Implicit Mean-Variance Approach for Optimal Management of a Water Supply System under Uncertainty

AbstractThis study addresses the management of a water supply system under uncertainty. Water is taken from sources that include aquifers and desalination plants and conveyed through a distribution system to consumers under constraints of quantity and quality. The replenishment into the aquifers is stochastic, whereas the desalination plants can produce a large and reliable amount, but at a higher cost. The cost is stochastic because it depends on the realization of the replenishment into the aquifer. A new implicit mean-variance approach is developed and applied. It utilizes the advantages of implicit stochastic programming to formulate a small size and easy to solve convex external optimization problem (quadratic objective and linear constraints) that generates the mean-variance tradeoff without the need to solve a large-scale problem. The results are presented as a tradeoff between the expected value versus the standard deviation. At one end of the tradeoff curve, dependence on the aquifer results in l...

[1]  John M. Mulvey,et al.  A New Scenario Decomposition Method for Large-Scale Stochastic Optimization , 1995, Oper. Res..

[2]  Cheng-shuang Peng,et al.  PRACTICAL ESTIMATION OF INFLOWS INTO MULTIRESERVOIR SYSTEM , 2000 .

[3]  George M. Hornberger,et al.  Sustainable water resource management under hydrological uncertainty , 2008 .

[4]  Frank T.-C. Tsai,et al.  Optimization of Large-Scale Hydropower System Operations , 2003 .

[5]  Graeme C. Dandy,et al.  Optimal Operation of Multiple-Reservoir System , 1993 .

[6]  Haralambos V. Vasiliadis,et al.  DEMAND – DRIVEN OPERATION OF RESERVOIRS USING UNCERTAINTY – BASED OPTIMAL OPERATING POLICIES , 1994 .

[7]  Maarouf Saad,et al.  Censored‐data correlation and principal component dynamic programming , 1992 .

[8]  Leon S. Lasdon,et al.  Solving nonlinear water management models using a combined genetic algorithm and linear programming approach , 2001 .

[9]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[10]  Keith W. Hipel,et al.  Interior-Point Method for Reservoir Operation with Stochastic Inflows , 2001 .

[11]  Peter K. Kitanidis,et al.  Limitations of Deterministic Optimization Applied to Reservoir Operations , 1999 .

[12]  T. M. Williams,et al.  Practical Methods of Optimization. Vol. 1: Unconstrained Optimization , 1980 .

[13]  Balaji Rajagopalan,et al.  Water Management Applications of Climate-Based Hydrologic Forecasts: Case Study of the Truckee-Carson River Basin , 2007 .

[14]  John M. Wilson,et al.  Introduction to Stochastic Programming , 1998, J. Oper. Res. Soc..

[15]  Leon S. Lasdon,et al.  Stochastic Optimization of the Highland Lakes System in Texas , 2006 .

[16]  David Yates,et al.  WEAP21—A Demand-, Priority-, and Preference-Driven Water Planning Model , 2005 .

[17]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[18]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[19]  Frank T.-C. Tsai,et al.  Optimization of Water Distribution and Water Quality by Hybrid Genetic Algorithm , 2005 .

[20]  Gideon Sinai,et al.  OPTIMAL OPERATION OF MULTIQUALITY WATER SUPPLY SYSTEMS-III: THE Q-C-H MODEL , 2000 .

[21]  Avi Ostfeld,et al.  Optimal Operation of Multiquality Networks. I: Steady-State Conditions , 1993 .

[22]  V. Chandramouli,et al.  Deriving a General Operating Policy for Reservoirs Using Neural Network , 1996 .

[23]  Avi Ostfeld,et al.  Seasonal multi-year optimal management of quantities and salinities in regional water supply systems , 2012, Environ. Model. Softw..

[24]  Jitka Dupacová,et al.  Scenarios for Multistage Stochastic Programs , 2000, Ann. Oper. Res..

[25]  Gideon Sinai,et al.  OPTIMAL OPERATION OF MULTI-QUALITY WATER SUPPLY SYSTEMS-I: INTRODUCTION AND THE Q-C MODEL , 2000 .

[26]  Jorge Nocedal,et al.  An interior algorithm for nonlinear optimization that combines line search and trust region steps , 2006, Math. Program..

[27]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[28]  John W. Labadie,et al.  Optimal Operational Analysis of the Colorado-Big Thompson Project , 1989 .

[29]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

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

[31]  David W. Watkins,et al.  Finding Robust Solutions to Water Resources Problems , 1997 .

[32]  John W. Labadie,et al.  Optimal Operation of Multireservoir Systems: State-of-the-Art Review , 2004 .