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A Two-Stage Constraint Programming Approach for Artificial Teeth Scheduling

Author Felix Winter

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LIPIcs.CP.2026.58.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Applied computing → Industry and manufacturing
Keywords
  • Artificial Teeth Scheduling
  • Constraint Programming
  • Local Search
  • Metaheuristics
  • Hyper-Heuristics
  • Hybrid Approach

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Abstract

The large-scale requirements of modern tooth manufacturing call for automated scheduling methods that can optimize multiple cost objectives while accounting for complex constraints.
Previously, the artificial teeth scheduling problem (ATP) was formally introduced, along with exact and heuristic methods to approach challenging real-life scenarios. Although existing approaches provide feasible solutions for all practical benchmarks evaluated, optimal results remain unknown.
We propose a novel solver-independent constraint modeling approach that solves the ATP through an innovative two-stage process. The first stage uses a subproblem formulation that batches product demands into compact jobs via constraint programming or column generation. In the second phase, the job sequence is optimized using a single-machine model with interval variables and global scheduling constraints.
Experimental results with state-of-the-art constraint solvers and a heuristic demonstrate the approach’s effectiveness, yielding improved solutions across the majority of realistically sized benchmark instances.

Cite As Get BibTex

Felix Winter. A Two-Stage Constraint Programming Approach for Artificial Teeth Scheduling. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 58:1-58:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.58

Author Details

Felix Winter
  • TU Wien, Vienna, Austria

Supplementary Materials

References

  1. Gleb Belov, Peter J. Stuckey, Guido Tack, and Mark Wallace. Improved Linearization of Constraint Programming Models. In Michel Rueher, editor, Principles and Practice of Constraint Programming, pages 49-65, Cham, 2016. Springer International Publishing. URL: https://doi.org/10.1007/978-3-319-44953-1_4.
  2. Geoffrey Chu. Improving Combinatorial Optimization. PhD thesis, Department of Computing and Information Systems, University of Melbourne, 2011. Google Scholar
  3. Karina Copil, Martin Wörbelauer, Herbert Meyr, and Horst Tempelmeier. Simultaneous lotsizing and scheduling problems: a classification and review of models. OR Spectr., 39(1):1-64, 2017. URL: https://doi.org/10.1007/S00291-015-0429-4.
  4. John H. Drake, Ahmed Kheiri, Ender Özcan, and Edmund K. Burke. Recent advances in selection hyper-heuristics. European Journal of Operational Research, 285(2):405-428, September 2020. URL: https://doi.org/10.1016/J.EJOR.2019.07.073.
  5. Jianzhong Du and Joseph Y.-T. Leung. Minimizing total tardiness on one machine is np-hard. Math. Oper. Res., 15(3):483-495, 1990. URL: https://doi.org/10.1287/MOOR.15.3.483.
  6. Romain Fontaine, Jilles Dibangoye, and Christine Solnon. Exact and anytime approach for solving the time dependent traveling salesman problem with time windows. Eur. J. Oper. Res., 311(3):833-844, 2023. URL: https://doi.org/10.1016/J.EJOR.2023.06.001.
  7. John W. Fowler and Lars Mönch. A survey of scheduling with parallel batch (p-batch) processing. Eur. J. Oper. Res., 298(1):1-24, 2022. URL: https://doi.org/10.1016/J.EJOR.2021.06.012.
  8. Kathryn Glenn Francis and Peter J. Stuckey. Explaining circuit propagation. Constraints An Int. J., 19(1):1-29, 2014. URL: https://doi.org/10.1007/S10601-013-9148-0.
  9. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2026. URL: https://www.gurobi.com.
  10. Richard M. Karp. Reducibility among combinatorial problems. In Complexity of Computer Computations, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972. URL: https://doi.org/10.1007/978-1-4684-2001-2_9.
  11. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by Simulated Annealing. Science, 220(4598):671-680, May 1983. URL: https://doi.org/10.1126/SCIENCE.220.4598.671.
  12. Philippe Laborie, Jerome Rogerie, Paul Shaw, and Petr Vilím. IBM ILOG CP optimizer for scheduling - 20+ years of scheduling with constraints at IBM/ILOG. Constraints An Int. J., 23(2):210-250, 2018. URL: https://doi.org/10.1007/S10601-018-9281-X.
  13. Nicholas Nethercote, Peter J. Stuckey, Ralph Becket, Sebastian Brand, Gregory J. Duck, and Guido Tack. Minizinc: Towards a standard CP modelling language. In CP, volume 4741 of Lecture Notes in Computer Science, pages 529-543. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74970-7_38.
  14. Laurent Perron and Frédéric Didier. Cp-sat. URL: https://developers.google.com/optimization/cp/cp_solver/.
  15. Chris N. Potts and Mikhail Y. Kovalyov. Scheduling with batching: A review. Eur. J. Oper. Res., 120(2):228-249, 2000. URL: https://doi.org/10.1016/S0377-2217(99)00153-8.
  16. Tanya Y. Tang and J. Christopher Beck. CP and Hybrid Models for Two-Stage Batching and Scheduling. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Lecture Notes in Computer Science, pages 431-446, 2020. URL: https://doi.org/10.1007/978-3-030-58942-4_28.
  17. Pamela H. Vance. Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problem. Computational Optimization and Applications, 9(3):211-228, March 1998. URL: https://doi.org/10.1023/A:1018346107246.
  18. Petr Vilím. Computing explanations for the unary resource constraint. In CPAIOR, volume 3524 of Lecture Notes in Computer Science, pages 396-409. Springer, 2005. URL: https://doi.org/10.1007/11493853_29.
  19. Felix Winter, Christoph Mrkvicka, Nysret Musliu, and Jakob Preininger. Automated Production Scheduling for Artificial Teeth Manufacturing. Proceedings of the International Conference on Automated Planning and Scheduling, 31:500-508, May 2021. URL: https://ojs.aaai.org/index.php/ICAPS/article/view/15997.
  20. Felix Winter and Nysret Musliu. An investigation of hyper-heuristic approaches for teeth scheduling. In MIC, volume 13838 of Lecture Notes in Computer Science, pages 274-289. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-26504-4_20.
  21. Z. Zhao, S. Liu, M. Zhou, X. Guo, and L. Qi. Decomposition Method for New Single-Machine Scheduling Problems From Steel Production Systems. IEEE Transactions on Automation Science and Engineering, 17(3):1376-1387, July 2020. URL: https://doi.org/10.1109/TASE.2019.2953669.
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