Model Matematika Optimasi Multi-Objektif Penurunan Beban Limbah Biochemical Oxygen Demand pada Instalasi Pengolahan Air Limbah

Shelly Sholatan Kamilah, Sunarsih Sunarsih, Titi Udjiani


The increase in community activities causes the amount of wastewater to increase. This wastewater comes from industrial production processes and from the community activities which are domestic wastewater. Domestic wastewater must be treated before being discharged to water sources because it contains pathogenic organisms. The place for treating domestic wastewater is Wastewater Treatment Plant (WWTP). The main purpose of WWTP is to degrade the Biochemical Oxygen Demand (BOD) and pathogenic organisms. This study develops a multi-objective optimization mathematical model for reducing the BOD load in the WWTP. This optimization model has three objective functions, namely maximizing the BOD load that is treated in the pond minimizing the difference between the BOD reduction efficiency value in the WWTP with the reference efficiency value and minimizing the power used by the aerator. The simulation results show that the maximum BOD load that can be treated in facultative ponds I and II is 1,589.688 Kg/day while for facultative ponds III and IV is 1,727.158 Kg/day. The efficiency value of reducing BOD load is influenced by the residence time variable, where the efficiency value of reducing the BOD load for facultative ponds I and II by 54% while for facultative ponds III and IV by 57%. The power used by the aerator is influenced by the treated BOD load variable, the aerator power in facultative ponds I and II is 49.67775 Kwh while in facultative ponds III and IV it is 53.97369 Kwh.


Multi-Objective Optimization; Biochemical Oxygen Demand Degradation Efficiency; Power Efficiency; Waste Water Treatment

Full Text:



D. Mara, Domestic wastewater treatment in developing countries. UK: Earthscan, 2004.

W. B. Suyasa, Pencemaran Air dan Pengolahan Air Limbah. Bali: Udayana University Press, 2015.

R. C. Umaly and L. A. Cuvin, Limnology: Laboratory and field guide psyco-chemical factors, biology factors. Manila: Natinal Book Store Publ, 1988.

Metcalf and Eddy, Wastewater and Engineering 3rd ed. Singapore: McGraw Hill International Engineering, 1991.

S. A. Ong, K. Uchiyama, X. Q. N. Nguyen, and C. Yoo, “Treatment of Azo Dye Acid Orange 7 Containing Wastewater Using Up-Flow Constructed Wetland With And Without Supplementary Aeration,” Bioresour. Technol., vol. 101, pp. 9049–9057, 2010.

J. Pan, H. Fei, S. Song, F. Yuan, and L. Yu, “Effects Of Intermittent Aeration On Pollutants Removal In Subsurface Wastewater Infiltration System,” Bioresour. Technol., vol. 191, pp. 327–331, 2015.

F. Cortés Martínez, A. Treviño Cansino, A. Sáenz López, J. L. González Barrios, and F. J. De La Cruz Acosta, “Mathematical modeling and optimization in the design of a maturation pond,” J. Appl. Res. Technol., vol. 14, no. 2, pp. 93–100, 2016, doi: 10.1016/j.jart.2016.04.004.

F. C. Martínez, A. T. Cansino, M. A. A. García, V. Kalashnikov, and R. L. Rojas, “Mathematical analysis for the optimization of a design in a facultative pond: Indicator organism and organic matter,” Math. Probl. Eng., vol. 2014, pp. 1–12, 2014, doi: 10.1155/2014/652509.

E. S. . Tejaswini, S. Panjawni, U. B. B. Gara, and S. R. Ambati, “Multi-objective optimization based controller design for improved wastewater treatment plant operation,” Environ. Technol. Innov., vol. 23, pp. 1–12, 2021.

P. E. Campana, M. Mainardis, A. Moretti, and M. Cottes, “100% renewable wastewater treatment plants techno economic.pdf,” Energy Convers. Manag., vol. 239, pp. 1–13, 2021.

H. T. Nguyen, U. Safder, X. Q. N. Nguyen, and C. Yoo, “Multi-objective decision making and optimal sizing to meet the dynamic energy demand of wastewater treatment plant,” Energy, vol. 191, pp. 1–18, 2020.

N. Shamloo, E. Bakhtavar, K. Hewage, and R. Sadiq, “Optimization of hydraulic fracturing wastewater management alternatives: A hybrid multi-objective linear programming model,” J. Clean. Prod., vol. 286, 2021, doi: 10.1016/j.jclepro.2020.124950.

H. Liu et al., “Optimizations on supply and distribution of dissolved oxygen in constructed wetlands: A review,” Bioresour. Technol., vol. 214, pp. 797–805, 2016, doi: 10.1016/j.biortech.2016.05.003.

R. Hreiz, N. Roche, B. Benyahia, and M. A. Latifi, “Chemical Engineering Research and Design Multi-objective optimal control of small-size wastewater treatment plants,” Chem. Eng. Res. Des., vol. 102, pp. 345–353, 2015.

F. Fang, B. Ni, W. Li, G. Sheng, and H. Yu, “A simulation-based integrated approach to optimize the biological nutrient removal process in a full-scale wastewater treatment plant,” Chem. Eng. J., vol. 174, no. 2–3, pp. 635–643, 2011, doi: 10.1016/j.cej.2011.09.079.

L. Changqing, L. Shuai, and Z. Feng, “The oxygen transfer efficiency and economic cost analysis of aeration system in municipal wastewater treatment plant,” Energy Procedia, vol. 5, pp. 2437–2443, 2011, doi: 10.1016/j.egypro.2011.03.419.

R. Sibil, M. Berkun, and S. Bekiroglu, “The comparison of different mathematical methods to determine the BOD parameters, a new developed method and impacts of these parameters variations on the design of WWTPs,” Appl. Math. Model., vol. 38, no. 2, pp. 641–658, 2014, doi: 10.1016/j.apm.2013.07.013.

S. Ihsan Wira and S. Sunarsih, “Facultative Stabilization Pond: Measuring Biological Oxygen Demand using Mathematical Approaches,” E3S Web Conf., vol. 31, pp. 1–4, 2018, doi: 10.1051/e3sconf/20183105009.

S. Sunarsih, Purwanto, and W. S. Budi, “Modeling of Domestic Wastewater Treatment Facultative Stabilization Ponds,” Int. J. Technol., vol. 4, pp. 689–698, 2015.

Sunarsih, Widowati, Kartono, and Sutrisno, “Mathematical Analysis for the Optimization of Wastewater Treatment Systems in Facultative Pond Indicator Organic Matter,” E3S Web Conf., vol. 31, pp. 2017–2019, 2018, doi: 10.1051/e3sconf/20183105008.

S. Sunarsih, D. P. Sasongko, and S. Sutrisno, “Process Improvement on Domestic Wastewater Treatment Stabilization Ponds by Using Mathematical Optimization Approach,” Matematika, vol. 35, no. 2, pp. 171–176, 2019, doi: 10.11113/matematika.v35.n2.1157.

Sunarsih and Sutrisno, “Multi-period Quadratic Programming Model for Sewon-Bantul Facultative Ponds Optimization,” Adv. Sci. Technol. Eng. Syst., vol. 4, no. 6, pp. 397–401, 2019, doi: 10.25046/aj040650.



  • There are currently no refbacks.

Copyright (c) 2022 Shelly Sholatan Kamilah, Sunarsih Sunarsih, Titi Udjiani

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi has been indexed by:


 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 +62-852-55230451 (Call/SMS/WA)
 Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi (p-ISSN: 2087-9393 | e-ISSN:2776-3706) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.