Controlling Water Quality of a Firm's Hydropower

https://doi.org/10.47194/ijgor.v4i2.217

Authors

  • Najeeb Al-Matar Department of Business Administration, Al-Baha University, Alaqiq, Saudi Arabia
  • Lotfi Tadj Department of Industrial Engineering, Alfaisal University, Riyadh, Saudi Arabia

Keywords:

Sustainability, green manufacturing, water quality, optimal control, tracking, pollution control.

Abstract

The problem considered in this paper concerns a manufacturing firm located at a lake. The firm uses the lake's water in its production process. However, the production process affects the quality of the water. The manufacturing firm will only survive if the natural resource it uses, namely water in this case, remains available for the long term. Sustainability can be achieved through green manufacturing practices. The problem is dynamic, and optimal control theory, namely model predictive control, is used to determine the optimal production rate and the optimal rate of expenditure for pollution control. A numerical example illustrates the results obtained. 

References

Brock, W.A. and Dechert, W.D. (2008). The polluted ecosystem game, Indian Growth and Development Review, Vol. 1, No. 1, 7- 31, doi:10.1108/17538250810868116.

Clarke HR. (1987). Production planning in a firm subject to environmental regulation, Resources and Energy, vol. 9(1), 35-44, doi:10.1016/0165-0572(87)90021-1.

da Silva AS, de Souza FMC. (2008). The economics of water resources for the generation of electricity and other uses, Annals of Operations Research, Vol. 164, 41-61, DOI: 10.1007/s10479-008-0360-z.

Feichtinger G. (1982). The Nash solution of a maintenance-production differential game, European Journal of Operational Research, Vol. 10, 165-172, doi:10.1016/0377-2217(82)90156-4.

Feichtinger G. (1988). Production-pollution cycles. In: Kurzhanski A, Neumann K, Pallaschke D, editors. Optimization, Parallel Processing and Applications. Lecture Notes in Economics and Mathematical Systems. Berlin: Springer, doi:10.1007/978-3-642-46631-1_18.

Feichtinger G, Jørgensen, S. (1983). Differential game models in management science, European Journal of Operational Research, Vol. 14, 137-155, doi:10.1016/0377-2217(83)90308-9.

Hartl R. (1982). Optimal control of concave economic models with two control instruments. In: Feichtinger G, Kall P, editors, Operations Research in Progress. Dordrecht: Springer, doi:10.1007/978-94-009-7901-7.

Hartl R. (1983). Optimal maintenance and production rates for a machine: A nonlinear economic control problem. Journal of Economic Dynamics and Control, Vol. 6, 281-306, DOI: 10.1016/0165-1889(83)90055-6.

Hartl RF, Kirakossian GT, Hakobyan SR, Markaryan AH. (2006). A dynamical model of water recycling in a mine-processing enterprise, Central European Journal of Operations Research, Vol. 14, 45-57, DOI: 10.1007/s10100-006-0159-4.

Highfill J, McAsey M. (2001). An application of optimal control to the economics of recycling, SIAM Review, Vol. 43, 679-693, DOI:10.1137/S0036144599362698.

Jørgensen S, Martín-Herrán G, Zaccour G. (2010). Dynamic games in the economics and management of pollution, Environmental Modeling & Assessment, Vol. 15, 433-467, DOI:10.1007/s10666-010-9221-7

Kawaguchi K. (2003). Optimal control of pollution accumulation with long-run average welfare, Environmental and Resource Economics, Vol. 26, 457-468, DOI: 10.1023/B:EARE.0000003609.50884.41.

Kossioris G, Plexousakis M, Xepapadeas A, de Zeeuwe A, Mäler K-G. (2008). Feedback Nash equilibria for nonlinear differential games in pollution control, Journal of Economic Dynamics & Control, Vol. 32, 1312-1331, DOI:10.1016/j.jedc.2007.05.008.

Nævdal E. (2001). Optimal regulation of eutrophying lakes, fjords, and rivers in the presence of threshold effects, American Journal of Agricultural Economics, Vol. 83, 972-984, DOI:10.1111/0002-9092.00223.

Sethi SP. (1977). A linear bang-bang model of firm behavior and water quality, IEEE Transactions on Automatic Control, Vol. 22, 706-714, DOI: 10.1109/ TAC.1977.1101596.

Sethi SP. (2019). Optimal Control Theory: Applications to Management Science and Economics. 3rd ed, Cham: Springer, doi:10.1007/978-3-319-98237-3.

Tapiero CS. (2004). Environmental quality control and environmental games, Environmental Modeling and Assessment, Vol. 9, 201-206, DOI:10.1007/s10666-005-2451-4.

Tapiero CS. (2005). Environmental quality control: a queueing game, Stochastic Environmental Research and Risk Assessment, Vol. 19, 59-70, DOI:10.1007 / s00477-004-0206-4.

Tapiero CS. (2009). Energy consumption and environmental pollution: A stochastic model, IMA Journal of Management Mathematics, Vol, 20, 263-273, DOI:10.1093/imaman/dpn041.

Published

2023-05-26