Using NSGAII to Solve Bi-objective Bed Allocation Problems

  • Jalal A. Sultan Department of Mathematics, College of Al-Hamdaniah Education, University of Mosul, Al-Hamdaniah, Iraq
  • Ban A. Mitras Department of Statistics & Information, College of Mathematics and Computer Sciences, University of Mosul, Mosul, Iraq.
  • Raghad M. Jasim Department of Operation Research, College of Mathematics and Computer Sciences, University of Mosul, Mosul, Iraq


The Bed Allocation Problem (BAP) is NP-complete and always high dimensional. In this paper, a bi-objective decision aiding model based on queuing theory is introduced for allocation of beds in a hospital. The problem is modeled as an M/PH/n queue. The objectives include maximizing the patient admission rate human resources, in particular, maximization of the nursing work hours. The proposed model is solved by using Non-dominated Sorting Genetic Algorithm-II (NSGA-II), which is a very effective algorithm for solving multi-objective optimization problems and finding optimal Pareto front. The paper describes an application of the model, dealing with a public hospital in Iraq. The results related that multi-objective model was presented suitable framework for bed allocation and optimum use.


[1] A. Esogbue, A. Singh "A stochastic model for an optimal priority bed distribution problem in a hospital ward. Oper Res, vol. 24. No. 5, pp884–898,1976.
[2] A. Coello Coello, B. Lamon, A. Van Veldhuisen "Evolutionary Algorithms for Solving Multi-Objective Problems", Springer, 2007.
[3] B. Tomoiagă, M. Chindriş, A. Sumper, A. Sudria-Andreu, R. Villafafila-Robles, "Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II. Energies" vol. 6, pp. 1439-1455, 2003.
[4] D. J. Worthington and A. Wall, "Using the Discrete Time Modelling Approach to Evaluate the Time-Dependent Behaviour of Queueing Systems," The Journal of the Operational Research Society, vol. 50, no. 8, pp. 777-788, 1999.
[5] E. P. C. Kao and G. G. Tung, "Bed Allocation in a Public Health Care Delivery System," Management Science, vol. 27, no. 5, pp. 507-520, 198U.
[6] E. P. C. Kao and G. G. Tung, "Bed Allocation in a Public Health Care Delivery System", Management Science, vol. 27, no. 5, pp. 507-520,1981.
[7] F. Gorunescu, S. I. McClean and P. H. Millard, "A Queueing Model for Bed-Occupancy Management and Planning of Hospitals," The Journal of the Operational Research SOCiety, vol. 53, no. I, pp. 19-24, 2002.
[8] F. Gorunescu, S. I. McClean and P. H. Millard, "Using a Queueing Model to Help Plan Bed Allocation in a Department of Geriatric Medicine," Health Care Management Science, vol. 5, no. 4, 2002.
[9] H. R. Feili, “Improving the Health Care Systems Performance by Simulation Optimization,” J. Math. Comput. Sci., vol. 7, pp. 73–79, 2013.
[10] J. C Ridge, S. K. Jones, M. S. Nielsen and A. K. Shahani, "Capacity planning for intensive care units," European Journal of Operational Research, vol. 105, no. 2, pp. 346-355, 1998.
[11] J. Nguyen, P. Six, D. Antonioli, P. Glemain, G. Potel, P. Lombrail and P. Le Beux, "A simple method to optimize hospital beds capacity," International Journal of Medical l1iformatics, vol. 74, no. I, pp. 39-49, 2005.
[12] J. Oddoye, M. Tamiz, D. Jones, P. Schmidt "A simulation model for health planning in a medical assessment unit with multi-objective output analysis". Technical report, Management Mathematics Group, University of Portsmouth, UK, 2007.
[13] J. Oddoye, M. Yaghoobi, M. Tamiz, D. Jones, P. Schmidt "A multi-objective model determine efficient resource levels in a medical assessment unit". J Oper Res Soc, 2007.
[14] K. Deb, A. Agarwal, T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II". IEEE Transactions on Evolutionary Computation vol. 6, no. 2, pp. 182-202, 2002.
[15] L. V. Green and V. Nguyen, "Strategies for cutting hospital beds: the impact on patient service," Health Services Research, vol. 36, no. 2, pp. 421-442,2001.
[16] L. Green, "Queueing Analysis in Healthcare", Patient Flow: Reducing Delay in Healthcare Delivery, pp. 281-308, 2006.
[17] M. Cote, "A note on bed allocation techniques based on census data". Socioecon Plan Sci, vol. 39, pp183-192, 2005.
[18] S. C. Kim, I. Horowitz, K. K. Young and T. A. Buckley, "Flexible bed allocation and performance in the intensive care unit," Journal of Operations Management, vol. 18, no. 4, pp. 427-443, 2000.
[19] S. Lapierre, D. Goldsman, R. Cochran, J. DuBow "Bed allocation techniques based on census data", Socioecon Plan Sci, vol. 33pp. 25–38, 1999.
[20] S. M. Ballard and M. E. Kuhl, “The use of simulation to determine maximum capacity in the surgical suite operating room,” in Proceedings - Winter Simulation Conference, vol. 7, pp. 433–438,2006.
[21] T. Ibarraki and N. Katoh, Resource Allocation Problems, The MIT Press, Cambridge, MA, 1988.
[22] X.-D. Li, P. Beullens, D. Jones and M. Tamiz, "Optimal Bed Allocation in Hospitals," Lecture Notes in Economics and Mathematical Systems, vol. 618, pp. 253-265, 2009.
[23] Y. Tütüncü and D. Newlands, “Hospital Bed Capacity and Mix Problem for State Supported Public and Fee Paying Private Wards,” IÉSEG Sch. Manag. CNRSLEM (UMR 8179), no. Umr 8179, 2009.
How to Cite
SULTAN, Jalal A.; MITRAS, Ban A.; JASIM, Raghad M.. Using NSGAII to Solve Bi-objective Bed Allocation Problems. Journal of University of Human Development, [S.l.], v. 1, n. 3, p. 397-401, aug. 2015. ISSN 2411-7765. Available at: <>. Date accessed: 16 june 2021. doi: