Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article

A Progressive Hedging Approach for Surgery Planning Under Uncertainty

Published: 01 November 2015 Publication History

Abstract

We propose a multistage stochastic mixed-integer programming formulation for the assignment of surgeries to operating rooms over a finite planning horizon. We consider the demand for and the duration of surgery to be random variables. The objective is to minimize three competing criteria: expected cost of surgery cancellations, patient waiting time, and operating room overtime. We discuss properties of the model and an implementation of the progressive hedging algorithm to find near-optimal surgery schedules. We conduct numerical experiments using data from a large hospital to identify managerial insights related to surgery planning and the avoidance of surgery cancellations. We compare the progressive hedging algorithm to an easy-to-implement heuristic for practical problem instances to estimate the value of the stochastic solution. Finally, we discuss an implementation of the progressive hedging algorithm within a rolling horizon framework for extended planning periods.

References

[1]
Argo JL, Vick CC, Graham LA, Itani KMF, Bishop MJ, Hawn MT (2009) Elective surgical case cancellation in the Veterans Health Administration system: Identifying areas for improvement. Amer. J. Surgery 198:600-606.
[2]
Barro D, Canestrelli E (2005) Dynamic portfolio optimization: Time decomposition using the maximum principle with a scenario approach. Eur. J. Oper. Res. 163:217-229.
[3]
Batun S, Denton BT, Huschka TR, Schaefer AJ (2011) Operating room pooling and parallel surgery processing under uncertainty. INFORMS J. Comput. 23:220-237.
[4]
Chand S, Hsu VN, Sethi S (2002) Forecast, solution, and rolling horizons in operations management problems: A classified bibliography. Manufacturing Service Oper. Management 4:25-43.
[5]
Chiralaksanakul A, Morton DP (2004) Assessing policy quality in multi-stage stochastic programming. Higle JL, Römisch W, Sen S, eds. Stochastic Programming E-Print Ser. Accessed November 21, 2015, http://www.speps.org.
[6]
Crainic TG, Fu X, Gendreau M, Rei W, Wallace SW (2011) Progressive hedging-based metaheuristics for stochastic network design. Networks 58:114-124.
[7]
Dexter F, Maxbauer T, Stout C, Archbold L, Epstein R (2014) Relative influence on total cancelled operating room time from patients who are inpatients or outpatients preoperatively. Anesthesia Analgesia 118:1072-1080.
[8]
Epstein RH, Dexter F (2013) Rescheduling of previously cancelled surgical cases does not increase variability in operating room workload when cases are scheduled based on maximizing efficiency of use of operating room time. Anesthesia Analgesia 117:995-1002.
[9]
Fei H, Chu C, Meskens N (2009) Solving a tactical operating room planning problem by a column generation based heuristic procedure with four criteria. Ann. Oper. Res. 166:91-108.
[10]
Fei H, Meskens N, Chu C (2010) A planning and scheduling problem for an operating theatre using an open scheduling strategy. Comput. Indust. Engrg. 58:221-230.
[11]
Fei H, Chu C, Meskens N, Artiba A (2008) Solving surgical cases assignment problem by a branch-and-price approach. Internat. J. Production Econom. 112:96-108.
[12]
Gerchak Y, Gupta D, Henig M (1996) Reservation planning for elective surgery under uncertain demand for emergency surgery. Management Sci. 42:321-334.
[13]
Gillen SMI, Catchings K, Edney L, Prescott R, Andrews SM (2009) What's all the fuss about? Day-of-surgery cancellations and the role of perianesthesia nurses in prevention. J. Perianesthesia Nursing 26:396-398.
[14]
Guinet A, Chaabane S (2003) Operating theatre planning. Internat. J. Production Econom. 85:69-81.
[15]
Gul S, Denton B, Fowler J, Huschka T (2011) Bi-criteria scheduling of surgical services for an outpatient procedure center. Production Oper. Management 20:406-417.
[16]
Hans E, Wullink G, van Houdenhoven M, Kazemier G (2008) Robust surgery loading. Eur. J. Oper. Res. 185:1038-1050.
[17]
Haugen KK, Lokketangen A, Woodruff DL (2001) Progressive hedging as a meta-heuristic applied to stochastic lot-sizing. Eur. J. Oper. Res. 132:116-122.
[18]
Healthcare Financial Management Association (HFMA) (2003) Achieving operating room efficiency through process integration. Healthcare Financial Management 57(3, Suppl.):1-8.
[19]
Helgason T, Wallace SW (1991) Approximate scenario solutions in the progressive hedging algorithm. Ann. Oper. Res. 31: 425-444.
[20]
Huang K, Ahmed S (2009) The value of multistage stochastic programming in capacity planning under uncertainty. Oper. Res. 57:893-904.
[21]
Hvattum LM, Lokketangen A (2009) Using scenario trees and progressive hedging for stochastic inventory routing problems. J. Heuristics 15:527-557.
[22]
Korpeoglu E, Yaman H, Akturk MS (2011) A multi-stage stochastic programming approach in master production scheduling. Eur. J. Oper. Res. 213:166-179.
[23]
Lamiri M, Grimaud F, Xie X (2009) Optimization methods for a stochastic surgery planning problem. Internat. J. Production Econom. 120:400-410.
[24]
Lamiri M, Xie X, Zhang S (2008a) Column generation approach to operating theater planning with elective and emergency patients. IIE Trans. 40:838-852.
[25]
Lamiri M, Xie X, Dolgui A, Grimaud F (2008b) A stochastic model for operating room planning with elective and emergency demand for surgery. Eur. J. Oper. Res. 185:1026-1037.
[26]
Listes O, Dekker R (2005) A scenario aggregation-based approach for determining a robust airline fleet composition for dynamic capacity allocation. Transportation Sci. 39:367-382.
[27]
McManus ML, Long MC, Cooper A, Mandell J, Berwick DM, Pagano M, Litvak E (2003) Variability in surgical caseload and access to intensive care services. Anesthesiology 98:1491-1496.
[28]
Min D, Yih Y (2010) Scheduling elective surgery under uncertainty and downstream capacity constraints. Eur. J. Oper. Res. 206: 642-652.
[29]
Mulvey JM, Vladimirou H (1991a) Applying the progressive hedging algorithm to stochastic generalized networks. Ann. Oper. Res. 31:399-424.
[30]
Mulvey JM, Vladimirou H (1991b) Solving multistage stochastic networks: An application of scenario aggregation. Networks 21:619-643.
[31]
Mulvey JM, Vladimirou H (1992) Stochastic network programming for financial planning problems. Management Sci. 38:1642-1664.
[32]
Ovacik IM, Uzsoy R (1994) Rolling horizon algorithms for a single machine dynamic scheduling problem with sequence dependent setup times. Internat. J. Production Res. 32:1243-1263.
[33]
Ovacik IM, Uzsoy R (1995) Rolling horizon procedures for dynamic parallel machine scheduling with sequence dependent setup times. Internat. J. Production Res. 33:3173-3192.
[34]
Rockafellar RT (1976) Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14:877-898.
[35]
Rockafellar RT, Wets RJB (1991) Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16:119-147.
[36]
Rohleder TR, Klassen KJ (2002) Rolling horizon appointment scheduling: A simulation study. Health Care Management Sci. 5:201-209.
[37]
Santos MLLD, Silva ELD, Finardi EC, Goncalves REC (2009) Practical aspects in solving the medium-term operation planning problem of hydrothermal power systems by using the progressive hedging method. Electrical Power Energy Systems 31: 546-552.
[38]
Schuster M, Neumann C, Neumann K, Braun J, Geldner G, Martin J, Spies C, Bauer M, CASCAES Study Group (2011) The effect of hospital size and surgical service on case cancellation in elective surgery: Results from a prospective multicenter study. Anesthesia Analgesia 113:578-585.
[39]
Stepaniak PS, Mannaerts GH, de Quelerij M, de Vries G (2009) The effect of the operating room coordinator's risk appreciation on operating room efficiency. Anesthesia Analgesia 108: 1249-1256.
[40]
Takriti S, Birge JR (2000) Lagrangian solution techniques and bounds for loosely coupled mixed-integer stochastic programs. Oper. Res. 48:91-98.
[41]
Takriti S, Birge JR, Long E (1996) A stochastic model for the unit commitment problem. IEEE Trans. Power Systems 11:1497-1508.
[42]
Tessler MJ, Kleiman SJ, Huberman MM (1997) A zero tolerance for overtime increases surgical per case costs. Canadian J. Anesthesia 44:1036-1041.
[43]
Wallace SW, Helgason T (1991) Structural properties of the progressive hedging algorithm. Ann. Oper. Res. 31:445-456.
[44]
Watson JP, Woodruff DL (2011) Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Computational Management Sci. 8:355-370.
[45]
Zonderland ME, Boucherie RJ, Litvak N, Vleggeert-Lankamp CLAM (2010) Planning and scheduling of semi-urgent surgeries. Health Care Management Sci. 13:256-267.

Cited By

View all
  • (2024)Lagrangian Dual Decision Rules for Multistage Stochastic Mixed-Integer ProgrammingOperations Research10.1287/opre.2022.236672:2(717-737)Online publication date: 1-Mar-2024
  • (2023)A Three-Stage Relief Network Design Approach for Predictable Disasters Considering Time-Dependent UncertaintyIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.334231925:6(5418-5434)Online publication date: 20-Dec-2023
  • (2021)Day surgery appointment scheduling with patient preferences and stochastic operation durationTechnology and Health Care10.3233/THC-19208629:4(697-708)Online publication date: 1-Jan-2021
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image INFORMS Journal on Computing
INFORMS Journal on Computing  Volume 27, Issue 4
November 2015
69 pages

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 November 2015
Accepted: 01 May 2015
Received: 01 August 2013

Author Tags

  1. heuristics
  2. progressive hedging
  3. scheduling
  4. stochastic programming
  5. surgery planning

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 24 Dec 2024

Other Metrics

Citations

Cited By

View all
  • (2024)Lagrangian Dual Decision Rules for Multistage Stochastic Mixed-Integer ProgrammingOperations Research10.1287/opre.2022.236672:2(717-737)Online publication date: 1-Mar-2024
  • (2023)A Three-Stage Relief Network Design Approach for Predictable Disasters Considering Time-Dependent UncertaintyIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.334231925:6(5418-5434)Online publication date: 20-Dec-2023
  • (2021)Day surgery appointment scheduling with patient preferences and stochastic operation durationTechnology and Health Care10.3233/THC-19208629:4(697-708)Online publication date: 1-Jan-2021
  • (2021)Logic-Based Benders Decomposition and Binary Decision Diagram Based Approaches for Stochastic Distributed Operating Room SchedulingINFORMS Journal on Computing10.1287/ijoc.2020.103633:4(1551-1569)Online publication date: 1-Oct-2021
  • (2021)A Multistage Stochastic Programming Approach to the Optimal Surveillance and Control of the Emerald Ash Borer in CitiesINFORMS Journal on Computing10.1287/ijoc.2020.096333:2(808-834)Online publication date: 1-May-2021
  • (2021)Automatic Surgery Duration Prediction Using Artificial Neural NetworksProceedings of the 5th International Conference on Computer Science and Application Engineering10.1145/3487075.3487128(1-6)Online publication date: 19-Oct-2021
  • (2019)Planning for OvertimeINFORMS Journal on Computing10.1287/ijoc.2018.086531:4(732-744)Online publication date: 1-Oct-2019
  • (2018)An efficient computational method for large scale surgery scheduling problems with chance constraintsComputational Optimization and Applications10.1007/s10589-017-9947-069:2(535-561)Online publication date: 1-Mar-2018

View Options

View options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media