IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v316y2024i1p85-99.html
   My bibliography  Save this article

Solving the patient admission scheduling problem using constraint aggregation

Author

Listed:
  • Liu, Haichao
  • Wang, Yang
  • Hao, Jin-Kao

Abstract

Patient admission scheduling (PAS) consists of assigning patients to beds over a planning horizon to maximize treatment efficiency, patient satisfaction, and hospital utilization while meeting all necessary medical constraints and considering patient preferences as much as possible. There are several different variants of the PAS problem in the literature, which differ mainly in the constraints that must be satisfied (hard) or can be violated (soft). Due to the intrinsic difficulty of the PAS problem, solving large integer programming (IP) models to optimality is challenging. In this paper, we consider the widely studied variant of the PAS problem that has the maximum number of soft constraints, and focus on how to reduce the size of IP formulations of the PAS problem to improve the solving efficiency. We employ a two-stage optimization method where the first stage builds reduced models by constraint aggregation to improve the typical formulation of the PAS problem. Experimental results on the 13 benchmark instances in the literature indicate that our method can obtain new improved solutions (new upper bounds) for 6 instances, including one proven optimal solution. For the 5 other instances whose optimal solutions are known, our approach can reach these known optimal solutions in a shorter computation time compared to the existing methods. In addition, we apply our method to the original PAS problem, which has the maximum number of hard constraints, and perform computational experiments on the same 13 benchmark instances. Our method yields 5 new best solutions and proves optimality for 6 instances.

Suggested Citation

  • Liu, Haichao & Wang, Yang & Hao, Jin-Kao, 2024. "Solving the patient admission scheduling problem using constraint aggregation," European Journal of Operational Research, Elsevier, vol. 316(1), pages 85-99.
  • Handle: RePEc:eee:ejores:v:316:y:2024:i:1:p:85-99
    DOI: 10.1016/j.ejor.2024.02.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724001012
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2024.02.009?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Saddoune, Mohammed & Desaulniers, Guy & Elhallaoui, Issmail & Soumis, François, 2011. "Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods," European Journal of Operational Research, Elsevier, vol. 212(3), pages 445-454, August.
    2. Guido, Rosita & Groccia, Maria Carmela & Conforti, Domenico, 2018. "An efficient matheuristic for offline patient-to-bed assignment problems," European Journal of Operational Research, Elsevier, vol. 268(2), pages 486-503.
    3. Issmail Elhallaoui & Daniel Villeneuve & François Soumis & Guy Desaulniers, 2005. "Dynamic Aggregation of Set-Partitioning Constraints in Column Generation," Operations Research, INFORMS, vol. 53(4), pages 632-645, August.
    4. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    5. Wim Vancroonenburg & Patrick Causmaecker & Greet Vanden Berghe, 2016. "A study of decision support models for online patient-to-room assignment planning," Annals of Operations Research, Springer, vol. 239(1), pages 253-271, April.
    6. Daniel Porumbel & François Clautiaux, 2017. "Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 170-184, February.
    7. Ram, Balasubramanian & Karwan, Mark H. & Babu, A. J. G., 1988. "Aggregation of constraints in integer programming," European Journal of Operational Research, Elsevier, vol. 35(2), pages 216-227, May.
    8. Lusby, Richard Martin & Schwierz, Martin & Range, Troels Martin & Larsen, Jesper, 2016. "An Adaptive Large Neighbourhood Search Procedure Applied to the Dynamic Patient Admission Scheduling Problem," Discussion Papers on Economics 1/2016, University of Southern Denmark, Department of Economics.
    9. Benchimol, Pascal & Desaulniers, Guy & Desrosiers, Jacques, 2012. "Stabilized dynamic constraint aggregation for solving set partitioning problems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 360-371.
    10. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, August.
    11. Range, Troels Martin & Lusby, Richard Martin & Larsen, Jesper, 2014. "A column generation approach for solving the patient admission scheduling problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 252-264.
    12. Bastos, Leonardo S.L. & Marchesi, Janaina F. & Hamacher, Silvio & Fleck, Julia L., 2019. "A mixed integer programming approach to the patient admission scheduling problem," European Journal of Operational Research, Elsevier, vol. 273(3), pages 831-840.
    Full references (including those not matched with items on IDEAS)

    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. Fabian Schäfer & Manuel Walther & Dominik G. Grimm & Alexander Hübner, 2023. "Combining machine learning and optimization for the operational patient-bed assignment problem," Health Care Management Science, Springer, vol. 26(4), pages 785-806, December.
    2. Guido, Rosita & Groccia, Maria Carmela & Conforti, Domenico, 2018. "An efficient matheuristic for offline patient-to-bed assignment problems," European Journal of Operational Research, Elsevier, vol. 268(2), pages 486-503.
    3. Sebastian Ruther & Natashia Boland & Faramroze G. Engineer & Ian Evans, 2017. "Integrated Aircraft Routing, Crew Pairing, and Tail Assignment: Branch-and-Price with Many Pricing Problems," Transportation Science, INFORMS, vol. 51(1), pages 177-195, February.
    4. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    5. Daniel Porumbel & François Clautiaux, 2017. "Constraint Aggregation in Column Generation Models for Resource-Constrained Covering Problems," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 170-184, February.
    6. Jean Bertrand Gauthier & Jacques Desrosiers & Marco E. Lübbecke, 2016. "Tools for primal degenerate linear programs: IPS, DCA, and PE," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(2), pages 161-204, June.
    7. Bouarab, Hocine & El Hallaoui, Issmail & Metrane, Abdelmoutalib & Soumis, François, 2017. "Dynamic constraint and variable aggregation in column generation," European Journal of Operational Research, Elsevier, vol. 262(3), pages 835-850.
    8. Chengliang Wang & Feifei Yang & Quan-Lin Li, 2023. "Optimal Decision of Dynamic Bed Allocation and Patient Admission with Buffer Wards during an Epidemic," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    9. Aleida Braaksma & Martin S. Copenhaver & Ana C. Zenteno & Elizabeth Ugarph & Retsef Levi & Bethany J. Daily & Benjamin Orcutt & Kathryn M. Turcotte & Peter F. Dunn, 2023. "Evaluation and implementation of a Just-In-Time bed-assignment strategy to reduce wait times for surgical inpatients," Health Care Management Science, Springer, vol. 26(3), pages 501-515, September.
    10. Atoosa Kasirzadeh & Mohammed Saddoune & François Soumis, 2017. "Airline crew scheduling: models, algorithms, and data sets," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 111-137, June.
    11. Fabian Schäfer & Manuel Walther & Alexander Hübner & Heinrich Kuhn, 2019. "Operational patient-bed assignment problem in large hospital settings including overflow and uncertainty management," Flexible Services and Manufacturing Journal, Springer, vol. 31(4), pages 1012-1041, December.
    12. Edirisinghe, Chanaka & Jeong, Jaehwan, 2019. "Indefinite multi-constrained separable quadratic optimization: Large-scale efficient solution," European Journal of Operational Research, Elsevier, vol. 278(1), pages 49-63.
    13. Christensen, Tue R.L. & Labbé, Martine, 2015. "A branch-cut-and-price algorithm for the piecewise linear transportation problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 645-655.
    14. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    15. Wilhelm, Wilbert E. & Xu, Kaihong, 2002. "Prescribing product upgrades, prices and production levels over time in a stochastic environment," European Journal of Operational Research, Elsevier, vol. 138(3), pages 601-621, May.
    16. Vicens, E. & Alemany, M. E. & Andres, C. & Guarch, J. J., 2001. "A design and application methodology for hierarchical production planning decision support systems in an enterprise integration context," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 5-20, December.
    17. Merrick, James H. & Bistline, John E.T. & Blanford, Geoffrey J., 2024. "On representation of energy storage in electricity planning models," Energy Economics, Elsevier, vol. 136(C).
    18. Kulkarni, Sarang & Krishnamoorthy, Mohan & Ranade, Abhiram & Ernst, Andreas T. & Patil, Rahul, 2018. "A new formulation and a column generation-based heuristic for the multiple depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 457-487.
    19. Renaud Chicoisne, 2023. "Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes," Computational Optimization and Applications, Springer, vol. 84(3), pages 789-831, April.
    20. Srinivasa, Anand V. & Wilhelm, Wilbert E., 1997. "A procedure for optimizing tactical response in oil spill clean up operations," European Journal of Operational Research, Elsevier, vol. 102(3), pages 554-574, November.

    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:eee:ejores:v:316:y:2024:i:1:p:85-99. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.