Stability of Waste Paper Recycling through Graph Theory

The process in which waste paper is collected and then reprocessed for reuse is called paper recycling. Paper recycling is very often routine of human life. Paper recycling is very important to reduce deforestation and pollution. It has been analyzed that scrap dealer plays a vital role in this cycle that collects waste paper from distributor and customer and then sent it to the paper industry, so the effect of scrap dealers is observed here. This waste paper recycling model is divided into four compartments namely paper industry, distributor, customer and scrap dealer. The model is proposed as a system of non-linear differential equation. The basic reproduction number is computed to see the impact of scrap dealer.

Keywords:

Dynamical model, System of non-linear ordinary differential equation, Basic reproduction number, Local stability Global stability, Weighted graphs, Paper,

PDF

___

[1] Back, Sangho, et al. "Production of soft paper products from old newspaper." U.S. Patent No. 5,582,681. 10 Dec. 1996.
[2] Bleakley, Ian Stuart, and Hannu Olavi Ensio Toivonen. "Waste paper treatment process." U.S. Patent No. 6,159,381. 12 Dec. 2000.
[3] Byström, Stig, and Lars Lönnstedt. "Paper recycling: environmental and economic impact." Resources, Conservation and Recycling 21.2 (1997): 109-127.
[4] Clement, Jean Marie. "Method for producing pulp from printed unselected waste paper." U.S. Patent No. 4,780,179. 25 Oct. 1988.
[5] Denen, Dennis Joseph, et al. "Waste minimizing paper dispenser." U.S. Patent No. 6,793,170. 21 Sep. 2004.
[6] Harary, Frank. Graph theory. 1969.
[7] http://mathinsight.org/definition/directed_graph
[8] https://en.wikipedia.org/wiki/Cycle_graph
[9] https://en.wikipedia.org/wiki/Loop_(graph_theory)
[10] https://en.wikipedia.org/wiki/Path_(graph_theory)
[11] https://en.wikipedia.org/wiki/Spanning_tree
[12] https://en.wikipedia.org/wiki/Tree_(graph_theory)
[13] Kara, S. Soner, and S. Onut. "A stochastic optimization approach for paper recycling reverse logistics network design under uncertainty." International Journal of Environmental Science & Technology 7.4 (2010): 717-730.
[14] Kleineidam, U., et al. "Optimising product recycling chains by control theory." International Journal of Production Economics66.2 (2000): 185-195.
[15] McKinney, Roland, ed. Technology of paper recycling. Springer Science & Business Media, 1994.
[16] Merrild, Hanna, Anders Damgaard, and Thomas H. Christensen. "Life cycle assessment of waste paper management: the importance of technology data and system boundaries in assessing recycling and incineration." Resources, Conservation and Recycling 52.12 (2008): 1391-1398.
[17] Miranda, Ruben, and Angeles Blanco. "Environmental awareness and paper recycling." Cellulose Chemistry & Technology 44.10 (2010): 431.
[18] Nadeau, Allan. "Integrated wastepaper treatment process." U.S. Patent No. 5,302,245. 12 Apr. 1994.
[19] Pati, Rupesh Kumar, Prem Vrat, and Pradeep Kumar. "A goal programming model for paper recycling system." Omega 36.3 (2008): 405-417.
[20] Routh, E. J. (1877). A treatise on the stability of a given state of motion: particularly steady motion. Macmillan and Company.
[21] Shah, Nita H., H. Satia, and M. Yeolekar. "Optimal Control on depletion of Green Belt due to Industries." Advances in Dynamical Systems and Applications 12.3 (2017): 217-232.
[22] Shah, Nita H., Moksha H. Satia, and Bijal M. Yeolekar. "Optimum Control for Spread of Pollutants through Forest Resources." Applied Mathematics 8.05 (2017): 607.
[23] Virtanen, Yrjo, and Sten Nilsson. Environmental impacts of waste paper recycling. Routledge, 2013.
[24] West, Douglas Brent. Introduction to graph theory. Vol. 2. Upper Saddle River: Prentice hall, 2001.

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

Arşiv