Annals of Operations Research

, Volume 132, Issue 1–4, pp 207–221 | Cite as

Stochastic Dynamic Programming Formulation for a Wastewater Treatment Decision-Making Framework

  • Julia C.C. Tsai
  • Victoria C.P. Chen
  • M. Bruce Beck
  • Jining Chen


In this paper, a decision-making framework (DMF) based on stochastic dynamic programming (SDP) is presented for a wastewater treatment system, consisting of a liquid treatment line with eleven levels and a solid treatment line with six levels (Chen and Beck, 1997). A continuous-state SDP solution approach based on the OA/MARS method (Chen, Ruppert, and Shoemaker, 1999) is employed, which provides an efficient method for representing a wide range of possible influent conditions. The DMF is used to evaluate current and emerging technologies for the multi-level liquid and solid lines of the wastewater treatment system. At each level, one technology unit is selected out of a set of options which includes the empty unit. The DMF provides a comparison on possible technologies for screening which types of technologies may best be further developed in order for an urban wastewater infrastructure to be judged progressively more sustainable. The results indicate that one or a pair of technologies are dominant in each level. The cheap, lower-technology unit processes receive a mixed review. Some of them are selected as the most promising technology units while the others are not considered as good candidates.

dynamic programming orthogonal arrays Latin hypercubes regression splines wastewater treatment 


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  1. Baglietto, M., C. Cervellera, T. Parisini, M. Sanguineti, and R. Zoppoli. (2001). "Approximating Networks for the Solution of T-Stage Stochastic Optimal Control Problems." In Proceedings of the IFAC Workshop on Adaptation and Modeling in Control and Signal Processing.Google Scholar
  2. Beck, M.B. and R.G. Cummings. (1996). "Wastewater Infrastructures: Challenges for the Sustainable City in the New Millennium." Habitat International 20(3), 405–420.CrossRefGoogle Scholar
  3. Bellman, R.E. (1957). Dynamic Programming. Princeton: Princeton University Press.Google Scholar
  4. Chen, J. (1993). "Environmentally Efficient Urban Drainage for the 21st Century: A Literature Review." Technical Report, Department of Civil Engineering, Imperial College of Science, Technology and Medicine, London, UK.Google Scholar
  5. Chen, J. and M.B. Beck. (1997). "Towards Designing Sustainable Urban Wastewater Infrastructures: A Screening Analysis." Water Sciences Technology 15, 99–112.Google Scholar
  6. Chen, V.C.P. (1999). "Application of MARS and Orthogonal Arrays to Inventory Forecasting Stochastic Dynamic Programs." Computational Statistics and Data Analysis 30, 317–341.CrossRefGoogle Scholar
  7. Chen, V.C.P. (2001). "Measuring the Goodness of Orthogonal Array Discretizations for Stochastic Pro-gramming and Stochastic Dynamic Programming." SIAM Journal of Optimization 12, 322–344.CrossRefGoogle Scholar
  8. Chen, V.C.P., J. Chen, and M.B. Beck. (2000). "Statistical Learning within a Decision-Making Framework for more Sustainable Urban Environments." In Proceedings of the Joint Research Conference on Statistics in Quality, Industry, and Technology, Seattle, WA, June 2000.Google Scholar
  9. Chen, V.C.P., D. Ruppert, and C.A. Shoemaker. (1999). "Applying Experimental Design and Regression Splines to High-Dimensional Continuous-State Stochastic Dynamic Programming." Operations Research 47, 38–53.Google Scholar
  10. Chen, V.C.P., J.C.C. Tsai, E.K. Lee, and E.L. Johnson. (2001). "A Decision-Making Framework for Evaluating Wastewater Treatment Technologies." In Proceedings of the 5th Annual Green Chemistry and Engineering Conference, Washington, DC, June 2001.Google Scholar
  11. Foufoula-Georgiou, E. and P.K. Kitanidis. (1988). "Gradient Dynamic Programming for Stochastic Optimal Control of Multidimensional Water Resources Systems." Water Resources Research 24, 1345–1359.Google Scholar
  12. Friedman, J.H. (1991). "Multivariate Adaptive Regression Splines" (with discussion). Annals of Statistics 19, 1–141.Google Scholar
  13. Johnson, S.A., J.R. Stedinger, C.A. Shoemaker, Y. Li, and J.A. Tejada-Guibert. (1993). "Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation." Operations Research 41, 484–500.Google Scholar
  14. Plackett, R.L. and J.P. Burman. (1946). "The Design of Multifactorial Experiments." Biometrika 33, 305–325.Google Scholar
  15. Puterman, M.L. (1994). Markov Decision Processes. New York: Wiley.Google Scholar
  16. Rossman, L.A. (1980). "Synthesis of Waste Treatment Systems by Implicit Enumeration." Journal Water Pollution Control Federation 52(1), 148–160.Google Scholar
  17. Shih, C.S. and J.A. DeFilippi. (1970). “System Optimization of Waste Treatment Plant Process Design.” Journal of the Sanitary Engineering Division96(2), 409-421.Google Scholar
  18. Tang, B. (1993). “Orthogonal Array-Based Latin Hypercubes.” Journal of the American Statistical Association88, 1392-1397.Google Scholar
  19. Tang, C.-C., E.D. Brill, Jr., and J.T. Pfeffer. (1987). "Optimization Techniques for Secondary Wastewater Treatment Systems." Journal of Environmental Engineering, ASCE 113(5), 935–951.Google Scholar
  20. Tsai, J.C.C. (2002). Statistical Modeling of the Value Function in High-Dimensional, Continuous-State Stochastic Dynamic Programming. Ph.D. Dissertation, Georgia Institute of Technology.Google Scholar
  21. Tyteca, D. (1981). "Nonlinear Programming Model of Wastewater Treatment Plant." Journal of the Environmental Engineering Division 107(4), 747–766.Google Scholar
  22. Tyteca, D. and Y. Smeers. (1981). "Nonlinear Programming Design of Wastewater Treatment Plant." Journal of the Environmental Engineering Division 107(4), 767–779.Google Scholar
  23. Uber, J.G., E.D. Brill, Jr., and J.T. Pfeffer. (1991a). "Robust Optimal Design for Wastewater Treatment. I: General Approach." Journal of Environmental Engineering, ASCE 117(4), 425–437.Google Scholar
  24. Uber, J.G., E.D. Brill, Jr., and J.T. Pfeffer. (1991b). "Robust Optimal Design for Wastewater Treatment. II: Application." Journal of Environmental Engineering, ASCE 117(4), 438–456.Google Scholar
  25. Wagner, B. (1999). "Evaluating Data Worth for Ground-Water Management under Uncertainty." Journal of Water Resources Planning and Management 125(5), 281–288.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Julia C.C. Tsai
    • 1
  • Victoria C.P. Chen
    • 2
  • M. Bruce Beck
    • 3
  • Jining Chen
    • 4
  1. 1.Krannert School of ManagementPurdue UniversityWest LafayetteUSA
  2. 2.Department of Industrial and Manufacturing Systems EngineeringUniversity of Texas at ArlingtonArlingtonUSA
  3. 3.Warnell School of Forest ResourcesUniversity of GeorgiaAthensUSA
  4. 4.Department of Environmental Science and EngineeringTsinghua UniversityBeijingChina

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