Health Care Management Science

, Volume 20, Issue 2, pp 246–264 | Cite as

Stochastic multi-objective auto-optimization for resource allocation decision-making in fixed-input health systems

  • Nathaniel D. Bastian
  • Tahir Ekin
  • Hyojung Kang
  • Paul M. Griffin
  • Lawrence V. Fulton
  • Benjamin C. Grannan


The management of hospitals within fixed-input health systems such as the U.S. Military Health System (MHS) can be challenging due to the large number of hospitals, as well as the uncertainty in input resources and achievable outputs. This paper introduces a stochastic multi-objective auto-optimization model (SMAOM) for resource allocation decision-making in fixed-input health systems. The model can automatically identify where to re-allocate system input resources at the hospital level in order to optimize overall system performance, while considering uncertainty in the model parameters. The model is applied to 128 hospitals in the three services (Air Force, Army, and Navy) in the MHS using hospital-level data from 2009 – 2013. The results are compared to the traditional input-oriented variable returns-to-scale Data Envelopment Analysis (DEA) model. The application of SMAOM to the MHS increases the expected system-wide technical efficiency by 18 % over the DEA model while also accounting for uncertainty of health system inputs and outputs. The developed method is useful for decision-makers in the Defense Health Agency (DHA), who have a strategic level objective of integrating clinical and business processes through better sharing of resources across the MHS and through system-wide standardization across the services. It is also less sensitive to data outliers or sampling errors than traditional DEA methods.


Multi-objective optimization Stochastic programming Resource allocation Performance measurement Productivity analysis Health systems Military medicine 



This work was supported by the National Science Foundation under Grant No. DGE1255832. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation, Pennsylvania State University, Texas State University, University of Virginia, Georgia Institute of Technology, Texas Tech University, or Virginia Military Institute.


  1. 1.
    Aktas E, Ulengin F, Sahin SO (2007) A decision support system to improve the efficiency of resource allocation in healthcare management. Socio Econ Plan Sci 41(2):130–146CrossRefGoogle Scholar
  2. 2.
    Banker RD (1993) Maximum likelihood, consistency and DEA: Statistical foundations. Manag Sci 39 (10):1265–1273CrossRefGoogle Scholar
  3. 3.
    Bastian N, Fulton L, Shah V, Ekin T (2014) Resource allocation decision-making in the military health system. IIE Trans Healt Syst Engin 4(2):80–87CrossRefGoogle Scholar
  4. 4.
    Bastian N, Kang H, Swensen E, Fulton L, Griffin P (2015) Evaluating the impact of hospital efficiency on wellness in the Military Health System. (Military Medicine), in pressGoogle Scholar
  5. 5.
    Bastian N, McMurry P, Fulton L, Griffin P, Cui S, Hanson T, Srinivas S (2015) The AMEDD uses goal programming to optimize workforce planning decisions. Interfaces 45(4):305–324CrossRefGoogle Scholar
  6. 6.
    Charnes A, Cooper W, Dieck-Assad M, Golany B, Wiggins D (1985) Efficiency Analysis of Medical Care Resources in the U.S. Army Health Service Command. The University of Texas at Austin, Center for Cybernetic Studies.Washington, DC: Defense Technical Information Service (ADA 159742)Google Scholar
  7. 7.
    Charnes A, Cooper WW, Rhodes E (1978) Measuring efficiency of decision making units. Eur J Oper Res 2(6):429–444CrossRefGoogle Scholar
  8. 8.
    Cooper WW, Li S, Seiford LM, Tone K, Thrall RM, Zhu J (2001) Sensitivity and stability analysis in DEA: some recent developments. J Prod Anal 15(3):217–246CrossRefGoogle Scholar
  9. 9.
    Cooper W, Seifer L, Tone K (2007) Data Envelopment Analysis, 2nd Edition. Springer, New YorkGoogle Scholar
  10. 10.
    Cooper WW, Huang Z, Li SX (1996) Satisficing DEA models under chance constraints. Ann Oper Res 66(4):279–295CrossRefGoogle Scholar
  11. 11.
    Cooper W, Huang Z, Lelas V, Li S, Olesen O (1998) Chance constrained programming formulations for stochastic characterizations of efficiency and dominance in DEA. J Prod Anal 9(1):53–79CrossRefGoogle Scholar
  12. 12.
    Cooper WW, Park KS, Yu G (1999) IDEA and AR-IDEA: Models for dealing with imprecise data in DEA. Manag Sci 45(4):597–607CrossRefGoogle Scholar
  13. 13.
    Cooper WW, Park KS, Pastor JT (1999) RAM: A range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J Prod Anal 11(1):5–42CrossRefGoogle Scholar
  14. 14.
    Corrigan JM (2005) Crossing the Quality Chasm. Building a Better Delivery System. National Academies PressGoogle Scholar
  15. 15.
    Defense Health Agency (2015) The Defense Health Agency: Reflections on Our First Year and Future. Retrieved May 21, 2015. Available at
  16. 16.
    Drud A (1992) CONOPT–A Large-Scale GRG Code. ORSA J Comput 6:207–216CrossRefGoogle Scholar
  17. 17.
    Dyson RG, Shale EA (2010) Data envelopment analysis, operational research and uncertainty. J Oper Res Soc 61(1):25–34CrossRefGoogle Scholar
  18. 18.
    Eichler HG, Kong SX, Gerth WC, Mavros P, Jnsson B (2004) Use of cost-effectiveness analysis in health-care resource allocation decision-making: How are cost-effectiveness thresholds expected to emerge?. Value Health 7(5):518– 528CrossRefGoogle Scholar
  19. 19.
    Ekin T, Kocadagli O, Bastian N, Fulton L, Griffin P (2015) Fuzzy Decision-Making in Health Systems: A Resource Allocation Model. EURO Journal on Decision Processes. OnlineFirst, pp. 1–23Google Scholar
  20. 20.
    Ferrier GD, Trivitt JS (2013) Incorporating quality into the measurement of hospital efficiency: a double DEA approach. J Prod Anal 40(3):337–355CrossRefGoogle Scholar
  21. 21.
    Fulton L, Lasdon L, McDaniel R (2007) Cost drivers and resource allocation in military health care systems. Mil Med 172(3):244–249CrossRefGoogle Scholar
  22. 22.
    Fulton L, Lasdon L, McDaniel R, Coppola N (2008) Including quality, access and efficiency in health care cost models. Hosp Top 86(4):3–16CrossRefGoogle Scholar
  23. 23.
    (2014). In: Emrouznejad A., Tavana M (eds) Performance Measurement with Fuzzy Data Envelopment Analysis. Springer, ChicagoGoogle Scholar
  24. 24.
    GAMS Development Corporation (2014) The General Algebraic Modeling System (GAMS)Google Scholar
  25. 25.
    Grosskopf S (1996) Statistical inference and nonparametric efficiency: A selective survey. J Prod Anal 7 (2-3):161–176CrossRefGoogle Scholar
  26. 26.
    Hatami-Marbini A, Emrouznejad A, Tavana M (2011) A Taxonomy and Review of the Fuzzy Data Envelopment Analysis Literature: Two Decades in the Making. Eur J Oper Res 214(3):457–472CrossRefGoogle Scholar
  27. 27.
    Hollingsworth B (2003) Non-parametric and parametric applications measuring efficiency in health care. Health Care Manag Sci 6(4):203–218CrossRefGoogle Scholar
  28. 28.
    Hollingsworth B, Dawson PJ, Maniadakis N (1999) Efficiency measurement of health care: a review of non-parametric methods and applications. Health Care Manag Sci 2(3):161–172CrossRefGoogle Scholar
  29. 29.
    Huang Z, Li SX (2001) Stochastic DEA models with different types of input-output disturbances. J Prod Anal 15(2):95–113CrossRefGoogle Scholar
  30. 30.
    Huang Z, Li SX (1996) Dominance stochastic models in data envelopment analysis. Eur J Oper Res 95 (2):390–403CrossRefGoogle Scholar
  31. 31.
    IBM ILOG (2010) CPLEX 12.1 User ManualGoogle Scholar
  32. 32.
    Jacobs R (2001) Alternative methods to examine hospital efficiency: data envelopment analysis and stochastic frontier analysis. Health Care Manag Sci 4(2):103–115CrossRefGoogle Scholar
  33. 33.
    Torres-Jimnez M, Garc?a-Alonso CR, Salvador-Carulla L, Fernndez-Rodr?guez V (2015) Evaluation of system efficiency using the Monte Carlo DEA: The case of small health areas. Eur J Oper Res 242(2):525–535Google Scholar
  34. 34.
    Kim SH, Park CG, Park KS (1999) An application of data envelopment analysis in telephone offices evaluation with partial data. Comput Oper Res 26(1):59–72CrossRefGoogle Scholar
  35. 35.
    Kuosmanen T, Post T (2002) Nonparametric efficiency analysis under price uncertainty: A first-order stochastic dominance approach. J Prod Anal 17(3):183–200CrossRefGoogle Scholar
  36. 36.
    Kwak NK, Chang WL (2002) Business process reengineering for health-care system using multicriteria mathematical programming. Eur J Oper Res 140(2):447–458CrossRefGoogle Scholar
  37. 37.
    Kwak NK, Lee C (1997) A linear goal programming model for human resource allocation in a health-care organization. J Med Syst 21(3):129–140CrossRefGoogle Scholar
  38. 38.
    Land K, Lovell CAK, Thore S (1993) Chance-constrained data envelopment analysis. Manag Decis Econ 14(6):541–554CrossRefGoogle Scholar
  39. 39.
    Land KC, Lovell CK, Thore S (1994) Productive efficiency under capitalism and state socialism:: An empirical inquiry using chance-constrained data envelopment analysis. Technol Forecast Soc Chang 46(2):139–152CrossRefGoogle Scholar
  40. 40.
    Li SX (1998) Stochastic models and variable returns to scales in data envelopment analysis. Eur J Oper Res 104(3):532–548CrossRefGoogle Scholar
  41. 41.
    Lin RC, Sir MY, Pasupathy KS (2013) Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services. Omega 41(5):881–892CrossRefGoogle Scholar
  42. 42.
    Lovell CAK (1994) Linear Programming Approaches to the Measurement and Analysis of Productive Efficiency. TOP 2(2):175–224CrossRefGoogle Scholar
  43. 43.
    Mitropoulos P, Talias ?. A, Mitropoulos I (2014) Combining stochastic DEA with Bayesian analysis to obtain statistical properties of the efficiency scores: An application to Greek public hospitals. Eur J Oper Res 243 (1):302–311CrossRefGoogle Scholar
  44. 44.
    Nayar P, Ozcan YA (2008) Data envelopment analysis comparison of hospital efficiency and quality. J Med Syst 32(3):193–199CrossRefGoogle Scholar
  45. 45.
    O’Donnell CJ, Chambers RG, Quiggin J (2010) Efficiency analysis in the presence of uncertainty. J Prod Anal 33(1):1–17CrossRefGoogle Scholar
  46. 46.
    Olesen OB (2006) Comparing and combining two approaches for chance constrained DEA. J Prod Anal 26 (2):103–119CrossRefGoogle Scholar
  47. 47.
    Olesen OB, Petersen NC (1995) Chance constrained efficiency evaluation. Manag Sci 41(3):442–457CrossRefGoogle Scholar
  48. 48.
    Ozcan Y, Bannick R (1994) Trends in Department of Defense hospital efficiency. J Med Syst 18(2):69–83CrossRefGoogle Scholar
  49. 49.
    Seiford LM (1996) Data envelopment analysis: the evolution of the state of the art (1978–1995). J Prod Anal 7(2-3):99–137CrossRefGoogle Scholar
  50. 50.
    Sengupta JK (1988) Robust efficiency measures in a stochastic efficiency model. Int J Syst Sci 19(5):779–791CrossRefGoogle Scholar
  51. 51.
    Sengupta JK (1987) Data envelopment analysis for efficiency measurement in the stochastic case. Comput Oper Res 14(2):117–129CrossRefGoogle Scholar
  52. 52.
    Sengupta JK (1989) Measuring economic efficiency with stochastic input-output data. Int J Syst Sci 20 (2):203–213CrossRefGoogle Scholar
  53. 53.
    Sengupta JK (1982) Efficiency measurement in stochastic input-output systems. Int J Syst Sci 13(3):273–287CrossRefGoogle Scholar
  54. 54.
    Simar L (1996) Aspects of statistical analysis in DEA-type frontier models. J Prod Anal 7(2-3):177–185CrossRefGoogle Scholar
  55. 55.
    Simar L, Wilson P (2000) Statistical Inference in Nonparametric Frontier Models: The State of the Art. J Prod Anal 13(1):49–78CrossRefGoogle Scholar
  56. 56.
    Tsionas EG, Papadakis EN (2010) A Bayesian approach to statistical inference in stochastic DEA. Omega 38(5):309– 314CrossRefGoogle Scholar
  57. 57.
    Zhu J (2003) Imprecise data envelopment analysis (IDEA): A review and improvement with an application. Eur J Oper Res 144(3):513–529CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Nathaniel D. Bastian
    • 1
  • Tahir Ekin
    • 2
  • Hyojung Kang
    • 3
  • Paul M. Griffin
    • 4
  • Lawrence V. Fulton
    • 5
  • Benjamin C. Grannan
    • 6
  1. 1.Department of Industrial & Manufacturing EngineeringThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.McCoy College of Business AdministrationTexas State UniversitySan MarcosUSA
  3. 3.Department of Systems & Information EngineeringUniversity of VirginiaCharlottesvilleUSA
  4. 4.School of Industrial & Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  5. 5.Rawls College of Business AdministrationTexas Tech UniversityLubbockUSA
  6. 6.Department of Economics & BusinessVirginia Military InstituteLexingtonUSA

Personalised recommendations