IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v3y2022i3d10.1007_s43069-022-00145-9.html
   My bibliography  Save this article

A Linearized Mathematical Formulation for Combined Centralized and Distributed Waste Water Treatment Network Design

Author

Listed:
  • Pantelis Broukos

    (Urban Energy Systems
    BATI Energie Sarl)

  • Antonios Fragkogios

    (University of Thessaly)

  • Nilay Shah

    (Urban Energy Systems)

Abstract

Waste water treatment (WWT) is a very important issue affecting both the environment and public health in the twenty-first century. The increasing earth’s population together with the growing urbanism leads to the need of redesigning effective WWT. In this paper, the problem of optimal Waste Water Treatment Network Design (WWTND) is addressed. To this end, various parameters affecting the problem have been taken into consideration, such as the distance between the residential areas and the treatment plants, estimations for future population of towns and costs of expanding existing network or building a new one. The last parameter of cost has a lot of components (pipeline cost, treatment plant cost, etc.), all of which are non-linear functions depending on the amount of waste water produced and treated within the network. The authors have developed a mathematical model for the solution of WWTND problem and have applied piecewise linearization in order to deal with the non-linear terms. The developed model has been implemented on an area in Luxemburg, for which data were collected. The results prove the model’s validity and usefulness, while its solution is computationally affordable.

Suggested Citation

  • Pantelis Broukos & Antonios Fragkogios & Nilay Shah, 2022. "A Linearized Mathematical Formulation for Combined Centralized and Distributed Waste Water Treatment Network Design," SN Operations Research Forum, Springer, vol. 3(3), pages 1-29, September.
    • Handle: RePEc:spr:snopef:v:3:y:2022:i:3:d:10.1007_s43069-022-00145-9
    DOI: 10.1007/s43069-022-00145-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-022-00145-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s43069-022-00145-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John J. Jarvis & Ronald L. Rardin & V. E. Unger & Richard W. Moore & Charles C. Schimpeler, 1978. "Optimal Design of Regional Wastewater Systems: A Fixed-Charge Network Flow Model," Operations Research, INFORMS, vol. 26(4), pages 538-550, August.
    2. Ali Haghighi & Amin Bakhshipour, 2012. "Optimization of Sewer Networks Using an Adaptive Genetic Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(12), pages 3441-3456, September.
    3. De Meyer, Annelies & Cattrysse, Dirk & Ostermeyer, Pieter & Van Orshoven, Jos, 2016. "Implementation of OPTIMASS to optimise municipal wastewater sludge processing chains: Proof of concept," Resources, Conservation & Recycling, Elsevier, vol. 114(C), pages 168-178.
    4. Ming-Hua Lin & John Gunnar Carlsson & Dongdong Ge & Jianming Shi & Jung-Fa Tsai, 2013. "A Review of Piecewise Linearization Methods," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, November.
    5. J. J. H. Forrest & J. P. H. Hirst & J. A. Tomlin, 1974. "Practical Solution of Large Mixed Integer Programming Problems with Umpire," Management Science, INFORMS, vol. 20(5), pages 736-773, January.
    6. Waqed H. Hassan & Musa H. Jassem & Safaa S. Mohammed, 2018. "A GA-HP Model for the Optimal Design of Sewer Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(3), pages 865-879, February.
    7. de Melo, Joao Joanaz & Camara, Antonio S., 1994. "Models for the optimization of regional wastewater treatment systems," European Journal of Operational Research, Elsevier, vol. 73(1), pages 1-16, February.
    8. R. Misener & C. A. Floudas, 2010. "Piecewise-Linear Approximations of Multidimensional Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 120-147, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Faisal M. Alfaisal & Larry W. Mays, 2021. "Optimization Models for Layout and Pipe Design for Storm Sewer Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(14), pages 4841-4854, November.
    2. Yves SMEERS & Daniel TYTECA, 1980. "Optimisation Économique Et Fiabilité Des Réseaux Intercommunaux De Stations D'Épuration," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 51(1-2), pages 69-95, 01-06.
    3. Codas, Andrés & Camponogara, Eduardo, 2012. "Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing," European Journal of Operational Research, Elsevier, vol. 217(1), pages 222-231.
    4. Zong Woo Geem & Jin-Hong Kim, 2016. "Sustainable Optimization for Wastewater Treatment System Using PSF-HS," Sustainability, MDPI, vol. 8(4), pages 1-13, March.
    5. Iman Ahmadianfar & Bijay Halder & Salim Heddam & Leonardo Goliatt & Mou Leong Tan & Zulfaqar Sa’adi & Zainab Al-Khafaji & Raad Z. Homod & Tarik A. Rashid & Zaher Mundher Yaseen, 2023. "An Enhanced Multioperator Runge–Kutta Algorithm for Optimizing Complex Water Engineering Problems," Sustainability, MDPI, vol. 15(3), pages 1-28, January.
    6. Erika Buson & Roberto Roberti & Paolo Toth, 2014. "A Reduced-Cost Iterated Local Search Heuristic for the Fixed-Charge Transportation Problem," Operations Research, INFORMS, vol. 62(5), pages 1095-1106, October.
    7. Praveen K. Navin & Yogesh P. Mathur, 2016. "Layout and Component Size Optimization of Sewer Network Using Spanning Tree and Modified PSO Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3627-3643, August.
    8. Siqian Shen & Murat Kurt & Jue Wang, 2015. "Chance-Constrained Programming Models and Approximations for General Stochastic Bottleneck Spanning Tree Problems," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 301-316, May.
    9. Derpich, Ivan & Vera, Jorge R., 2006. "Improving the efficiency of the Branch and Bound algorithm for integer programming based on "flatness" information," European Journal of Operational Research, Elsevier, vol. 174(1), pages 92-101, October.
    10. Michelle L. Blom & Christina N. Burt & Adrian R. Pearce & Peter J. Stuckey, 2014. "A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 658-676, November.
    11. Kazda, Kody & Li, Xiang, 2024. "A linear programming approach to difference-of-convex piecewise linear approximation," European Journal of Operational Research, Elsevier, vol. 312(2), pages 493-511.
    12. Waqed H. Hassan & Hussein H. Hussein & Duaa H. Khashan & Musa H. Alshammari & Basim K. Nile, 2022. "Application of the Coupled Simulation–optimization Method for the Optimum Cut-off Design Under a Hydraulic Structure," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(12), pages 4619-4636, September.
    13. Bloemhof-Ruwaard, Jacqueline M. & van Beek, Paul & Hordijk, Leen & Van Wassenhove, Luk N., 1995. "Interactions between operational research and environmental management," European Journal of Operational Research, Elsevier, vol. 85(2), pages 229-243, September.
    14. Peter Kirst & Oliver Stein & Paul Steuermann, 2015. "Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 591-616, July.
    15. Bitencourt, Leonardo & Dias, Bruno & Soares, Tiago & Borba, Bruno & Quirós-Tortós, Jairo, 2023. "e-Carsharing siting and sizing DLMP-based under demand uncertainty," Applied Energy, Elsevier, vol. 330(PB).
    16. Anna Petit-Boix & David Sanjuan-Delmás & Sergio Chenel & Desirée Marín & Carles Gasol & Ramon Farreny & Gara Villalba & María Suárez-Ojeda & Xavier Gabarrell & Alejandro Josa & Joan Rieradevall, 2015. "Assessing the Energetic and Environmental Impacts of the Operation and Maintenance of Spanish Sewer Networks from a Life-Cycle Perspective," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(8), pages 2581-2597, June.
    17. Valentina Marchionni & Nuno Lopes & Luis Mamouros & Dídia Covas, 2014. "Modelling Sewer Systems Costs with Multiple Linear Regression," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(13), pages 4415-4431, October.
    18. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    19. Zhang, Yi & Cheng, Chuntian & Cao, Rui & Li, Gang & Shen, Jianjian & Wu, Xinyu, 2021. "Multivariate probabilistic forecasting and its performance’s impacts on long-term dispatch of hydro-wind hybrid systems," Applied Energy, Elsevier, vol. 283(C).
    20. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:snopef:v:3:y:2022:i:3:d:10.1007_s43069-022-00145-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.