Skip to main content
Log in

A dual two-stage stochastic model for flood management with inexact-integer analysis under multiple uncertainties

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

This study introduces a hybrid optimization approach for flood management under multiple uncertainties. An inexact two-stage integer programming (ITIP) model and its dual formation are developed by integrating the concepts of mixed-integer and interval-parameter programming techniques into a general framework of two-stage stochastic programming. The proposed approach provides a linkage to pre-defined management policies, deals with capacity-expansion planning issues, and reflects various uncertainties expressed as probability distributions and discrete intervals for a flood management system. Penalties are imposed when the policies are violated. The marginal costs are determined based on dual formulation of the ITIP model, and their effects on the optimal solutions are investigated. The developed model is applied to a case study of flood management. The solutions of binary variables represent the decisions of flood-diversion–capacity expansion within a multi-region, multi-flow-level, and multi-option context. The solutions of continuous variables are related to decisions of flood diversion toward different regions. The solutions of dual variables indicate the decisions of marginal costs associated with the resources of regions’ capacity, water availability, and allowable diversions. The results show that the proposed approach could obtain reliable solutions and adequately support decision making in flood management.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Altman A, Gondzio J (1993) HOPDM-A higher order primal–dual method for large scale linear programming. Eur J Oper Res 66:159–161

    Article  Google Scholar 

  • Barnes E, Chen V, Gopalakrishnan B, Johnson EL (2002) A least-squares primal–dual algorithm for solving linear programming problems. Oper Res Lett 30:289–294

    Article  Google Scholar 

  • Berkelaar A, Dert C, Oldenkamp B, Zhang S (2002) A primal–dual decomposition-based interior point approach to two-stage stochastic linear programming. Oper Res Int J 50:904–915

    Article  Google Scholar 

  • Butts MB (2000) Coupling of catchment modeling and meteorological information in flow forecasting. In: Bronstert A et al (eds) European Conference on Advan in Flood Research, Report No. 65:476–487. Potsdam Institute for Climate Impact Research, Potsdam

  • Cao MF, Huang GH (2011) Scenario-based methods for interval linear programming problems. J Environ Inform 17(2):65–74

    Article  Google Scholar 

  • Chang NB, Chen HW (1997) Water pollution control in a river basin by interactive fuzzy interval multi-objective programming. J Environ Eng 123:1208–1216

    Article  CAS  Google Scholar 

  • Chang NB, Wen CG, Chen YL, Yong YC (1996) Optimal planning of the reservoir watershed by grey fuzzy multi-objective programming (I): theory. Water Res 30:2329–2334

    Article  CAS  Google Scholar 

  • Cheung RK, Chen CY (1998) A two-stage stochastic network model and solution methods for the dynamic empty container allocation problem. Transp Sci 32:142–162

    Article  Google Scholar 

  • Darby-Dowman K et al (2000) A two-stage stochastic programming with recourse model for determining robust planting plans in horticulture. J Oper Res Soc 51:83–98

    Google Scholar 

  • Day JC, Weisz RN (1976) A linear programming model for use in guiding urban floodplain management. Water Resour Res 12:349–359

    Article  Google Scholar 

  • Fan YR, Huang GH (2012) A robust two-step method for solving interval linear programming problems within an environmental management context. J Environ Inform 19(1):1–12

    Article  Google Scholar 

  • FEMA (Federal Emergency Management Agency) (2002) Reducing risk through mitigation [online]. http://www.fema.gov. Accessed 20 June 2002

  • Gill PE, Murray W, Ponceleon DB, Saunders MA (1995) Primal–dual methods for linear programming. Math Program 70:251–278

    Google Scholar 

  • Guo P, Huang G (2009) Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties. Stoch Environ Res Risk Assess 23:349–359

    Article  Google Scholar 

  • Guo P, Huang GH, He L, Sun BW (2008) ITSSIP: interval-parameter two-stage stochastic semi-infinite programming for environmental management under uncertainty. Environ Model Softw 23:1422–1437

    Article  Google Scholar 

  • Hager WW (2002) The dual active set algorithm and its application to linear programming. Comput Optim Appl 21:263–275

    Article  Google Scholar 

  • Huang GH, Cao MF (2011) Analysis of solution methods for interval linear programming. J Environ Inform 17(2):54–64

    Article  Google Scholar 

  • Huang GH, Loucks DP (2000) An inexact two-stage stochastic programming model for water resources management under uncertainty. Civil Eng Environ Syst 17:95–118

    Article  Google Scholar 

  • Jansen B, Roos C, Terlaky TA (1996) Polynomial primal–dual dikin-type algorithm for linear programming. Math Oper Res 21:341–353

    Article  Google Scholar 

  • Li YP, Huang GH (2012) A recourse-based nonlinear programming model for stream water quality management. Stoch Environ Res Risk Assess 26:207–223

    Article  Google Scholar 

  • Li YP, Huang GH, Nie SL (2007) IFTSQP: an inexact optimization model for water resources management under uncertainty. Water Int 32:439–456

    Article  Google Scholar 

  • Li YP, Huang GH, Chen X (2009) Multistage scenario-based interval-stochastic programming for planning water resources allocation. Stoch Environ Res Risk Assess 23:781–792

    Article  Google Scholar 

  • Lu HW, Huang GH, Zeng GM, Maqsood I, He L (2008) An inexact two-stage fuzzy-stochastic programming model for water resources management. Water Resour Manag 22:991–1016

    Article  Google Scholar 

  • Lv Y, Huang GH, Li YP, Yang ZF, Liu Y, Cheng GH (2010) Planning regional water resources system using an interval fuzzy bi-level programming method. J Environ Inform 16:43–56

    Article  Google Scholar 

  • Madsen M, Butts MB, Khu ST, Liong SY (2000) Data assimilation in rainfall-runoff forecasting. In: 4th International conference on hydroinformatics. University of Iowa, Cedar Rapids

  • Maqsood I, Huang GH (2003) A two-stage interval-stochastic programming model for waste management under uncertainty. J Air Waste Manag Assoc 53:540–552

    Article  Google Scholar 

  • Maqsood I, Huang GH, Huang YF, Chen B (2005) ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems. Stoch Environ Res Risk Assess 19:125–133

    Article  Google Scholar 

  • Mobasheri F, Harboe RC (1970) A two-stage optimization model for design of a multipurpose reservoir. Water Resour Res 6:22–31

    Article  Google Scholar 

  • Myers DC (1992) A dual simplex implementation of a constraint selection algorithm for linear programming. J Oper Res Soc 43:177–180

    Google Scholar 

  • Needham JT, Watkins DW Jr, Lund JR, Nanda SK (2000) Linear programming for flood control in the Iowa and Des Moines rivers. J Water Resour Plan Manag 126:118–127

    Article  Google Scholar 

  • Olsen JR, Beling PA, Lambert JH (2000) Dynamic models for floodplain management. J Water Resour Plan Manag 126:167–171

    Article  Google Scholar 

  • Pereira MVF, Pinto LMV (1991) Multi-stage stochastic optimization applied to energy planning. Math Program 52:359–375

    Article  Google Scholar 

  • Phillips DT, Ravindran A, Solberg JJ (1976) Operations research: principles and practice. Wiley, New York

    Google Scholar 

  • Randall D, Cleland L, Kuehne CS, Buzz GW, Sheer DP (1997) A water supply planning simulation model using mixed-integer linear programming “engine”. J Water Resour Plan Manag 123:116–124

    Article  Google Scholar 

  • Ruszczynski A, Swietanowski A (1997) Accelerating the regularized decomposition method for two-stage stochastic linear problems. Eur J Oper Res 101:328–342

    Article  Google Scholar 

  • Schultz R, Stougie L, van der Vlerk MH (1996) Two-stage stochastic integer programming: a survey. Stat Neerl 50:404–416

    Article  Google Scholar 

  • Seifi A, Hipel KW (2001) Interior-point method for reservoir operation with stochastic inflows. J Water Resour Plan Manag 127:48–57

    Article  Google Scholar 

  • Smith AA, Hinton E, Lewis RW (1983) Civil engineering systems analysis and design. Wiley, New York

    Google Scholar 

  • Srinivasan K, Neelakantan TR, Narayan P (1999) Mixed-integer programming model for reservoir performance optimization. J Water Resour Plan Manag 125:298–301

    Article  CAS  Google Scholar 

  • Sun XF, Zhang HY, Fan YZ (2003) Recursive dual-linear-programming approach for parameter-uncertainty-interval estimation. IEEE Proc Control Theory Appl 150:303–310

    Article  Google Scholar 

  • Suo MQ, Li YP, Huang GH (2011) An inventory-theory-based interval-parameter two-stage stochastic programming model for water resources management. Eng Optim 43:999–1018

    Article  Google Scholar 

  • Tutuncu RH (2000) A primal–dual variant of the Iri-Imai algorithm for linear programming. Math Oper Res 25:195–213

    Article  Google Scholar 

  • Windsor JS (1981) Model for the optimal planning of structural flood control systems. Water Resour Res 17:289–292

    Article  Google Scholar 

  • Xu X, Hung PF, Ye Y (1996) A simplified homogeneous and self-dual linear programming algorithm and its implementation. Ann Oper Res 62:151–172

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Natural Science and Engineering Research Council of Canada. The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Imran Maqsood.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maqsood, I., Huang, G.H. A dual two-stage stochastic model for flood management with inexact-integer analysis under multiple uncertainties. Stoch Environ Res Risk Assess 27, 643–657 (2013). https://doi.org/10.1007/s00477-012-0629-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-012-0629-2

Keywords

Navigation