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January 2018, 14(1): 135-164. doi: 10.3934/jimo.2017040

Joint decision on pricing and waste emission level in industrial symbiosis chain

1. 

School of Management, Xi'an Jiaotong University, The Key Lab of the Ministry of Education for Process Control & Efficiency Engineering, Xi'an, Shanxi 710049, China

2. 

School of Management, Xi'an Jiaotong University, Xi'an, Shanxi 710049, China

3. 

Xi'an Research Institute of Hi-Technology, Xi'an, Shanxi 710025, China

* Corresponding author: Zhongdong Xiao, Email: xzd@mail.xjtu.edu.cn

Received  January 2015 Revised  January 2017 Published  April 2017

Based on a monopoly model in industrial symbiosis chain including one upstream manufacturer and one downstream manufacturer, the price sensitive-environmental concern demand is introduced into the paper. The decision behaviors of the manufacturers in industrial symbiosis chain under environmental regulations imposed by the policy makers or the government in waste emission standard, waste emission tax and subsidy for waste usage are investigated. The results show the operational factors of the manufacturers must be taken into account in the right formulation of waste emission standard, and the simultaneous implementation of waste emission tax and subsidy for external environmental performance of the manufacturers is superior to a single policy. Environmental concerned consumers with stronger green attitude who are more willing to buy environmentally friendly products could pressurize the manufacturers into decreasing waste emission level, and the manufacturers will affirmatively involve in industrial symbiosis chain due to the intervention of environmental regulations. Especially, integrated industrial symbiosis becomes the optimal decision for the manufacturers to boost both economic benefit and environmental performance. Waste emission contract and quantity discount contract can be techniques to improve the performance of non-integrated industrial symbiosis chain.

Citation: Binbin Cao, Zhongdong Xiao, Xiaojun Li. Joint decision on pricing and waste emission level in industrial symbiosis chain. Journal of Industrial & Management Optimization, 2018, 14 (1) : 135-164. doi: 10.3934/jimo.2017040
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A. ChoudharyR. SumanV. DixitM. K. TiwariK. J. Fernandes and P. C. Chang, An optimization model for a monopolistic firm serving an environmentally conscious market: Use of chemical reaction optimization algorithm, International Journal of Production Economics, 164 (2015), 409-420. doi: 10.1016/j.ijpe.2014.10.011.

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P. Bansal and B. McKnight, Looking forward, pushing back and peering sideways: Analyzing the sustainability of industrial symbiosis, Journal of Supply Chain Management, 45 (2009), 26-37. doi: 10.1111/j.1745-493X.2009.03174.x.

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S. BenjaafarY. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transactions on Automation Science and Engineering, 10 (2013), 99-116. doi: 10.1109/TASE.2012.2203304.

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B. M. SophaA. M. FetM. M. Keitsch and C. Haskins, Using systems engineering to create a framework for evaluating industrial symbiosis, Systems Engineering, 13 (2010), 149-160. doi: 10.1002/sys.20139.

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B. Kim and J. E. Sim, Impacts of government and market on firm's efforts to reduce pollution, Cogent Economics & Finance, 3 (2015), 1062634. doi: 10.1080/23322039.2015.1062634.

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K. K. BoyerA. M. Prud'homme and W. Chung, The last mile challenge: evaluating the effects of customer density and delivery window patterns, Journal of Business Logistics, 30 (2009), 185-202. doi: 10.1002/j.2158-1592.2009.tb00104.x.

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C. L. Chen and G. E. Monahan, Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning, inventory control, and environmental performance, European Journal of Operational Research, 207 (2010), 1280-1292. doi: 10.1016/j.ejor.2010.06.028.

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C.-C. HsuK. C. TanS. H. M. Zailani and V. Jayaraman, Supply chain drivers that foster the development of green initiatives in an emerging economy, International Journal of Operations & Production Management, 33 (2013), 656-688. doi: 10.1108/IJOPM-10-2011-0401.

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J. D. LintonR. Klassen and V. Jayaraman, Sustainable supply chains: An introduction, Journal of Operations Management, 25 (2007), 1075-1082. doi: 10.1016/j.jom.2007.01.012.

[27]

Z. L. LiuT. D. Anderson and J. M. Cruz, Consumer environmental awareness and competition in two-stage supply chains, European Journal of Operational Research, 218 (2012), 602-613. doi: 10.1016/j.ejor.2011.11.027.

[28]

M. KurdveS. ShahbaziM. WendinC. Bengtsson and M. Wiktorsson, Waste flow mapping to improve sustainability of waste management: A case study approach, Journal of Cleaner Production, 98 (2015), 304-315. doi: 10.1016/j.jclepro.2014.06.076.

[29]

M. Y. JaberC. H. Glock and A. M. A. El Saadany, Supply chain coordination with emissions reduction incentives, International Journal of Production Research, 51 (2013), 69-82. doi: 10.1080/00207543.2011.651656.

[30]

W. MoonW. J. FlorkowskiB. Brückner and I. Schonhof, Willingness to pay for environmental practices: Implications for eco-labeling, Land Economics, 78 (2002), 88-102. doi: 10.2307/3146925.

[31]

S. Muthulingam, C. J. Corbett, S. Benartzi and B. Oppenheim, Managerial biases and energy savings: An empirical analysis of the adoption of process improvement recommendations, UCLA Anderson School of Management Working Paper, (2009).

[32]

N. MurovecR. S. Erker and I. Prodan, Determinants of environmental investments: Testing the structural model, Journal of Cleaner Production, 37 (2012), 265-277. doi: 10.1016/j.jclepro.2012.07.024.

[33]

M. Pagell and Z. Wu, Building a more complete theory of sustainable supply chain management using case studies of 10 exemplars, Journal of Supply Chain Management, 45 (2009), 37-56. doi: 10.1111/j.1745-493X.2009.03162.x.

[34]

K. PalmerW. E. Oates and P. R. Portney, Tightening environmental standards: The benefit-cost or the no-cost paradigm?, Journal of Economic Perspectives, 9 (1995), 119-133. doi: 10.1257/jep.9.4.119.

[35]

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D. Popp, Lessons from patents: Using patents to measure technological change in environmental models, Ecological Economics, 54 (2005), 209-226. doi: 10.1016/j.ecolecon.2005.01.001.

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A. RobotisT. Boyaci and V. Verter, Investing in reusability of products of uncertain remanufacturing cost: The role of inspection capabilities, International Journal of Production Economics, 140 (2012), 385-395. doi: 10.1016/j.ijpe.2012.04.017.

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S. PatalaS. HämäläinenA. Jalkala and H.-L. Pesonen, Towards a broader perspective on the forms of eco-industrial networks, Journal of Cleaner Production, 82 (2014), 166-178. doi: 10.1016/j.jclepro.2014.06.059.

[40]

J. SarkisQ. Zhu and K.-H. Lai, An organizational theoretic review of green supply chain management literature, International Journal of Production Economics, 130 (2011), 1-15. doi: 10.1016/j.ijpe.2010.11.010.

[41]

I. Schumacher, Ecolabeling, consumers' preferences and taxation, Ecological Economics, 69 (2010), 2202-2212. doi: 10.1016/j.ecolecon.2010.06.005.

[42]

S. Seuring, Integrated chain management and supply chain management comparative analysis and illustrative cases, Journal of Cleaner Production, 12 (2004), 1059-1071. doi: 10.1016/j.jclepro.2004.02.006.

[43]

S. ZanoniL. Mazzoldi and M. Y. Jaber, Vendor-managed inventory with consignment stock agreement for single vendor-single buyer under the emission-trading scheme, International Journal of Production Research, 52 (2014), 20-31. doi: 10.1080/00207543.2013.812812.

[44]

B. SundarakaniR. de SouzaM. GohS. M. Wagner and S. Manikandan, Modeling carbon footprints across the supply chain, International Journal of Production Economics, 128 (2010), 43-50. doi: 10.1016/j.ijpe.2010.01.018.

[45]

A. ToptalH. Özlü and D. Konur, Joint decisions on inventory replenishment and emission reduction investment under different emission regulations, International Journal of Production Research, 52 (2014), 243-269. doi: 10.1080/00207543.2013.836615.

[46]

G. T. Tsoulfas and C. P. Pappis, Environmental principles applicable to supply chains design and operation, Journal of Cleaner Production, 14 (2006), 1593-1602. doi: 10.1016/j.jclepro.2005.05.021.

[47]

P. WindrumT. Ciarli and C. Birchenhall, Environmental impact, quality, and price: Consumer trade-offs and the development of environmentally friendly technologies, Technological Forecasting and Social Change, 76 (2009), 552-566. doi: 10.1016/j.techfore.2008.04.012.

[48]

C.-H. Wu, Price and service competition between new and remanufactured products in a two-echelon supply chain, International Journal of Production Economics, 140 (2012), 496-507. doi: 10.1016/j.ijpe.2012.06.034.

[49]

J. M. Yu and M. L. Mallory, An optimal hybrid emission control system in a multiple compliance period model, Resource and Energy Economics, 39 (2015), 16-28. doi: 10.1016/j.reseneeco.2014.11.003.

[50]

Z. D. XiaoB. B. CaoJ. N. Sun and G. H. Zhou, Culture of the stability in an eco-industrial system centered on complex network theory, Journal of Cleaner Production, 113 (2016), 730-742. doi: 10.1016/j.jclepro.2015.11.096.

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G. Xie, Modeling decision processes of a green supply chain with regulation on energy saving level, Computers and Operations Research, 54 (2015), 266-273. doi: 10.1016/j.cor.2013.11.020.

[52]

G. Xie, Cooperative strategies for sustainability in a decentralized supply chain with competing suppliers, Journal of Cleaner Production, 113 (2016), 807-821. doi: 10.1016/j.jclepro.2015.11.013.

[53]

G. XieW. Y. Yue and S. Y. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal of Industrial and Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.

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A. Z. Zeng, Coordination mechanisms for a three-stage reverse supply chain to increase profitable returns, Naval Research Logistics, 60 (2013), 31-45. doi: 10.1002/nav.21517.

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Q. ZhangW. S. Tang and J. X. Zhang, Green supply chain performance with cost learning and operational inefficiency effects, Journal of Cleaner Production, 112 (2016), 3267-3284. doi: 10.1016/j.jclepro.2015.10.069.

show all references

References:
[1]

A. ChoudharyR. SumanV. DixitM. K. TiwariK. J. Fernandes and P. C. Chang, An optimization model for a monopolistic firm serving an environmentally conscious market: Use of chemical reaction optimization algorithm, International Journal of Production Economics, 164 (2015), 409-420. doi: 10.1016/j.ijpe.2014.10.011.

[2]

P. Bansal and B. McKnight, Looking forward, pushing back and peering sideways: Analyzing the sustainability of industrial symbiosis, Journal of Supply Chain Management, 45 (2009), 26-37. doi: 10.1111/j.1745-493X.2009.03174.x.

[3]

B. Yalabik and R. J. Fairchild, Customer, regulatory, and competitive pressure as drivers of environmental innovation, International Journal of Production Economics, 131 (2011), 519-527. doi: 10.1016/j.ijpe.2011.01.020.

[4]

S. BenjaafarY. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transactions on Automation Science and Engineering, 10 (2013), 99-116. doi: 10.1109/TASE.2012.2203304.

[5]

B. M. SophaA. M. FetM. M. Keitsch and C. Haskins, Using systems engineering to create a framework for evaluating industrial symbiosis, Systems Engineering, 13 (2010), 149-160. doi: 10.1002/sys.20139.

[6]

B. Kim and J. E. Sim, Impacts of government and market on firm's efforts to reduce pollution, Cogent Economics & Finance, 3 (2015), 1062634. doi: 10.1080/23322039.2015.1062634.

[7]

K. K. BoyerA. M. Prud'homme and W. Chung, The last mile challenge: evaluating the effects of customer density and delivery window patterns, Journal of Business Logistics, 30 (2009), 185-202. doi: 10.1002/j.2158-1592.2009.tb00104.x.

[8]

C. L. Chen, Design for the environment: A quality-based model for green product development, Management Science, 47 (2001), 250-263. doi: 10.1287/mnsc.47.2.250.9841.

[9]

C. L. Chen and G. E. Monahan, Environmental safety stock: The impacts of regulatory and voluntary control policies on production planning, inventory control, and environmental performance, European Journal of Operational Research, 207 (2010), 1280-1292. doi: 10.1016/j.ejor.2010.06.028.

[10]

C.-C. HsuK. C. TanS. H. M. Zailani and V. Jayaraman, Supply chain drivers that foster the development of green initiatives in an emerging economy, International Journal of Operations & Production Management, 33 (2013), 656-688. doi: 10.1108/IJOPM-10-2011-0401.

[11]

C. J. Corbett and R. D. Klassen, Extending the horizons: Environmental excellence as key to improving operations, Manufacturing & Service Operations Management, 8 (2006), 5-22. doi: 10.1287/msom.1060.0095.

[12]

D. Lee, Turning waste into by-product, Manufacturing & Service Operations Management, 14 (2012), 115-127. doi: 10.1287/msom.1110.0352.

[13]

C. DingK. H. Wang and S. Y. Lai, Channel coordination mechanism with retailers having fairness preference-An improved quantity discount mechanism, Journal of Industrial and Management Optimization, 9 (2013), 967-982. doi: 10.3934/jimo.2013.9.967.

[14]

S. F. DuL. Hu and L. Wang, Low-carbon supply policies and supply chain performance with carbon concerned demand, Annals of Operations Research, (2015), 1-22. doi: 10.1007/s10479-015-1988-0.

[15]

G. Herczeg, R. Akkerman and M. Z. Hauschild, Supply chain coordination in industrial symbiosis, Proceedings of the 20th International EurOMA Conference, June 7-12, Dublin, Ireland, (2013), paper SCM-19.

[16]

B. C. Giri and S. Bardhan, Coordinating a two-echelon supply chain with environmentally aware consumers, International Journal of Management Science and Engineering Management, 11 (2015), 178-185. doi: 10.1080/17509653.2015.1004203.

[17]

N. Hamza and D. Greenwood, Energy conservation regulations: Impacts on design and procurement flow energy buildings, Build Environment, 44 (2009), 929-936. doi: 10.1016/j.buildenv.2008.06.010.

[18]

S. L. Hart, A natural-resource-based view of the firm, Academy of Management Review, 20 (1995), 986-1014.

[19]

A. J. Hoffman and M. H. Bazerman, Changing environmental practice: Understanding and overcoming the organizational and psychological barriers, Harvard Business School Working Paper, (2005), 5-43.

[20]

X. P. HongZ. J. WangD. Z. Wang and H. G. Zhang, Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection, International Journal of Advance Manufacture Technology, 68 (2013), 1851-1865. doi: 10.1007/s00170-013-4982-1.

[21]

M. HuangM. SongL. H. Lee and W. K. Ching, Analysis for strategy of closed-loop supply chain with dual recycling channel, International Journal of Production Economics, 144 (2013), 510-520. doi: 10.1016/j.ijpe.2013.04.002.

[22]

V. JayaramanR. Klassen and J. D. Linton, Supply chain management in a sustainable environment, Journal of Operations Management, 25 (2007), 1071-1074. doi: 10.1016/j.jom.2007.01.016.

[23]

J. K. Stranlund and L. J. Moffitt, Enforcement and price controls in emissions trading, Journal of Environmental Economics and Management, 67 (2014), 20-38. doi: 10.1016/j.jeem.2013.10.001.

[24]

J. R. DuflouJ. W. SutherlandD. DornfeldC. HerrmannJ. JeswietS. KaraM. Hauschild and K. Kellens, Towards energy and resource efficient manufacturing: A process and system approach, CIRP Annals-Manufacturing Technology, 61 (2012), 587-609. doi: 10.1016/j.cirp.2012.05.002.

[25]

J. M. Cruz, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision making, European Journal of Operational Research, 184 (2008), 1005-1031. doi: 10.1016/j.ejor.2006.12.012.

[26]

J. D. LintonR. Klassen and V. Jayaraman, Sustainable supply chains: An introduction, Journal of Operations Management, 25 (2007), 1075-1082. doi: 10.1016/j.jom.2007.01.012.

[27]

Z. L. LiuT. D. Anderson and J. M. Cruz, Consumer environmental awareness and competition in two-stage supply chains, European Journal of Operational Research, 218 (2012), 602-613. doi: 10.1016/j.ejor.2011.11.027.

[28]

M. KurdveS. ShahbaziM. WendinC. Bengtsson and M. Wiktorsson, Waste flow mapping to improve sustainability of waste management: A case study approach, Journal of Cleaner Production, 98 (2015), 304-315. doi: 10.1016/j.jclepro.2014.06.076.

[29]

M. Y. JaberC. H. Glock and A. M. A. El Saadany, Supply chain coordination with emissions reduction incentives, International Journal of Production Research, 51 (2013), 69-82. doi: 10.1080/00207543.2011.651656.

[30]

W. MoonW. J. FlorkowskiB. Brückner and I. Schonhof, Willingness to pay for environmental practices: Implications for eco-labeling, Land Economics, 78 (2002), 88-102. doi: 10.2307/3146925.

[31]

S. Muthulingam, C. J. Corbett, S. Benartzi and B. Oppenheim, Managerial biases and energy savings: An empirical analysis of the adoption of process improvement recommendations, UCLA Anderson School of Management Working Paper, (2009).

[32]

N. MurovecR. S. Erker and I. Prodan, Determinants of environmental investments: Testing the structural model, Journal of Cleaner Production, 37 (2012), 265-277. doi: 10.1016/j.jclepro.2012.07.024.

[33]

M. Pagell and Z. Wu, Building a more complete theory of sustainable supply chain management using case studies of 10 exemplars, Journal of Supply Chain Management, 45 (2009), 37-56. doi: 10.1111/j.1745-493X.2009.03162.x.

[34]

K. PalmerW. E. Oates and P. R. Portney, Tightening environmental standards: The benefit-cost or the no-cost paradigm?, Journal of Economic Perspectives, 9 (1995), 119-133. doi: 10.1257/jep.9.4.119.

[35]

R. L. Paquin and J. Howard-Grenville, Blind dates and arranged marriages: Longitudinal processes of network orchestration, Organization Studies, 34 (2013), 1623-1653. doi: 10.1177/0170840612470230.

[36]

C. C. PoirierM. L. Swink and F. J. Quinn, Sixth annual global survey of supply chain progress: Still chasing the leaders, Supply Chain Management Review, 12 (2008), 26-32.

[37]

D. Popp, Lessons from patents: Using patents to measure technological change in environmental models, Ecological Economics, 54 (2005), 209-226. doi: 10.1016/j.ecolecon.2005.01.001.

[38]

A. RobotisT. Boyaci and V. Verter, Investing in reusability of products of uncertain remanufacturing cost: The role of inspection capabilities, International Journal of Production Economics, 140 (2012), 385-395. doi: 10.1016/j.ijpe.2012.04.017.

[39]

S. PatalaS. HämäläinenA. Jalkala and H.-L. Pesonen, Towards a broader perspective on the forms of eco-industrial networks, Journal of Cleaner Production, 82 (2014), 166-178. doi: 10.1016/j.jclepro.2014.06.059.

[40]

J. SarkisQ. Zhu and K.-H. Lai, An organizational theoretic review of green supply chain management literature, International Journal of Production Economics, 130 (2011), 1-15. doi: 10.1016/j.ijpe.2010.11.010.

[41]

I. Schumacher, Ecolabeling, consumers' preferences and taxation, Ecological Economics, 69 (2010), 2202-2212. doi: 10.1016/j.ecolecon.2010.06.005.

[42]

S. Seuring, Integrated chain management and supply chain management comparative analysis and illustrative cases, Journal of Cleaner Production, 12 (2004), 1059-1071. doi: 10.1016/j.jclepro.2004.02.006.

[43]

S. ZanoniL. Mazzoldi and M. Y. Jaber, Vendor-managed inventory with consignment stock agreement for single vendor-single buyer under the emission-trading scheme, International Journal of Production Research, 52 (2014), 20-31. doi: 10.1080/00207543.2013.812812.

[44]

B. SundarakaniR. de SouzaM. GohS. M. Wagner and S. Manikandan, Modeling carbon footprints across the supply chain, International Journal of Production Economics, 128 (2010), 43-50. doi: 10.1016/j.ijpe.2010.01.018.

[45]

A. ToptalH. Özlü and D. Konur, Joint decisions on inventory replenishment and emission reduction investment under different emission regulations, International Journal of Production Research, 52 (2014), 243-269. doi: 10.1080/00207543.2013.836615.

[46]

G. T. Tsoulfas and C. P. Pappis, Environmental principles applicable to supply chains design and operation, Journal of Cleaner Production, 14 (2006), 1593-1602. doi: 10.1016/j.jclepro.2005.05.021.

[47]

P. WindrumT. Ciarli and C. Birchenhall, Environmental impact, quality, and price: Consumer trade-offs and the development of environmentally friendly technologies, Technological Forecasting and Social Change, 76 (2009), 552-566. doi: 10.1016/j.techfore.2008.04.012.

[48]

C.-H. Wu, Price and service competition between new and remanufactured products in a two-echelon supply chain, International Journal of Production Economics, 140 (2012), 496-507. doi: 10.1016/j.ijpe.2012.06.034.

[49]

J. M. Yu and M. L. Mallory, An optimal hybrid emission control system in a multiple compliance period model, Resource and Energy Economics, 39 (2015), 16-28. doi: 10.1016/j.reseneeco.2014.11.003.

[50]

Z. D. XiaoB. B. CaoJ. N. Sun and G. H. Zhou, Culture of the stability in an eco-industrial system centered on complex network theory, Journal of Cleaner Production, 113 (2016), 730-742. doi: 10.1016/j.jclepro.2015.11.096.

[51]

G. Xie, Modeling decision processes of a green supply chain with regulation on energy saving level, Computers and Operations Research, 54 (2015), 266-273. doi: 10.1016/j.cor.2013.11.020.

[52]

G. Xie, Cooperative strategies for sustainability in a decentralized supply chain with competing suppliers, Journal of Cleaner Production, 113 (2016), 807-821. doi: 10.1016/j.jclepro.2015.11.013.

[53]

G. XieW. Y. Yue and S. Y. Wang, Optimal selection of cleaner products in a green supply chain with risk aversion, Journal of Industrial and Management Optimization, 11 (2015), 515-528. doi: 10.3934/jimo.2015.11.515.

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Figure 1.  Environmental regulations and waste flow in industrial symbiosis chain
Figure 2.  Effect of $\alpha_{2}$ on price of product A
Figure 3.  Effect of $\alpha_{2}$ on waste emission level of product A
Figure 4.  Effect of $\beta_{2}$ on price of product B
Figure 5.  Effect of $\beta_{2}$ on waste emission level of product B
Figure 6.  Effect of $\alpha_{2}$ and $\beta_{2}$ on the system profit
Figure 7.  Effect of $\alpha_{1}$ on price of product A
Figure 8.  Effect of $\alpha_{1}$ on waste emission level of product A
Figure 9.  Effect of $\beta_{1}$ on price of product B
Figure 10.  Effect of $\beta_{1}$ on waste emission level of product B
Figure 11.  Effect of $\alpha_{1}$ and $\beta_{1}$ on the system profit
Table 1.  The optimal interval of waste emission standard (only for product A)
Waste emission standardOptimal waste emission level and price
$\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}\le\bar\gamma_{A}^{I} < \bar U_{A}^{I}$$\gamma_{A}^{I^{*}}=\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}$
$p_{A}^{I^{*}}=p^{I}$
$\underline U_{A}^{I} < \bar\gamma_{A}^{I} < \frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}$$\gamma_{A}^{I^{*}}=\bar\gamma_{A}^{I}$
$p_{A}^{I^{*}}=\frac{-\alpha_{1}\bar\gamma_{A}^{I}\tau-\alpha_{2}\bar\gamma_{A}^{I}+\alpha_{1}c_{A}+a}{2\alpha_{1}}$
$\bar\gamma_{A}^{I}\ge\bar U_{A}^{I}$ or $\bar\gamma_{A}^{I}\le\underline U_{A}^{I}$withdraw from the market
$\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}\le\bar\gamma_{A}^{NI} < \bar U_{A}^{NI}$$\gamma_{A}^{NI^{*}}=\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}$
$p_{A}^{NI^{*}}=p^{NI}$
$\underline U_{A}^{NI} < \bar\gamma_{A}^{NI} < \frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}$$\gamma_{A}^{NI^{*}}=\bar\gamma_{A}^{NI}$
$p_{A}^{NI^{*}}=\frac{-\alpha_{1}\bar\gamma_{A}^{NI}p_{W}-\alpha_{2}\bar\gamma_{A}^{NI}+\alpha_{1}c_{A}+a}{2\alpha_{1}}$
$\bar\gamma_{A}^{NI}\ge\bar U_{A}^{NI}$ or $\bar\gamma_{A}^{NI}\le\underline U_{A}^{NI}$withdraw from the market
Waste emission standardOptimal waste emission level and price
$\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}\le\bar\gamma_{A}^{I} < \bar U_{A}^{I}$$\gamma_{A}^{I^{*}}=\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}$
$p_{A}^{I^{*}}=p^{I}$
$\underline U_{A}^{I} < \bar\gamma_{A}^{I} < \frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}$$\gamma_{A}^{I^{*}}=\bar\gamma_{A}^{I}$
$p_{A}^{I^{*}}=\frac{-\alpha_{1}\bar\gamma_{A}^{I}\tau-\alpha_{2}\bar\gamma_{A}^{I}+\alpha_{1}c_{A}+a}{2\alpha_{1}}$
$\bar\gamma_{A}^{I}\ge\bar U_{A}^{I}$ or $\bar\gamma_{A}^{I}\le\underline U_{A}^{I}$withdraw from the market
$\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}\le\bar\gamma_{A}^{NI} < \bar U_{A}^{NI}$$\gamma_{A}^{NI^{*}}=\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}$
$p_{A}^{NI^{*}}=p^{NI}$
$\underline U_{A}^{NI} < \bar\gamma_{A}^{NI} < \frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}$$\gamma_{A}^{NI^{*}}=\bar\gamma_{A}^{NI}$
$p_{A}^{NI^{*}}=\frac{-\alpha_{1}\bar\gamma_{A}^{NI}p_{W}-\alpha_{2}\bar\gamma_{A}^{NI}+\alpha_{1}c_{A}+a}{2\alpha_{1}}$
$\bar\gamma_{A}^{NI}\ge\bar U_{A}^{NI}$ or $\bar\gamma_{A}^{NI}\le\underline U_{A}^{NI}$withdraw from the market
Table 2.  The optimal price, waste emission level and system profit
ParametersBase
model
Integrated
model
Non-integrated
model
Price of product A188140.51128.13
Waste emission level of product A3835.8936.60
Price of product B124.86124.57138.86
Waste emission level of product B17.4317.2924.43
System profit8427.8624173.9023115.00
ParametersBase
model
Integrated
model
Non-integrated
model
Price of product A188140.51128.13
Waste emission level of product A3835.8936.60
Price of product B124.86124.57138.86
Waste emission level of product B17.4317.2924.43
System profit8427.8624173.9023115.00
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