TECHNICAL PAPERS
Jan 1, 1997

Finding Robust Solutions to Water Resources Problems

Publication: Journal of Water Resources Planning and Management
Volume 123, Issue 1

Abstract

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 related to system reliability. Results show that RO can be a useful framework for evaluating the intrinsic trade-offs involving risk and finding solutions that hedge against inherent and parameter uncertainty.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Andricevic, R., and Kitanidis, P. K.(1990). “Optimization of the pumping schedule in aquifer remediation under uncertainty.”Water Resour. Res., 26(5), 875–885.
2.
Beale, E. M. L.(1955). “On minimizing a convex function subject to linear inequalities.”J. Royal Statistical Soc. Ser. B, 17(2), 173–184.
3.
Benders, J. F.(1962). “Partitioning procedures for solving mixed variables programming problems.”Numerische Mathematik, Berlin, Germany, 4, 238–252.
4.
Bertsekas, D. P. (1987). Dynamic programming and stochastic control. Academic Press, New York, N.Y.
5.
Birge, J. R., and Louveaux, F. V.(1988). “A multicut algorithm for two-stage stochastic linear programs.”Eur. J. Operational Res., 34, 384–392.
6.
Bredehoeft, J. D., and Young, R. A.(1983). “Conjunctive use of groundwater and surface water for irrigated agriculture: risk aversion.”Water Resour. Res., 19(5), 1111–1121.
7.
Brooke, A., Kendrick, D., and Meeraus, A. (1992). GAMS: a user's guide, release 2.25. The Scientific Press, San Francisco, Calif.
8.
Chan, N.(1994). “Partial infeasibility method for chance-constrained aquifer management.”J. Water Resour. Plng. and Mgmt., ASCE, 120(1), 70–89.
9.
Cohon, J. L. (1978). Multiobjective programming and planning. Academic Press, New York, N.Y.
10.
Dantzig, G. B.(1955). “Linear programming under uncertainty.”Mgmt. Sci., 1(3), 197–206.
11.
Eiger, G., and Shamir, U.(1991). “Optimal operation of reservoirs by stochastic programming.”Engrg. Optimization, 17, 293–312.
12.
Fiering, M. B.(1982). “Alternative indices of resilience.”Water Resour. Res., 18(1), 33–39.
13.
Fiering, M. B., and Matalas, N. C. (1990). “Decision making under uncertainty.”Climate change and U.S. water resources, P. E. Waggoner, ed., John Wiley & Sons, Inc., New York, N.Y., 75–86.
14.
Geoffrion, A. M.(1972). “Generalized Benders decomposition.”J. Optimization Theory and Appl., 10(4), 237–260.
15.
Georgakakos, A. P., and Marks, D. H.(1987). “A new method for the real-time operation of reservoir systems.”Water Resour. Res., 23(7), 1376–1390.
16.
Georgakakos, A. P., and Vlatsa, D. A.(1991). “Stochastic control of groundwater systems.”Water Resour. Res., 27(8), 2077–2090.
17.
Goicoechea, A., Duckstein, L., and Fogel, M.(1979). “Multiple objectives under uncertainty: an illustrative application of PROTRADE.”Water Resour. Res., 15(2), 210–230.
18.
Gorelick, S. M. (1987). “Sensitivity analysis of optimal groundwater contaminant capture curves: spatial variability and robust solutions.”Solving groundwater problems with models, Nat. Water Well Assn., Denver, Colo., 133–146.
19.
Hashimoto, T., Stedinger, J. R., and Loucks, D. P.(1982a). “Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation.”Water Resour. Res., 18(1), 14–20.
20.
Hashimoto, T., Loucks, D. P., and Stedinger, J. R.(1982b). “Robustness of water resources systems.”Water Resour. Res., 18(1), 21–26.
21.
Hooper, E. R., Georgakakos, A. P., and Lettenmaier, D. P.(1991). “Optimal stochastic operation of Salt River project, Arizona.”J. Water Resour. Plng. and Mgmt., ASCE, 117(5), 566–587.
22.
Jacobs, J. et al. (1995). “SOCRATES: a system for scheduling hydroelectric generation under uncertainty.”Ann. of Operations Res., 59, 99–134.
23.
Keeney, R. L., and Raiffa, H. (1976). Decisions with multiple objectives: preferences and value tradeoffs. John Wiley & Sons, Inc., New York, N.Y.
24.
Keeney, R. L., and Wood, E. F.(1977). “An illustrative example of the use of multiattribute utility theory for water resources planning.”Water Resour. Res., 13(4), 705–712.
25.
Kelman, J., Stedinger, J. R., Cooper, L. A., Hsu, E., and Yuan, S.-Q.(1990). “Sampling stochastic dynamic programming applied to reservoir operation.”Water Resour. Res., 26(3), 447–454.
26.
King, A. J.(1993). “Asymmetric risk measures and tracking models or portfolio optimization under uncertainty.”Ann. of Operations Res., 45, 165–177.
27.
Loucks, D. P. (1968). “Computer models for reservoir regulation.”J. Sanitary Engrg. Div., ASCE, 94(S4), 657–669.
28.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resource systems planning and analysis. Prentice-Hall, Inc., Englewood Cliffs, N.J.
29.
Lund, J. R., and Israel, M.(1995). “Optimization of transfers in urban water supply planning.”J. Water Resour. Plng. and Mgmt., ASCE, 121(1), 41–48.
30.
Markowitz, H. M. (1959). Portfolio selection: efficient diversification of investments. John Wiley & Sons, Inc., New York, N.Y.
31.
Matalas, N. C., and Fiering, M. B. (1977). “Water-resource systems planning.”Climate, climatic change, and water supply, Nat. Acad. of Sci., Washington, D.C., 99–110.
32.
Morgan, D. R., Eheart, J. W., and Valocchi, A. J.(1993). “Aquifer remediation design under uncertainty using a new chance constrained programming technique.”Water Resour. Res., 29(3), 551–561.
33.
Mulvey, J. M., Vanderbei, R. J., and Zenios, S. A.(1995). “Robust optimization of large-scale systems.”Operations Res., 43(2), 264–281.
34.
Paules, G. E. IV, and Floudas, C. A.(1989). “APROS: algorithmic development methodology for discrete-continuous optimization problems.”Operations Res., 37(6), 902–915.
35.
Pereira, M. V. F., and Pinto, L. M. V. G.(1985). “Stochastic optimization of a multireservoir hydroelectric system: a decomposition approach.”Water Resour. Res., 21(6), 779–792.
36.
Pereira, M. V. F., and Pinto, L. M. V. G.(1991). “Multi-stage stochastic optimization applied to energy planning.”Math. Programming, 52, 359–375.
37.
Provencher, B., and Burt, O.(1994). “Approximating the optimal groundwater pumping policy in a multiaquifer stochastic conjunctive use setting.”Water Resour. Res., 30(3), 833–843.
38.
Raj Onta, P., Das Gupta, A., and Harboe, R.(1991). “Multistep planning model for conjunctive use of surfaceand ground-water resources.”J. Water Resour. Plng. and Mgmt., ASCE, 117(6), 662–677.
39.
Ranjithan, S., Eheart, J. W., and Garrett, J. H. Jr.(1993). “Neural network-based screening for groundwater reclamation under uncertainty.”Water Resour. Res., 29(3), 563–574.
40.
ReVelle, C., Joeres, E., and Kirby, W.(1969). “Linear decision rule in reservoir management and design. 1: Development of the stochastic model.”Water Resour. Res., 5(4), 767–777.
41.
Rogers, P. P., and Fiering, M. B. (1986). “Use of systems analysis in water management.”Water Resour. Res., 22(9), 146S–156S.
42.
Somlyódy, L., and Wets, R. J.-B.(1988). “Stochastic optimization models for lake eutrophication management.”Operations Res., 36(5), 660–681.
43.
Stedinger, J. R., Sule, B. F., and Loucks, D. P.(1984). “Stochastic dynamic programming models for reservoir operation optimization.”Water Resour. Res., 20(11), 1499–1505.
44.
Trezos, T., and Yeh, W. W.-G.(1987). “Use of stochastic dynamic programming for reservoir management.”Water Resour. Res., 23(6), 983–996.
45.
Tung, Y.-K.(1986). “Groundwater management by chance-constrained model.”J. Water Resour. Plng. and Mgmt., ASCE, 112(1), 1–19.
46.
Uber, J. G., Brill, E. D. Jr., and Pfeffer, J. T.(1991). “Robust optimal design for wastewater treatment. II: Application.”J. Envir. Engrg., ASCE, 117(4), 438–456.
47.
Uber, J. G., Brill, E. D. Jr., and Pfeffer, J. T.(1992). “Use of mathematical programming methods for complex system.”J. Water Resour. Plng. and Mgmt., ASCE, 118(3), 281–294.
48.
Van Slyke, R. M., and Wets, R. J.-B.(1969). “L-shaped linear programs with applications to optimal control and stochastic programming.”SIAM J. Appl. Math., 17, 638–663.
49.
Wagner, B. J., and Gorelick, S. M.(1987). “Optimal groundwater quality management under parameter uncertainty.”Water Resour. Res., 23(7), 1162–1174.
50.
Wagner, J. M., Shamir, U., and Nemati, H. R.(1992). “Groundwater quality management under uncertainty: stochastic programming approaches and the value of information.”Water Resour. Res., 28(5), 1233–1246.
51.
Wang, H. F., and Anderson, M. P. (1982). Introduction to groundwater modeling: finite difference and finite element methods. Freeman Publishers, San Francisco, Calif.
52.
Watkins, D. W. Jr., and McKinney, D. C. (1996). “Robust optimization for water resources planning under uncertainty: algorithms and applications.”CRWR Tech. Rep., Univ. of Texas, Austin, Tex.
53.
Whiffen, G. J., and Shoemaker, C. A.(1993). “Nonlinear weighted feedback control of groundwater remediation under uncertainty.”Water Resour. Res., 29(9), 3277–3289.
54.
Yang, A. P. (1990). “Stochastic heterogeneity and dispersion,” PhD dissertation, Univ. of Texas, Austin, Tex.
55.
Young, R. A., and Bredehoeft, J. D.(1972). “Digital computer simulation for solving management problems of conjunctive groundwater and surface water systems.”Water Resour. Res., 8, 533–556.
56.
Zhao, B., and Mays, L. W.(1995). “Estuary management by stochastic linear quadratic optimal control.”J. Water Resour. Plng. and Mgmt., ASCE, 121(5), 382–391.
57.
Ziari, H. A., McCarl, B. A., and Stockle, C.(1995). “A nonlinear mixed integer program model for evaluating runoff impoundments for supplemental irrigation.”Water Resour. Res., 31(6), 1585–1594.

Information & Authors

Information

Published In

Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 123Issue 1January 1997
Pages: 49 - 58

History

Published online: Jan 1, 1997
Published in print: Jan 1997

Permissions

Request permissions for this article.

Authors

Affiliations

David W. Watkins, Jr., Student Member, ASCE
Grad. Student, Dept. of Civ. Engrg., Univ. of Texas at Austin, Austin, TX 78712.
Daene C. McKinney, Associate Member, ASCE
Assoc. Prof., Dept. of Civ. Engrg., Univ. of Texas at Austin, Austin, TX.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share