A Reference Point Method to Triple-Objective Assignment of Supporting Services in a Healthcare Institution
DOI:
https://doi.org/10.7494/dmms.2010.4.2.37Keywords:
reference point method, assignment problem, mixed integer programming, ser- vices operations management, healthcare planningAbstract
This paper presents an application of mixed integer programming model for op- timal allocation of workers among supporting services in a hospital. The services include logistics, inventory management, financial management, operations management, medical analysis, etc. The optimality criterion of the problem is to minimize operational costs of supporting services subject to some specific constraints. The constraints represent specific conditions for resource allocation in a hospital. The overall problem is formulated as a triple- objective assignment model, where the decision variables represent the assignment of people to various jobs. A reference point approach with the Chebyshev metric is applied for the problem solution. The results of computational experiments modeled on a real data from a hospital in Lesser Poland are reported.
References
Alves M.J. & Clímaco J. (2007). A review of interactive methods for multiobjective integer and mixed-integer programming. European Journal of Operational Research, 180(1), pp. 99–115. DOI: https://doi.org/10.1016/j.ejor.2006.02.033.
Bowman V.J. Jr. (1976). On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives. In: H. Thiriez & S. Zionts (Eds.), Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, 130, pp. 76–86. Berlin–Heidelberg: Springer. DOI: https://doi.org/10.1007/978-3-642-87563-2_5.
Brandeau M.L., Sainfort F. & Pierskalla W.P. (Eds.) (2004). Operations Research and Health Care: A Handbook of Methods and Applications. International Series in Operations Research & Management Science, 70. Boston, MA: Kluwer Academic Publishers. DOI: https://doi.org/10.1007/b106574.
Burkard R.E., Dell’Amico M. & Martello S. (2009). Assignment Problems. Philadelphia: Society for Industrial and Applied Mathematics. DOI: https://doi.org/10.1137/1.9780898717754.
Ehrgott M. (2005). Multicriteria Optimization. 2nd Edition. Berlin–Heidelberg: Springer. DOI: https://doi.org/10.1007/3-540-27659-9.
Fourer R., Gay D.M. & Kernighan B.W. (1990). A modeling language for mathematical programming. Management Science, 36(5), pp. 519–554. DOI: https://doi.org/10.1287/mnsc.36.5.519.
Nemhauser G.L. & Wolsey L.A. (1988). Integer and Combinatorial Optimization. New York: John Wiley & Sons. DOI: https://doi.org/10.1002/9781118627372.
Sawik B. (2010). Reference point approach to assignment of supporting services in a healthcare institution. In: A. Świerniak & J. Krystek (Eds.), Automatyzacja procesów dyskretnych: teoria i zastosowania, Vol. 2, pp. 187–196. Gliwice: Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego.
Sawik B. & Mikulik J. (2008a). Optimal assignment of workers to supporting services in a hospital. Polish Journal of Medical Physics and Engineering, 14(4), pp. 197–206. DOI: https://doi.org/10.2478/v10013-008-0016-y.
Sawik B. & Mikulik J. (2008b). Model for supporting service optimization in a public health care institution. In: European Conference Medical Physics and Engineering: 110 Years after the Discovery of Polonium and Radium, Kraków, Poland, September 17–21, 2008.
Sawik B. (2008c). Bi-objective integer programming approach to optimal assignment of supporting services in a health-care institution. In: 21st Conference of the European Chapter on Combinatorial Optimization – ECCO XXI, Dubrovnik, Croatia, May 29–31, 2008.
Steuer R.E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. New York: John Wiley & Sons.