Finding Robust Solutions to Water Resources Problems

Water resources planners and managers are continually faced with decisions to be made under uncertainty. In planning problems such as water supply, flood control, and ground-water remediation, the trade-offs among expected cost, cost variability, and system performance and reliability must be assessed amidst inherent variability and imperfect information. Robust optimization (RO) is introduced as a framework for evaluating these trade-offs and controlling the effects of uncertainty in water resources screening models. Upon the introduction of scenarios, which represent realizations of the random parameters in the model, two types of robustness are defined: a policy is optimality-robust if it remains optimal or nearly optimal for all scenarios, and feasibility-robust if it remains feasible or nearly feasible for all scenarios. Applications to urban water transfer planning and ground-water quality management are presented, with optimality robustness related to cost variability and feasibility robustness rel...

[1]  R. Wets,et al.  L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING. , 1969 .

[2]  J. Birge,et al.  A multicut algorithm for two-stage stochastic linear programs , 1988 .

[3]  C. Shoemaker,et al.  Nonlinear weighted feedback control of groundwater remediation under uncertainty , 1993 .

[4]  Roger J.-B. Wets,et al.  Stochastic Optimization Models for Lake Eutrophication Management , 1988, Oper. Res..

[5]  Daniel P. Loucks,et al.  Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation , 1982 .

[6]  Daniel P. Loucks,et al.  Computer Models for Reservoir Regulation , 1968 .

[7]  R. Keeney,et al.  An illustrative example of the use of multiattribute utility theory for water resource planning , 1977 .

[8]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Stochastic Control , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  E. Beale ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES , 1955 .

[10]  M. V. F. Pereira,et al.  Multi-stage stochastic optimization applied to energy planning , 1991, Math. Program..

[11]  Ricardo Harboe,et al.  Multistep Planning Model for Conjunctive Use of Surface‐ and Ground‐Water Resources , 1991 .

[12]  J. Eheart,et al.  Aquifer remediation design under uncertainty using a new chance constrained programming technique , 1993 .

[13]  Ambrose Goicoechea,et al.  Multiple objectives under uncertainty: An illustrative application of protrade , 1979 .

[14]  A. M. Geoffrion Generalized Benders decomposition , 1972 .

[15]  J. Stedinger,et al.  Robustness of water resources systems , 1982 .

[16]  Nathan Chan,et al.  Partial Infeasibility Method for Chance‐Constrained Aquifer Management , 1994 .

[17]  J. Eheart,et al.  Neural network-based screening for groundwater reclamation under uncertainty , 1993 .

[18]  S. Gorelick,et al.  Optimal groundwater quality management under parameter uncertainty , 1987 .

[19]  Bruce A. McCarl,et al.  A Nonlinear Mixed Integer Program Model for Evaluating Runoff Impoundments for Supplemental Irrigation , 1995 .

[20]  J. Stedinger,et al.  Water resource systems planning and analysis , 1981 .

[21]  James G. Uber,et al.  Use of Mathematical Programming Methods for Complex Systems , 1992 .

[22]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  Christodoulos A. Floudas,et al.  APROS: Algorithmic Development Methodology for Discrete-Continuous Optimization Problems , 1989, Oper. Res..

[24]  B. F. Sule,et al.  Stochastic dynamic programming models for reservoir operation optimization , 1984 .

[25]  James G. Uber,et al.  Robust Optimal Design for Wastewater Treatment. Part II: Application , 1991 .

[26]  J. Stedinger,et al.  Sampling stochastic dynamic programming applied to reservoir operation , 1990 .

[27]  Aris P. Georgakakos,et al.  Stochastic Control of Groundwater Systems , 1991 .

[28]  Aris P. Georgakakos,et al.  Optimal Stochastic Operation of Salt River Project, Arizona , 1991 .

[29]  B. Zhao,et al.  Estuary management by stochastic linear quadratic optimal control , 1995 .

[30]  John D. Bredehoeft,et al.  Conjunctive use of groundwater and surface water for irrigated agriculture: Risk aversion , 1983 .

[31]  Yeou-Koung Tung,et al.  Groundwater Management by Chance‐Constrained Model , 1986 .

[32]  Peter Rogers,et al.  Use of systems analysis in water management , 1986 .

[33]  William W.-G. Yeh,et al.  Use of stochastic dynamic programming for reservoir management , 1987 .

[34]  P. Kitanidis,et al.  Optimization of the pumping schedule in aquifer remediation under uncertainty , 1990 .

[35]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[36]  Robert A. Young,et al.  Digital computer simulation for solving management problems of conjunctive groundwater and surface water systems , 1972 .

[37]  Jery R. Stedinger,et al.  SOCRATES: A system for scheduling hydroelectric generation under uncertainty , 1995, Ann. Oper. Res..

[38]  M. Pereira,et al.  Stochastic Optimization of a Multireservoir Hydroelectric System: A Decomposition Approach , 1985 .

[39]  David A. Kendrick,et al.  GAMS : a user's guide, Release 2.25 , 1992 .

[40]  Jay R. Lund,et al.  Optimization of Transfers in Urban Water Supply Planning , 1995 .

[41]  J. F. Benders Partitioning procedures for solving mixed-variables programming problems , 1962 .

[42]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[43]  Hamid R. Nemati,et al.  Groundwater quality management under uncertainty: stochastic programming approaches and the value of information , 1992 .

[44]  D. H. Marks,et al.  A New Method for the Real-Time Operation of Reservoir Systems , 1987 .

[45]  Alan J. King,et al.  Asymmetric risk measures and tracking models for portfolio optimization under uncertainty , 1993, Ann. Oper. Res..

[46]  C. Revelle,et al.  The Linear Decision Rule in Reservoir Management and Design: 1, Development of the Stochastic Model , 1969 .

[47]  Bill Provencher,et al.  Approximating the optimal groundwater pumping policy in a multiaquifer stochastic conjunctive use setting , 1994 .

[48]  Myron B Fiering,et al.  Alternative indices of resilience , 1982 .

[49]  Uri Shamir,et al.  OPTIMAL OPERATION OF RESERVOIRS BY STOCHASTIC PROGRAMMING , 1991 .