Abstract
As a side-effect of the Covid-19 pandemic, significant decreases in medical procedures for noncommunicable diseases have been observed. This calls for a decision support assisting in the analysis of opportunities to relocate procedures among hospitals in an efficient or, preferably, optimal manner. In the current paper we formulate corresponding decision problems and develop linear (mixed integer) programming models for them. Since solving mixed integer programming problems is NP-complete, we verify experimentally their usefulness using real-world data about urological procedures. We show that even for large models, with millions of variables, the problems’ instances are solved in perfectly acceptable time.
Keywords: Integer linear programming, Medical information systems, Optimal relocation, Public healthcare
References
- 1.Apt K., Wallace M. Constraint Logic Programming using ECLiPSe. Cambridge University Press; 2006. [Google Scholar]
- 2.Buecker A., Ageeva Y., Blanchard V., Bloom J., Candas M.F., Chaves J., Feng G., Raman A., Schlenker H. Optimization and Decision Support Design Guide Using IBM ILOG Optimization Decision Manager. IBM; 2012. [Google Scholar]
- 3.Chang A.Y., Cullen M.R., Harrington M., Barry R.A. The impact of novel coronavirus COVID-19 on noncommunicable disease patients and health systems: a review. J. Internal Medicine. 2020 doi: 10.1111/joim.13184. doi: 10.1111/joim.13184. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4.Frühwirth T. Constraint handling rules. Cambridge Univ. Press; 2009. [Google Scholar]
- 5.Karp R.M. In: Complexity of Computer Computations. Miller R.E., Thatcher J.W., Bohlinger J.D., editors. Plenum; New York: 1972. Reducibility among combinatorial problems; pp. 85–103. [Google Scholar]
- 6.Miyawaki A., Tomio J., Nakamura M., Ninomiya H., Kobayashi Y. Changes in surgeries and therapeutic procedures during the COVID-19 outbreak: A longitudinal study of acute care hospitals in japan. Annals of Surgery. 2020 doi: 10.1097/SLA.0000000000004528. doi: 10.1097/SLA.0000000000004528. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 7.Papadimitriou Ch.H. On the complexity of integer programming. J. ACM. 1981;28(4):765–768. [Google Scholar]
- 8.Pinedo M.L. Scheduling: Theory, Algorithms, and Systems. 5th edition. Springer; 2016. [Google Scholar]
- 9.Sevastyanov S.V., Lin B.M.T., Huang H.-L. Tight complexity analysis of the relocation problem with arbitrary release dates. Theoretical Computer Science. 2011;412(35):4536–4544. [Google Scholar]
- 10.WHO . The Impact of the COVID-19 Pandemic on Noncommunicable Disease Resources and Services: Results of a Rapid Assessment. World Health Organization; Geneva: 2020. [Google Scholar]
