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Planning water resources systems with interval stochastic dynamic programming

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Abstract

This study addresses water resources system planning problems with capacity expansion in an uncertain environment. An interval stochastic dynamic programming (SDP) model is presented, which is a hybrid of interval-number optimization and SDP. Besides the dynamic features of the model, it can incorporate and reflect uncertainties expressed as probability distribution functions and discrete intervals. The solution method for the proposed model is computationally effective, which makes it applicable to practical problems. The results acquired through a case study indicate that reasonable solutions have been obtained. They are further analyzed and interpreted for identifying significant factors that affect the system's performance. The information obtained through these post-optimality analyses can provide useful decision support for water authorities.

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References

  • Ahmed A, King AJ, Parija G (2003) A multi-stage stochastic integer programming approach for capacity expansion under uncertainty. J Global Optim 26:3–24

    Article  Google Scholar 

  • Alefeld G, Herzberger J (1983) Introduction to interval computations. Academic Press, New York

    Google Scholar 

  • Beaumont O (1998) Solving interval linear systems with linear programming techniques. Lin Alg Appl 281:293–309

    Article  Google Scholar 

  • Birge JR (1984) Decomposition and partitioning methods for multistage stochastic linear programs. Oper Res 33(5):989–1007

    Google Scholar 

  • Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer-Verlag, New York, USA

    Google Scholar 

  • Bitran GR (1980) Linear multiple objective problems with interval coefficients. Manage. Science 26:694–706

    Article  Google Scholar 

  • Chen L (2004) Inflow pattern stochastic dynamic programming and its application in reservoir operation optimization, PhD thesis. Civil Engineering, the University of Calgary, Alberta, Canada

  • Chen XJ, Qi LQ (1995) Womersley, R.S., Newton's method for quadratic stochastic programs with recourse. J Comput Appl Math 60:29–46

    Article  Google Scholar 

  • Chinneck JW, Ramadan K (2000) Linear programming with interval coefficients. J Oper Res Soc 51:209–220

    Article  Google Scholar 

  • Chiu C-K, Lee JH-M (2002) Efficient interval linear equality solving in constraint logic programming. Reliab Comput 8:139–174

    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

    Google Scholar 

  • Ishibuchi H, Tanaka H (1989) Formulation and analysis of linear programming problem with interval coefficients. J Jpn Ind Manage Assoc 40:320–329

    Google Scholar 

  • Jiménez F, Verdegay JL (1998) Uncertain solid transportation problems. Fuzzy Set Syst 100:45–57

    Article  Google Scholar 

  • Karamouz M, Mousavi SJ (2003) Uncertainty based operation of large scale reservoir systems: Dez and Karoon experience. J Am Water Resour Assoc 39(4):961–975

    Google Scholar 

  • Karamouz M, Vasiliadis HV (1992) Bayesian stochastic optimization of reservoir operation using uncertain forecasts. Water Resour Res 28:1221–1232

    Article  Google Scholar 

  • Kelman J, Stedinger JR, Cooper LA, Hsu E, Yuan SQ (1990) Sampling stochastic dynamic programming applied to reservoir operation. Water Resour Res 26:447–454

    Article  Google Scholar 

  • Lai KK, Wang SY, Xu JP, Zhu SS, Fang Y (2002) A Class of Linear Interval Programming Problems and Its Application to Portfolio Selection. IEEE Trans Fuzzy Syst 10(6):698–704

    Article  Google Scholar 

  • Lau KK, Womersley RS (2001) Multistage quadratic stochastic programming. J Comput Appl Math 129:105–138

    Article  Google Scholar 

  • Loucks DP, Stedinger JR, Haith DA (1981) Water resource systems planning and analysis. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Louveaus FV (1986) Multistage stochastic programs with block-separable recourse. Math Program Stud 28:48–62

    Google Scholar 

  • Luo B, Huang GH, Zou Y, Yin YY (2006) Toward quantifying the effectiveness of water trading under uncertainty. J Environ Manage In press

  • Maqsood I, Huang GH, Yeomans JS (2005) An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty. Eur J Oper Res 167(1):208–225

    Article  Google Scholar 

  • Moore RE (1979) Method and application of interval analysis. SIAM, Philadelphia

    Google Scholar 

  • Nakahara Y, Sasaki M, Gen M (1992) On the linear programming with interval coefficients. Comput Ind Eng 23:301–304

    Article  Google Scholar 

  • Perera BJC, Codner GP (1996) Reservoir targets for urban water supply systems. J Water Resour Plann Manage 122 (4):270–279

    Article  Google Scholar 

  • Perera BJC, Codner GP (1998) Computational improvement for stochastic dynamic programming models of urban water supply reservoirs. J Am Water Resour Assoc 34(2):267–278

    Google Scholar 

  • Philbrick CR, Kitanidis PK (2001) Improved dynamic programming methods for optimal control of lumped-parameter stochastic systems. Oper Res 49(3):398–412

    Article  Google Scholar 

  • Rajagopalan S, Singh MR, Morton TE (1998) Capacity expansion and replacement in growing markets with uncertain technological breakthrough. Math Sci 44:12–30

    Google Scholar 

  • Slowñski R, Teghem J (1990) Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Stedinger JR, Sule BF, Loucks DP (1984) Stochastic dynamic programming models for reservoir operation optimization. Water Resour Res 20(11):1499–1505

    Article  Google Scholar 

  • Tilmant A, Persoons E, Vanclooster M (2001) Deriving efficient reservoir operating rules using flexible stochastic dynamic programming, In: Proceedings of the First International Conference on Water Resources Management, WIT Press, UK

    Google Scholar 

  • Tong SC (1994) Interval number and fuzzy number linear programming. Fuzzy Set Syst 66:301–306

    Article  Google Scholar 

  • Vasiliadis HV, Karamouz M (1994) Demand-driven operation of reservoirs using uncertainty-based optimal operating policies. J Water Resour Plann Manage 120(1):101–114

    Article  Google Scholar 

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Luo, B., Maqsood, I. & Huang, G.H. Planning water resources systems with interval stochastic dynamic programming. Water Resour Manage 21, 997–1014 (2007). https://doi.org/10.1007/s11269-006-9069-4

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  • DOI: https://doi.org/10.1007/s11269-006-9069-4

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