaele A (2014) Towards an efficient resolution of printing problems. Discret Optim 14(1):126–146
Yiu K, Mak K, Lau H (2007) A heuristic for the label printing problem. Comput Oper Res 34(9):2576–2588
Acknowledgements
We would like to thank Daniel Tuyttens for sharing the instances used in the computational study and for the new results of \(\text{GRASP}_{{\text{m}}}.\)
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Çankaya, E., Ekici, A. & Özener, O.Ö. A two-phase heuristic algorithm for the label printing problem. TOP 31, 110–138 (2023). https://doi.org/10.1007/s11750-022-00624-6
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DOI: https://doi.org/10.1007/s11750-022-00624-6