Multistage scenario-based interval-stochastic programming for planning water resources allocation.

*(English)*Zbl 1418.90183Summary: In this study, a multistage scenario-based interval-stochastic programming (MSISP) method is developed for water-resources allocation under uncertainty. MSISP improves upon the existing multistage optimization methods with advantages in uncertainty reflection, dynamics facilitation, and risk analysis. It can directly handle uncertainties presented as both interval numbers and probability distributions, and can support the assessment of the reliability of satisfying (or the risk of violating) system constraints within a multistage context. It can also reflect the dynamics of system uncertainties and decision processes under a representative set of scenarios. The developed MSISP method is then applied to a case of water resources management planning within a multi-reservoir system associated with joint probabilities. A range of violation levels for capacity and environment constraints are analyzed under uncertainty. Solutions associated different risk levels of constraint violation have been
obtained. They can be used for generating decision alternatives and thus help water managers to identify desired policies under various economic, environmental and system-reliability conditions. Besides, sensitivity analyses demonstrate that the violation of the environmental constraint has a significant effect on the system benefit.

##### MSC:

90C15 | Stochastic programming |

62P12 | Applications of statistics to environmental and related topics |

##### Keywords:

dynamics; interval; optimization; risk analysis; scenario-based; stochastic; uncertainty; water resources
PDF
BibTeX
XML
Cite

\textit{Y. P. Li} et al., Stoch. Environ. Res. Risk Assess. 23, No. 6, 781--792 (2009; Zbl 1418.90183)

Full Text:
DOI

##### References:

[1] | Anderson, ML; Mierzwa, MD; Kavvas, ML, Probabilistic seasonal forecasts of droughts with a simplified coupled hydrologic-atmospheric model for water resources planning, Stoch Environ Res Risk Assess, 14, 263-274, (2000) |

[2] | Basağaoğlu, H.; Mariño, MA; Shumwag, RH, δ-form approximating problem for a conjunctive water resource management model, Adv Water Resour, 23, 69-81, (1999) |

[3] | Bazaare, MS; Bouzaher, A., A linear goal programming model for developing economics with an illustration from agricultural sector in Egypt, Manage Sci, 27, 396-413, (1981) |

[4] | Birge, JR, Decomposition and partitioning methods for multistage stochastic linear programs, Oper Res, 33, 989-1007, (1985) · Zbl 0581.90065 |

[5] | Birge JR, Louveaux FV (1997) Introduction to stochastic programming. Springer, New York |

[6] | Camacho, F.; McLeod, AI; Hipel, KW, Multivariate contemporaneous ARMA model with hydrological applications, Stoch Environ Res Risk Assess, 1, 141-154, (1987) · Zbl 0658.76006 |

[7] | Chang, NB; Wen, CG; Chen, YL; Yong, YC, A grey fuzzy multiobjective programming approach for the optimal planning of a reservoir watershed, part A: theoretical development, Water Res, 30, 2329-2340, (1996) |

[8] | Chang, NB; Wen, CG; Chen, YL; Yong, YC, A grey fuzzy multiobjective programming approach for the optimal planning of a reservoir watershed. Part B: application, Water Res, 30, 2341-2352, (1996) |

[9] | Charnes, A, Cooper, WW, Kirby, P (1972) Chance constrained programming: an extension of statistical method. In: Optimizing methods in statistics. Academic Press, New York, pp 391-402 |

[10] | Charnes, A.; Cooper, WW, Response to decision problems under risk and chance constrained programming: dilemmas in the transitions, Manage Sci, 29, 750-753, (1983) |

[11] | Curi, RC; Unny, TE; Hipel, KW; Ponnambalam, K., Application of the distributed parameter filter to predict simulated tidal induced shallow water flow, Stoch Environ Res Risk Assess, 9, 13-32, (1995) · Zbl 0823.76063 |

[12] | Dupačová, J., Applications of stochastic programming: achievements and questions, Eur J Oper Res, 140, 281-290, (2002) · Zbl 1025.90014 |

[13] | Dupačová, J.; Gaivoronski, A.; Kos, Z.; Szantai, T., Stochastic programming in water management: a case study and a comparison of solution techniques, Eur J Oper Res, 52, 28-44, (1991) · Zbl 0726.90048 |

[14] | Edirisinghe, NCP; Patterson, EI; Saadouli, N., Capacity planning model for a multipurpose water reservoir with target-priority operation, Ann Oper Res, 100, 273-303, (2000) · Zbl 1017.90069 |

[15] | Ellis, JH, Stochastic programs for identifying critical structural collapse mechanisms, Appl Math Model, 15, 367-379, (1991) · Zbl 0837.90094 |

[16] | Gang, DC; Clevenger, TE; Banerji, SK, Modeling chlorine decay in surface water, J Environ Inform, 1, 21-27, (2003) |

[17] | Guo P, Huang GH (2008) Two-stage fuzzy chance-constrained programming: application to water resources management under dual uncertainties. Stoch Environ Res Risk Asses Online, doi: 10.1007/s00477-008-0221-y · Zbl 1411.90360 |

[18] | Howe, B.; Maier, D.; Baptista, A., A language for spatial data manipulation, J Environ Inform, 2, 23-37, (2003) |

[19] | Huang, GH, IPWM: an interval parameter water quality management model, Eng Optim, 26, 79-103, (1996) |

[20] | Huang, GH, A hybrid inexact-stochastic water management model, Eur J Oper Res, 107, 137-158, (1998) · Zbl 0943.90592 |

[21] | Infanger, G., Monte Carlo (importance) sampling within a benders decomposition algorithm for stochastic linear programs, Ann Oper Res, 39, 69-81, (1993) · Zbl 0773.90054 |

[22] | Infanger, G.; Morton, DP, Cut sharing for multistage stochastic linear programs with interstage dependency, Math Programm, 75, 241-251, (1996) · Zbl 0874.90147 |

[23] | Jacovkis, PM; Gradowczyk, H.; Freisztav, AM; Tabak, EG, A linear programming approach to water-resources optimization, Math Methods Oper Res, 33, 341-362, (1989) · Zbl 0675.90047 |

[24] | Jairaj, PG; Vedula, S., Multi-reservoir system optimization using fuzzy mathematical programming, Water Res Manage, 14, 457-472, (2000) |

[25] | Ji, JH; Chang, NB, Risk assessment for optimal freshwater inflow in response to sustainability indicators in semi-arid coastal bay, Stoch Environ Res Risk Assess, 19, 111-124, (2005) · Zbl 1120.91325 |

[26] | Li, YP; Huang, GH; Nie, SL, An interval-parameter multistage stochastic programming model for water resources management under uncertainty, Adv Water Resour, 29, 776-789, (2006) |

[27] | Li, YP; Huang, GH; Baetz, BW, Environmental management under uncertainty-an interval-parameter two-stage chance-constrained mixed integer linear programming method, Environ Eng Sci, 23, 761-779, (2006) |

[28] | Li, YP; Huang, GH; Nie, SL, Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning, Eng Optimiz, 39, 163-183, (2007) |

[29] | Li, YP; Huang, GH; Nie, SL; Qin, XS, ITCLP: an inexact two-stage chance-constrained program for planning waste management systems, Resour Conserv Recycl, 49, 284-307, (2007) |

[30] | Li, YP; Huang, GH; Nie, SL; Liu, L., Inexact multi-stage stochastic integer programming for water resources management under uncertainty, J Environ Manage, 88, 93-107, (2008) |

[31] | Loucks DP, Stedinger JR, Haith DA (1981) Water resource systems planning and analysis. Prentice-Hall, Englewood Cliffs |

[32] | Maqsood, I.; Huang, GH; Huang, YF; Chen, B., ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems, Stoch Environ Res Risk Assess, 19, 125-133, (2005) · Zbl 1120.91326 |

[33] | Morgan, DR; Eheart, JW; Valocchi, AJ, Aquifer remediation design under uncertainty using a new chance constrained programming technique, Water Resour Res, 29, 551-568, (1993) |

[34] | Paudyal, GN; Manguerra, HB, Two-step dynamic programming approach for optimal irrigation water allocation, Water Resour Manage, 4, 187-204, (1990) |

[35] | Pereira, MVF; Pinto, LMVG, Multistage stochastic optimization applied to energy planning, Math Programm, 52, 359-375, (1991) · Zbl 0749.90057 |

[36] | Rangarajan S (1995) Sustainable planning of the operation of reservoirs for hydropower generation, PhD thesis, Department of Civil Engineering, University of Manitoba, Winnipeg |

[37] | ReVelle C (1999) Optimizing reservoir resources including a new model for reservoir reliability. Wiley, New York |

[38] | Russell, SO; Campbell, PF, Reservoir operating rules with fuzzy programming, ASCE J Water Resour Plann Manage, 122, 165-170, (1996) |

[39] | Seifi, A.; Hipel, KW, Interior-point method for reservoir operation with stochastic inflows, ASCE J Water Resour Plann Manage, 127, 48-57, (2001) |

[40] | Sethi, LN; Kumar, DN; Panda, SN; Mal, BC, Optimal crop planning and conjunctive use of water resources in a coastal river basin, Water Resour Manage, 16, 145-169, (2002) |

[41] | Slowinski, R., A multicriteria fuzzy linear programming method for water supply system development planning, Fuzzy Sets Syst, 19, 217-237, (1986) · Zbl 0626.90085 |

[42] | Srinivasan, K.; Neelakantan, TR; Narayan, P., Mixed-integer programming model for reservoir performance optimization, ASCE J Water Res Plann Manage, 125, 298-301, (1999) |

[43] | Srinivasan, R.; Simonovic, SP, A reliability programming model for hydropower optimization, Can J Civil Eng, 21, 1061-1073, (1994) |

[44] | Sylla, C., A penalty-based optimization for reservoirs system management, Comput Ind Eng, 28, 409-422, (1995) |

[45] | Watkins, DW; Mckinney, DC; Lasdon, LS; Nielsen, SS; Martin, QW, A scenario-based stochastic programming model for water supplies from the highland lakes, Int Transit Oper Res, 7, 211-230, (2000) |

[46] | Zare, Y.; Daneshmand, A., A linear approximation method for solving a special class of the chance constrained programming problem, Eur J Oper Res, 80, 213-225, (1995) · Zbl 0915.90216 |

[47] | Zarghami M, Szidarovszky F (2008) Stochastic-fuzzy multi criteria decision making for robust water resources management. Stoch Environ Res Risk Assess Online (doi: 10.1007/s00477-008-0218-6) · Zbl 1140.90435 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.