A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

Published Online:https://doi.org/10.1287/opre.2015.1421

References

  • Aardal K, Lenstra AK, Lenstra HW (2002) Hard equality constrained integer knapsacks. Cook WJ, Schulz AS, eds. IPCO (Springer, Berlin), 350–366.CrossrefGoogle Scholar
  • Abernathy WJ, Baloff N, Hershey JC, Wandel S (1973) A three-stage manpower planning and scheduling model—a service-sector example. Oper. Res. 21(3):693–711.LinkGoogle Scholar
  • Ahmed S, Tawarmalani M, Sahinidis NV (2004) A finite branch-and-bound algorithm for two-stage stochastic integer programs. Math. Programming 100(2):355–377.CrossrefGoogle Scholar
  • Bard JF, Purnomo HW (2004) Real-time scheduling for nurses in response to demand fluctuations and personnel shortages. Burke E, Trick M, eds. Proc. 5th Internat. Conf. Practice and Theory of Automated Timetabling (Springer, Berlin), 67–87.Google Scholar
  • Bard JF, Purnomo HW (2005a) A column generation-based approach to solve the preference scheduling problem for nurses with downgrading. Socio-Econom. Planning Sci. 39(3):193–213.CrossrefGoogle Scholar
  • Bard JF, Purnomo HW (2005b) Hospital-wide reactive scheduling of nurses with preference considerations. IIE Trans. 37(7):589–608.CrossrefGoogle Scholar
  • Bard JF, Purnomo HW (2005c) Preference scheduling for nurses using column generation. Eur. J. Oper. Res. 164(2):510–534.CrossrefGoogle Scholar
  • Bard JF, Purnomo HW (2005d) Short-term nurse scheduling in response to daily fluctuations in supply and demand. Health Care Management Sci. 8(4):315–324.CrossrefGoogle Scholar
  • Bard JF, Purnomo HW (2007) Cyclic preference scheduling of nurses using a Lagrangian-based heuristic. J. Scheduling 10(1):5–23.CrossrefGoogle Scholar
  • Bard JF, Morton DP, Wang YM (2007) Workforce planning at USPS mail processing and distribution centers using stochastic optimization. Ann. Oper. Res. 155(1):51–78.CrossrefGoogle Scholar
  • Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4(1):238–252.CrossrefGoogle Scholar
  • Birge JR (1982) The value of the stochastic solution in stochastic linear programs with fixed recourse. Math. Programming 24(1):314–325.CrossrefGoogle Scholar
  • Birge JR, Louveaux FV (1988) A multicut algorithm for two-stage stochastic linear programs. Eur. J. Oper. Res. 34(3):384–392.CrossrefGoogle Scholar
  • Birge JR, Louveaux FV (1997) Introduction to Stochastic Programming (Springer, New York).Google Scholar
  • Bodur M, Luedtke J (2014) Mixed-integer rounding enhanced Benders decomposition for multiclass service system staffing and scheduling with arrival rate uncertainty. www.optimization-online.org/DB_FILE/2013/10/4080.pdf.Google Scholar
  • Burke EK, Li J, Qu R (2012) A pareto-based search methodology for multi-objective nurse scheduling. Ann. Oper. Res. 196(1):91–109.CrossrefGoogle Scholar
  • Burke EK, De Causmaecker P, Berghe GV, Van Landeghem H (2004) The state of the art of nurse rostering. J. Scheduling 7(6):441–499.CrossrefGoogle Scholar
  • Carøe CC, Tind J (1997) A cutting-plane approach to mixed 0–1 stochastic integer programs. Eur. J. Oper. Res. 101(2):306–316.CrossrefGoogle Scholar
  • Cheang B, Li H, Lim A, Rodrigues B (2003) Nurse rostering problems—A bibliographic survey. Eur. J. Oper. Res. 151(3):447–460.CrossrefGoogle Scholar
  • Cornuéjols G, Liberti L, Nannicini G (2011) Improved strategies for branching on general disjunctions. Math. Programming 130(2): 225–247.CrossrefGoogle Scholar
  • CPLEX II (2009) V12. 1: Users manual for CPLEX. Internat. Bus. Machines Corporation 46(53):157.Google Scholar
  • Davis A, Mehrotra S, Holl J, Daskin MS (2014) Nurse staffing to reduce costs and enhance patient safety. Asia-Pacific J. Oper. Res. 31(1):1–19.CrossrefGoogle Scholar
  • Easton FF, Mansour N (1999) A distributed genetic algorithm for deterministic and stochastic labor scheduling problems. Eur. J. Oper. Res. 118(3):505–523.CrossrefGoogle Scholar
  • Easton FF, Rossin DF (1996) A stochastic goal program for employee scheduling*. Decision Sci. 27(3):541–568.CrossrefGoogle Scholar
  • Eddelbuettel D, François R (2010) RInside: C++ classes to embed R in C++ applications. R package version 0.2 3, http://dirk.eddelbuettel.com/code/rinside.html.Google Scholar
  • Gade D, Küçükyavuz S, Sen S (2014) Decomposition algorithms with parametric gomory cuts for two-stage stochastic integer programs. Math. Programming 144(1–2):39–64.CrossrefGoogle Scholar
  • Jaumard B, Semet F, Vovor T (1998) A generalized linear programming model for nurse scheduling. Eur. J. Oper. Res. 107(1):1–18.CrossrefGoogle Scholar
  • Kao EPC, Queyranne M (1985) Budgeting costs of nursing in a hospital. Management Sci. 31(5):608–621.LinkGoogle Scholar
  • Karamanov M, Cornuéjols G (2011) Branching on general disjunctions. Math. Programming 128(1-2):403–436.CrossrefGoogle Scholar
  • Kim K, Lee C, O’Leary K, Rosenauer S, Mehrotra S (2014) Predicting patient volumes in hospital medicine: A comparative study of different time series forecasting methods. Technical report, Northwestern University, Evanston, IL.Google Scholar
  • Kong N, Schaefer AJ, Ahmed S (2013) Totally unimodular stochastic programs. Math. Programming 138(1-2):1–13.CrossrefGoogle Scholar
  • Kong N, Schaefer AJ, Hunsaker B (2006) Two-stage integer programs with stochastic right-hand sides: A superadditive dual approach. Math. Programming 108(2–3):275–296.CrossrefGoogle Scholar
  • Laporte G, Louveaux FV (1993) The integer l-shaped method for stochastic integer programs with complete recourse. Oper. Res. Lett. 13(3):133–142.CrossrefGoogle Scholar
  • Lenstra HW (1983) Integer programming with a fixed number of variables. Math. Oper. Res. 8(4):538–548.LinkGoogle Scholar
  • Louveaux FV, Schultz R (2003) Stochastic integer programming. Handbooks in Oper. Res. Management Sci. 10:213–266.CrossrefGoogle Scholar
  • Lovász L, Scarf HE (1992) The generalized basis reduction algorithm. Math. Oper. Res. 17(3):751–764.LinkGoogle Scholar
  • Maenhout B, Vanhoucke M (2013a) Analyzing the nursing organizational structure and process from a scheduling perspective. Health Care Management Sci. 16(3):177–196.CrossrefGoogle Scholar
  • Maenhout B, Vanhoucke M (2013b) An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega 41(2):485–499.CrossrefGoogle Scholar
  • Mahajan A, Ralphs TK (2009) Experiments with branching using general disjunctions. Operations Research and Cyber-Infrastructure (Springer, New York), 101–118.CrossrefGoogle Scholar
  • Mehrotra S, Huang KL (2013) On implementing a general disjunctive branching algorithm using lattice basis reduction for mixed integer convex programming. Technical report, Northwestern University, Evanston, IL.Google Scholar
  • Mehrotra S, Li Z (2011) Branching on hyperplane methods for mixed integer linear and convex programming using adjoint lattices. J. Global Optim. 49(4):623–649.CrossrefGoogle Scholar
  • Miller AJ, Wolsey LA (2003) Tight formulations for some simple mixed integer programs and convex objective integer programs. Math. Programming 98(1–3):73–88.CrossrefGoogle Scholar
  • Nemhauser GL, Wolsey LA (1988) Integer and Combinatorial Optimization, Vol. 18 (Wiley, New York).CrossrefGoogle Scholar
  • Owen JH, Mehrotra S (2001) Experimental results on using general disjunctions in branch-and-bound for general-integer linear programs. Comput. Optim. Appl. 20(2):159–170.CrossrefGoogle Scholar
  • Parr D, Thompson JM (2007) Solving the multi-objective nurse scheduling problem with a weighted cost function. Ann. Oper. Res. 155(1): 279–288.CrossrefGoogle Scholar
  • Pratt JW, Raiffa H, Schlaifer R (1995) Introduction to Statistical Decision Theory (MIT Press, Cambridge, MA).Google Scholar
  • Punnakitikashem P, Rosenberger JM, Buckley-Behan DF (2008) Stochastic programming for nurse assignment. Comput. Optim. Appl. 40(3): 321–349.CrossrefGoogle Scholar
  • Punnakitikashem P, Rosenberger JM, Buckley-Behan DF (2013) A stochastic programming approach for integrated nurse staffing and assignment. IIE Trans. 45(10):1059–1076.CrossrefGoogle Scholar
  • Schultz R, Stougie L, Van Der Vlerk MH (1998) Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis. Math. Programming 83(1–3):229–252.CrossrefGoogle Scholar
  • Sen S (2005) Algorithms for stochastic mixed-integer programming models. Handbooks Oper. Res. Management Sci. 12:515–558.CrossrefGoogle Scholar
  • Sen S, Higle JL (2005) The C3 theorem and a D2 algorithm for large scale stochastic mixed-integer programming: Set convexification. Math. Programming 104(1):1–20.CrossrefGoogle Scholar
  • Sen S, Sherali HD (2006) Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming. Math. Programming 106(2):203–223.CrossrefGoogle Scholar
  • Sherali HD, Fraticelli BMP (2002) A modification of Benders’ decomposition algorithm for discrete subproblems: An approach for stochastic programs with integer recourse. J. Global Optim. 22(1–4):319–342.CrossrefGoogle Scholar
  • Sherali HD, Zhu X (2006) On solving discrete two-stage stochastic programs having mixed-integer first-and second-stage variables. Math. Programming 108(2–3):597–616.CrossrefGoogle Scholar
  • Trukhanov S, Ntaimo L, Schaefer A (2010) Adaptive multicut aggregation for two-stage stochastic linear programs with recourse. Eur. J. Oper. Res. 206(2):395–406.CrossrefGoogle Scholar
  • Van Slyke RM, Wets R (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 17(4):638–663.CrossrefGoogle Scholar
  • Venkataraman R, Brusco MJ (1996) An integrated analysis of nurse staffing and scheduling policies. Omega 24(1):57–71.CrossrefGoogle Scholar
  • Woodall JC, Gosselin T, Boswell A, Murr M, Denton BT (2013) Improving patient access to chemotherapy treatment at Duke Cancer Institute. Interfaces 43(5):449–461.LinkGoogle Scholar
  • Wright PD, Bretthauer KM (2010) Strategies for addressing the nursing shortage: Coordinated decision making and workforce flexibility. Decision Sci. 41(2):373–401.CrossrefGoogle Scholar
  • Wright PD, Mahar S (2013) Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction. Omega 41(6):1042–1052.CrossrefGoogle Scholar
  • Wright PD, Bretthauer KM, Côté MJ (2006) Reexamining the nurse scheduling problem: Staffing ratios and nursing shortages. Decision Sci. 37(1):39–70.CrossrefGoogle Scholar
  • Zhu X, Sherali HD (2007) Two-stage workforce planning under demand fluctuations and uncertainty. J. Oper. Res. Soc. 60(1):94–103.CrossrefGoogle Scholar
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