Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

Qingguo Bai; Jianteng Xu; Fanwen Meng; Niu Yu

doi:10.3934/jimo.2020126

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November 2021, 17(6): 3417-3444. doi: 10.3934/jimo.2020126

Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

Qingguo Bai ^1, , Jianteng Xu ^1, , Fanwen Meng ^2,, and Niu Yu ^3,

1.	School of Management, Qufu Normal University, Rizhao, Shandong, 276826, China
2.	Department of Health Services and Outcomes Research, National Healthcare Group, Singapore 138543
3.	School of Management, Wuhan Textile University, Wuhan, Hubei, 430200, China

^* Corresponding author: Fanwen Meng

Received January 2020 Revised March 2020 Published November 2021 Early access June 2020

Fund Project: The research is partly supported by the National Natural Science Foundation of China under grants 71771138, 71702087 and 71701154, Humanities and Social Sciences Youth Foundation of Ministry of Education of China under grant 17YJC630004, Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061, and Science and Technology Research Program for Higher Education of Shandong Province, China under Grant 2019KJI006

This paper incorporates carbon emission regulation and cost learning effects to examine a manufacturer-retailer supply chain for deteriorating items over a multi-period planning horizon. We investigate their impacts on supply chain coordination under the assumption that the product demand is affected by the selling price, promotional effort and inventory level. We first propose two algorithms for determining optimal solutions of the centralized and decentralized models. We show that the decentralized system can be coordinated perfectly with a two-part tariff contract. Further, we study necessary conditions under which members of the supply chain can accept this contract. At last, we conduct numerical experiment to illustrate the obtained theoretical results in impact analysis and the robustness of the coordinated model.

Keywords: Supply chain coordination, cap-and-trade, perishable product, cost learning, Taguchi method.

Mathematics Subject Classification: Primary: 90B60, 91A05; Secondary: 90C46.

Citation: Qingguo Bai, Jianteng Xu, Fanwen Meng, Niu Yu. Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3417-3444. doi: 10.3934/jimo.2020126

References:

[1]	Q. G. Bai, M. Y. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, Int. J. Prod. Econ., 187 (2017), 85-101. Google Scholar
[2]	Q. G. Bai, Y. M. Gong, M. Z. Jin and X. H. Xu, Effects of carbon emission reduction on supply chain coordination with vendor-managed deteriorating product inventory, Int. J. Prod. Econ., 208 (2019), 83-99. doi: 10.1016/j.ijpe.2018.11.008. Google Scholar
[3]	Q. G. Bai, X. H. Xu, J. T. Xu and D. Wang, Coordinating a supply chain for deteriorating items with multi-factor-dependent demand over a finite planning horizon, Appl. Math. Model., 40 (2016), 9342-9361. doi: 10.1016/j.apm.2016.06.021. Google Scholar
[4]	K. Biel and C. H. Glock, Governing the dynamics of multi-stage production systems subjects to learning and forgetting effects: A simulation study, Int. J. Prod. Res., 56 (2018), 3439-3461. doi: 10.1080/00207543.2017.1338780. Google Scholar
[5]	A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Manage. Sci., 51 (2015), 566-580. doi: 10.1287/mnsc.1040.0342. Google Scholar
[6]	L. T. Chen and C. C. Wei, Multi-period channel coordination in vendor-managed inventory for deteriorating goods, Int. J. Prod. Res., 50 (2012), 4396-4413. doi: 10.1080/00207543.2011.592159. Google Scholar
[7]	T. H. Chen and Y. C. Tsao, Optimal lot-sizing integration policy under learning and rework effects in a manufacturer-retailer chain, Int. J. Prod. Econ., 155 (2014), 239-248. doi: 10.1016/j.ijpe.2014.02.011. Google Scholar
[8]	S. H. Chung and C. Kwon, Integrated supply chain management for perishable products: Dynamics and oligopolistic competition perspectives with application to pharmaceuticals, Int. J. Prod. Econ., 179 (2016), 117-129. doi: 10.1016/j.ijpe.2016.05.021. Google Scholar
[9]	S. F. Du, L. Hu and M. L. Song, Production optimization considering environmental performance and preference in the cap-and-trade system, J. Clean. Prod., 112 (2016), 1600-1607. doi: 10.1016/j.jclepro.2014.08.086. Google Scholar
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[11]	European Commission, (2013), https://ec.europa.eu/clima/policies/ets_en. Google Scholar
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[13]	Q. Feng and L. X. Lu, Supply chain contracting under competition: Bilateral bargaining vs. stackelberg, Prod. Oper. Manag., 22 (2013), 661-675. Google Scholar
[14]	B. C. Giri and S. Bardhan, Supply chain coordination for a deteriorating item with stock and price-dependent demand under revenue sharing contract, Int. T. Oper. Res., 19 (2012), 753-768. doi: 10.1111/j.1475-3995.2011.00833.x. Google Scholar
[15]	B. C. Giri and C. H. Glock, A closed-loop supply chain with stochastic product returns and worker experience under learning and forgetting, Int. J. Prod. Res., 55 (2017), 6760-6778. doi: 10.1080/00207543.2017.1347301. Google Scholar
[16]	C. H. Glock and M. Y. Jaber, A multi-stage production-inventory model with learning and forgetting effects, rework and scrap, Comput. Ind. Eng., 64 (2013), 708-720. doi: 10.1016/j.cie.2012.08.018. Google Scholar
[17]	H. Gurnani and M. Erkoc, Supply contracts in manufacturer-retailer interactions with manufacturer-quality and retailer effort-induced demand, Nav. Res. Log., 55 (2008), 200-217. doi: 10.1002/nav.20277. Google Scholar
[18]	T.-W. Hung and P.-T. Chen, On the optimal replenishment in a finite planning horizon with learning effect of setup costs, J. Ind. Manag. Optim., 6 (2010), 425-433. doi: 10.3934/jimo.2010.6.425. Google Scholar
[19]	M. Y. Jaber and A. L. Guiffrida, Learning curves for imperfect production processes with reworks and process restoration interruptions, Eur. J. Oper. Res., 189 (2008), 93-104. doi: 10.1016/j.ejor.2007.05.024. Google Scholar
[20]	M. Y. Jaber and A. M. A. EI Saadany, An economic production and remanufacturing model with learning effects, Int. J. Prod. Econ., 131 (2011), 115-127. Google Scholar
[21]	N. Kazemi, E. U. Olugu, S. H. Abdul-Rashid and R. A. R. Ghazilla, A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters: An empirical study, Comput. Ind. Eng., 96 (2016), 140-148. doi: 10.1016/j.cie.2016.03.004. Google Scholar
[22]	N. Kazemi, E. Shekarian, L. E. Cárdenas-Barrón and E. U. Olugu, Incorporating human learning into a fuzzy EOQ inventory model with backorders, Comput. Ind. Eng., 87 (2015), 540-542. doi: 10.1016/j.cie.2015.05.014. Google Scholar
[23]	M. Khan, M. Hussain and L. E. C$\acute{a}$rdenas-Barr$\acute{o}$n, Learning and screening errors in an EPQ inventory model for supply chains with stochatic lead time demands, Int. J. Prod. Res., 55 (2017), 4816-4832. Google Scholar
[24]	M. Khan, M. Y. Jaber and A. R. Ahmad, An integrated supply chain model with errors in quality inspection and learning in production, Omega, 42 (2014), 16-24. doi: 10.1016/j.omega.2013.02.002. Google Scholar
[25]	K. Kogan, F. EI Ouardighi and A. Herbon, Production with learing and forgetting in a competitive environment, Int. J. Prod. Econ., 189 (2017), 52-62. Google Scholar
[26]	T. Li, S. P. Sethi and X. L. He, Dynamic pricing, production, and channel coordination with stochastic learning, Prod. Oper. Manag., 24 (2015), 857-882. doi: 10.1111/poms.12320. Google Scholar
[27]	C. Lin and Y. Lin, A cooperative inventory policy with deteriorating items for a two-echelon model, Eur. J. Oper. Res., 178 (2007), 92-111. doi: 10.1016/j.ejor.2006.01.012. Google Scholar
[28]	J. R. Luo and X. Chen, Coordination of random yield supply chains with improved revenue sharing contracts, Eur. J. Ind. Eng., 10 (2016), 81-102. doi: 10.1504/EJIE.2016.075105. Google Scholar
[29]	Z. Luo, X. Chen and X. J. Wang, The role of co-opetition in low carbon manufacturing, Eur. J. Oper. Res., 253 (2016), 392-403. doi: 10.1016/j.ejor.2016.02.030. Google Scholar
[30]	B. Lus and A. Muriel, Measuring the impact of increased product substitution on pricing and capacity decisions under linear demand models, Prod. Oper. Manag., 18 (2009), 95-113. doi: 10.1111/j.1937-5956.2009.01001.x. Google Scholar
[31]	L. Moussawi-Haidar, M. Salameh and W. Nasr, Production lot sizing with qualtiy screening and rework, Appl. Math. Model., 40 (2016), 3242-3256. doi: 10.1016/j.apm.2015.09.095. Google Scholar
[32]	E. L. Plambeck, Reducing greenhouse gas emissions through operations and supply chain management, Energ. Econ., 34 (2012), s64–s74. doi: 10.1016/j.eneco.2012.08.031. Google Scholar
[33]	B. R. Sarker and B. Wu, Optimal models for a single-producer multi-buyer integrated system of deteriorating items with raw materials storage costs, Int. J. Adv. Manu. Tech., 82 (2016), 49-63. doi: 10.1007/s00170-015-7340-7. Google Scholar
[34]	G. Taguchi, Tables of orthogonal arrays and linear graphs, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs., 7 (1960), 1-52. Google Scholar
[35]	G. Taguchi, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, Kraus International, White Plains, NY, 1987. Google Scholar
[36]	J.-T. Teng, K.-R. Lou and L. Wang, Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs, Int. J. Prod. Econ., 155 (2014), 318-323. doi: 10.1016/j.ijpe.2013.10.012. Google Scholar
[37]	Y.-C. Tsao and G.-J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Comput. Oper. Res., 39 (2012), 1872-1878. doi: 10.1016/j.cor.2011.07.009. Google Scholar
[38]	M. Wang, L. D. Zhao and M. Herty, Joint replenishement and carbon trading in fresh food supply chains, Eur. J. Oper. Res., 277 (2019), 561-573. doi: 10.1016/j.ejor.2019.03.004. Google Scholar
[39]	T. Wright, Factors affecting the cost of airplanes, J. Aeronaut. Sci., 3 (1936), 122-128. doi: 10.2514/8.155. Google Scholar
[40]	C. F. Wu and Q. H. Zhao, An uncoorperative ordering policy with time-varying price and learning curve for time-varying demand under trade credit, Eur. J. Ind. Eng., 11 (2017), 380-402. Google Scholar
[41]	J. C. P. Yu, A collaborative strategy for deteriorating inventory system with imperfect items and supplier credits, Int. J. Prod. Econ., 143 (2013), 403-409. Google Scholar
[42]	S. Zanoni, M. Y. Jaber and L. E. Zavanella, Vendor managed inventory (VMI) with consignment considering learning and forgetting effects, Int. J. Prod. Econ., 140 (2012), 721-730. doi: 10.1016/j.ijpe.2011.08.018. Google Scholar
[43]	J. Zhang, J. Li, L. Lu and R. Dai, Supply chain performance for deteriorating items with cooperative advertising, J. Syst. Sci. Syst. Eng., 26 (2017), 23-49. doi: 10.1007/s11518-015-5279-8. Google Scholar
[44]	J. X. Zhang, G. W. Liu, Q. Zhang and Z. Y. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49. doi: 10.1016/j.omega.2015.03.004. Google Scholar
[45]	S. Zhang and J. Zhang, Contract preference with stochastic cost leanring in a two-period supply chain under asymmetric information, Int. J. Prod. Econ., 196 (2018), 226-247. Google Scholar

show all references

References:

[1]	Q. G. Bai, M. Y. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, Int. J. Prod. Econ., 187 (2017), 85-101. Google Scholar
[2]	Q. G. Bai, Y. M. Gong, M. Z. Jin and X. H. Xu, Effects of carbon emission reduction on supply chain coordination with vendor-managed deteriorating product inventory, Int. J. Prod. Econ., 208 (2019), 83-99. doi: 10.1016/j.ijpe.2018.11.008. Google Scholar
[3]	Q. G. Bai, X. H. Xu, J. T. Xu and D. Wang, Coordinating a supply chain for deteriorating items with multi-factor-dependent demand over a finite planning horizon, Appl. Math. Model., 40 (2016), 9342-9361. doi: 10.1016/j.apm.2016.06.021. Google Scholar
[4]	K. Biel and C. H. Glock, Governing the dynamics of multi-stage production systems subjects to learning and forgetting effects: A simulation study, Int. J. Prod. Res., 56 (2018), 3439-3461. doi: 10.1080/00207543.2017.1338780. Google Scholar
[5]	A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Manage. Sci., 51 (2015), 566-580. doi: 10.1287/mnsc.1040.0342. Google Scholar
[6]	L. T. Chen and C. C. Wei, Multi-period channel coordination in vendor-managed inventory for deteriorating goods, Int. J. Prod. Res., 50 (2012), 4396-4413. doi: 10.1080/00207543.2011.592159. Google Scholar
[7]	T. H. Chen and Y. C. Tsao, Optimal lot-sizing integration policy under learning and rework effects in a manufacturer-retailer chain, Int. J. Prod. Econ., 155 (2014), 239-248. doi: 10.1016/j.ijpe.2014.02.011. Google Scholar
[8]	S. H. Chung and C. Kwon, Integrated supply chain management for perishable products: Dynamics and oligopolistic competition perspectives with application to pharmaceuticals, Int. J. Prod. Econ., 179 (2016), 117-129. doi: 10.1016/j.ijpe.2016.05.021. Google Scholar
[9]	S. F. Du, L. Hu and M. L. Song, Production optimization considering environmental performance and preference in the cap-and-trade system, J. Clean. Prod., 112 (2016), 1600-1607. doi: 10.1016/j.jclepro.2014.08.086. Google Scholar
[10]	C.-Y. Dye, Optimal joint dynamic pricing, advertising and inventory control model for perishable items with psychic stcok effect, Eur. J. Oper. Res., 283 (2020), 576-587. doi: 10.1016/j.ejor.2019.11.008. Google Scholar
[11]	European Commission, (2013), https://ec.europa.eu/clima/policies/ets_en. Google Scholar
[12]	L. Feng and Y.-L. Chan, Joint pricing and producdtion decisions for new products with learning curve effects under upstream and downstream trade credits., Eur. J. Oper. Res., 272 (2019), 905-913. doi: 10.1016/j.ejor.2018.07.003. Google Scholar
[13]	Q. Feng and L. X. Lu, Supply chain contracting under competition: Bilateral bargaining vs. stackelberg, Prod. Oper. Manag., 22 (2013), 661-675. Google Scholar
[14]	B. C. Giri and S. Bardhan, Supply chain coordination for a deteriorating item with stock and price-dependent demand under revenue sharing contract, Int. T. Oper. Res., 19 (2012), 753-768. doi: 10.1111/j.1475-3995.2011.00833.x. Google Scholar
[15]	B. C. Giri and C. H. Glock, A closed-loop supply chain with stochastic product returns and worker experience under learning and forgetting, Int. J. Prod. Res., 55 (2017), 6760-6778. doi: 10.1080/00207543.2017.1347301. Google Scholar
[16]	C. H. Glock and M. Y. Jaber, A multi-stage production-inventory model with learning and forgetting effects, rework and scrap, Comput. Ind. Eng., 64 (2013), 708-720. doi: 10.1016/j.cie.2012.08.018. Google Scholar
[17]	H. Gurnani and M. Erkoc, Supply contracts in manufacturer-retailer interactions with manufacturer-quality and retailer effort-induced demand, Nav. Res. Log., 55 (2008), 200-217. doi: 10.1002/nav.20277. Google Scholar
[18]	T.-W. Hung and P.-T. Chen, On the optimal replenishment in a finite planning horizon with learning effect of setup costs, J. Ind. Manag. Optim., 6 (2010), 425-433. doi: 10.3934/jimo.2010.6.425. Google Scholar
[19]	M. Y. Jaber and A. L. Guiffrida, Learning curves for imperfect production processes with reworks and process restoration interruptions, Eur. J. Oper. Res., 189 (2008), 93-104. doi: 10.1016/j.ejor.2007.05.024. Google Scholar
[20]	M. Y. Jaber and A. M. A. EI Saadany, An economic production and remanufacturing model with learning effects, Int. J. Prod. Econ., 131 (2011), 115-127. Google Scholar
[21]	N. Kazemi, E. U. Olugu, S. H. Abdul-Rashid and R. A. R. Ghazilla, A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters: An empirical study, Comput. Ind. Eng., 96 (2016), 140-148. doi: 10.1016/j.cie.2016.03.004. Google Scholar
[22]	N. Kazemi, E. Shekarian, L. E. Cárdenas-Barrón and E. U. Olugu, Incorporating human learning into a fuzzy EOQ inventory model with backorders, Comput. Ind. Eng., 87 (2015), 540-542. doi: 10.1016/j.cie.2015.05.014. Google Scholar
[23]	M. Khan, M. Hussain and L. E. C$\acute{a}$rdenas-Barr$\acute{o}$n, Learning and screening errors in an EPQ inventory model for supply chains with stochatic lead time demands, Int. J. Prod. Res., 55 (2017), 4816-4832. Google Scholar
[24]	M. Khan, M. Y. Jaber and A. R. Ahmad, An integrated supply chain model with errors in quality inspection and learning in production, Omega, 42 (2014), 16-24. doi: 10.1016/j.omega.2013.02.002. Google Scholar
[25]	K. Kogan, F. EI Ouardighi and A. Herbon, Production with learing and forgetting in a competitive environment, Int. J. Prod. Econ., 189 (2017), 52-62. Google Scholar
[26]	T. Li, S. P. Sethi and X. L. He, Dynamic pricing, production, and channel coordination with stochastic learning, Prod. Oper. Manag., 24 (2015), 857-882. doi: 10.1111/poms.12320. Google Scholar
[27]	C. Lin and Y. Lin, A cooperative inventory policy with deteriorating items for a two-echelon model, Eur. J. Oper. Res., 178 (2007), 92-111. doi: 10.1016/j.ejor.2006.01.012. Google Scholar
[28]	J. R. Luo and X. Chen, Coordination of random yield supply chains with improved revenue sharing contracts, Eur. J. Ind. Eng., 10 (2016), 81-102. doi: 10.1504/EJIE.2016.075105. Google Scholar
[29]	Z. Luo, X. Chen and X. J. Wang, The role of co-opetition in low carbon manufacturing, Eur. J. Oper. Res., 253 (2016), 392-403. doi: 10.1016/j.ejor.2016.02.030. Google Scholar
[30]	B. Lus and A. Muriel, Measuring the impact of increased product substitution on pricing and capacity decisions under linear demand models, Prod. Oper. Manag., 18 (2009), 95-113. doi: 10.1111/j.1937-5956.2009.01001.x. Google Scholar
[31]	L. Moussawi-Haidar, M. Salameh and W. Nasr, Production lot sizing with qualtiy screening and rework, Appl. Math. Model., 40 (2016), 3242-3256. doi: 10.1016/j.apm.2015.09.095. Google Scholar
[32]	E. L. Plambeck, Reducing greenhouse gas emissions through operations and supply chain management, Energ. Econ., 34 (2012), s64–s74. doi: 10.1016/j.eneco.2012.08.031. Google Scholar
[33]	B. R. Sarker and B. Wu, Optimal models for a single-producer multi-buyer integrated system of deteriorating items with raw materials storage costs, Int. J. Adv. Manu. Tech., 82 (2016), 49-63. doi: 10.1007/s00170-015-7340-7. Google Scholar
[34]	G. Taguchi, Tables of orthogonal arrays and linear graphs, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs., 7 (1960), 1-52. Google Scholar
[35]	G. Taguchi, System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Costs, Kraus International, White Plains, NY, 1987. Google Scholar
[36]	J.-T. Teng, K.-R. Lou and L. Wang, Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs, Int. J. Prod. Econ., 155 (2014), 318-323. doi: 10.1016/j.ijpe.2013.10.012. Google Scholar
[37]	Y.-C. Tsao and G.-J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Comput. Oper. Res., 39 (2012), 1872-1878. doi: 10.1016/j.cor.2011.07.009. Google Scholar
[38]	M. Wang, L. D. Zhao and M. Herty, Joint replenishement and carbon trading in fresh food supply chains, Eur. J. Oper. Res., 277 (2019), 561-573. doi: 10.1016/j.ejor.2019.03.004. Google Scholar
[39]	T. Wright, Factors affecting the cost of airplanes, J. Aeronaut. Sci., 3 (1936), 122-128. doi: 10.2514/8.155. Google Scholar
[40]	C. F. Wu and Q. H. Zhao, An uncoorperative ordering policy with time-varying price and learning curve for time-varying demand under trade credit, Eur. J. Ind. Eng., 11 (2017), 380-402. Google Scholar
[41]	J. C. P. Yu, A collaborative strategy for deteriorating inventory system with imperfect items and supplier credits, Int. J. Prod. Econ., 143 (2013), 403-409. Google Scholar
[42]	S. Zanoni, M. Y. Jaber and L. E. Zavanella, Vendor managed inventory (VMI) with consignment considering learning and forgetting effects, Int. J. Prod. Econ., 140 (2012), 721-730. doi: 10.1016/j.ijpe.2011.08.018. Google Scholar
[43]	J. Zhang, J. Li, L. Lu and R. Dai, Supply chain performance for deteriorating items with cooperative advertising, J. Syst. Sci. Syst. Eng., 26 (2017), 23-49. doi: 10.1007/s11518-015-5279-8. Google Scholar
[44]	J. X. Zhang, G. W. Liu, Q. Zhang and Z. Y. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49. doi: 10.1016/j.omega.2015.03.004. Google Scholar
[45]	S. Zhang and J. Zhang, Contract preference with stochastic cost leanring in a two-period supply chain under asymmetric information, Int. J. Prod. Econ., 196 (2018), 226-247. Google Scholar

Figure 1. Graphical representation of inventory level at the retailer

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Figure 2. Intervals of contract parameters to attain the win-win outcome

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Figure 3. Impacts of $ C $ on profit and total emissions amount

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Figure 4. Impacts of $ c_{p} $ on profit and total emissions amount

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Figure 5. Impacts of $ \phi $ on profit and total emissions amount

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Figure 6. Effects plot for the SN ratio of the coordination system

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Table 1. The optimal solution of the example

Model	$ w $	$ s $	$ p $	$ n $	Retailer's	Manufacturer's	Total	Total emissions
					profit	profit	profit	amount
Centralized	-	12.15	213.75	3	-	-	25589.00	285270
Decentralized	56.76	6.08	256.88	3	3622.10	17045.00	20667.10	142640
TT contract
$ F=9850 $	50	12.15	213.75	3	8539.00	17050.00	25589.00	285270
$ F=12000 $	50	12.15	213.75	3	6389.00	19200.00	25589.00	285270
$ F=14750 $	50	12.15	213.75	3	3639.00	21950.00	25589.00	285270

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Model	$ w $	$ s $	$ p $	$ n $	Retailer's	Manufacturer's	Total	Total emissions
					profit	profit	profit	amount
Centralized	-	12.15	213.75	3	-	-	25589.00	285270
Decentralized	56.76	6.08	256.88	3	3622.10	17045.00	20667.10	142640
TT contract
$ F=9850 $	50	12.15	213.75	3	8539.00	17050.00	25589.00	285270
$ F=12000 $	50	12.15	213.75	3	6389.00	19200.00	25589.00	285270
$ F=14750 $	50	12.15	213.75	3	3639.00	21950.00	25589.00	285270

Table 2. Calculation results of $ L_{8} $ orthogonal array experiment for the coordination model

No.	A	B	C	D	E	Total profit	SN ratio of	Total emissions	SN ratio of total
	$ h_{r} $	$ \theta $	$ \phi $	$ C $	$ c_{p} $		total profit	amount	emissions amount
1	1	1	1	1	1	43394	92.75	284600	-109.085
2	1	1	1	2	2	38191	91.64	309080	-109.801
3	1	2	2	1	1	15727	83.93	259150	-108.271
4	1	2	2	2	2	6371	76.08	280390	-108.955
5	2	1	2	1	2	39551	91.94	314060	-109.940
6	2	1	2	2	1	32531	90.25	289570	-109.235
7	2	2	1	1	2	15409	83.76	284830	-109.092
8	2	2	1	2	1	13943	82.89	263590	-108.419

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No.	A	B	C	D	E	Total profit	SN ratio of	Total emissions	SN ratio of total
	$ h_{r} $	$ \theta $	$ \phi $	$ C $	$ c_{p} $		total profit	amount	emissions amount
1	1	1	1	1	1	43394	92.75	284600	-109.085
2	1	1	1	2	2	38191	91.64	309080	-109.801
3	1	2	2	1	1	15727	83.93	259150	-108.271
4	1	2	2	2	2	6371	76.08	280390	-108.955
5	2	1	2	1	2	39551	91.94	314060	-109.940
6	2	1	2	2	1	32531	90.25	289570	-109.235
7	2	2	1	1	2	15409	83.76	284830	-109.092
8	2	2	1	2	1	13943	82.89	263590	-108.419

Table 3. Analysis of variance for the total profits and its SN ratio

(a) Analysis of variance for the total profits
Source	df	SS($ \times10^{8} $)	MS($ \times10^{8} $)	F	P
A	1	0.0063	0.0063	0.11	0.776
B	1	13.0604	13.0604	217.25	0.005
C	1	0.3510	0.3510	5.84	0.137
D	1	0.6639	0.6639	11.04	0.080
E	1	0.0461	0.0461	0.77	0.474
Error	2	0.1202	0.0601	-	-
Total	7	14.2480	-	-	-
(b) Analysis of variance for the SN ratio of the total profits
Source	df	SS	MS	F	P
A	1	2.450	2.450	0.43	0.581
B	1	199.178	199.178	34.55	0.028
C	1	9.734	9.734	1.69	0.323
D	1	16.603	16.603	2.88	0.232
E	1	5.109	5.109	0.89	0.446
Error	2	11.529	5.765	-	-
Total	7	244.604	-	-	-

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(a) Analysis of variance for the total profits
Source	df	SS($ \times10^{8} $)	MS($ \times10^{8} $)	F	P
A	1	0.0063	0.0063	0.11	0.776
B	1	13.0604	13.0604	217.25	0.005
C	1	0.3510	0.3510	5.84	0.137
D	1	0.6639	0.6639	11.04	0.080
E	1	0.0461	0.0461	0.77	0.474
Error	2	0.1202	0.0601	-	-
Total	7	14.2480	-	-	-
(b) Analysis of variance for the SN ratio of the total profits
Source	df	SS	MS	F	P
A	1	2.450	2.450	0.43	0.581
B	1	199.178	199.178	34.55	0.028
C	1	9.734	9.734	1.69	0.323
D	1	16.603	16.603	2.88	0.232
E	1	5.109	5.109	0.89	0.446
Error	2	11.529	5.765	-	-
Total	7	244.604	-	-	-

Table 4. Analysis of variance for the carbon emissions and its SN ratio

(a) Analysis of variance for the carbon emissions
Source	df	SS($ \times10^{8} $)	MS($ \times10^{8} $)	F	P
A	1	0.4432	0.4432	16.84	0.055
B	1	14.9468	14.9468	567.78	0.002
C	1	0.0014	0.0014	0.05	0.837
D	1	0.0000	0.0000	0.00	0.998
E	1	10.4539	10.4539	397.11	0.003
Error	2	0.0527	0.0263	-	-
Total	7	25.8979	-	-	-
(b) Analysis of variance for the SN ratio of the carbon emissions
Source	df	SS	MS	F	P
A	1	0.0411	0.04107	157.77	0.006
B	1	1.3819	1.3819	5307.76	0.000
C	1	0.0000	0.0000	0.01	0.920
D	1	0.0001	0.0001	0.25	0.669
E	1	0.9655	0.9655	3708.69	0.000
Error	2	0.0005	0.0003	-	-
Total	7	2.3891	-	-	-

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Download as excel

(a) Analysis of variance for the carbon emissions
Source	df	SS($ \times10^{8} $)	MS($ \times10^{8} $)	F	P
A	1	0.4432	0.4432	16.84	0.055
B	1	14.9468	14.9468	567.78	0.002
C	1	0.0014	0.0014	0.05	0.837
D	1	0.0000	0.0000	0.00	0.998
E	1	10.4539	10.4539	397.11	0.003
Error	2	0.0527	0.0263	-	-
Total	7	25.8979	-	-	-
(b) Analysis of variance for the SN ratio of the carbon emissions
Source	df	SS	MS	F	P
A	1	0.0411	0.04107	157.77	0.006
B	1	1.3819	1.3819	5307.76	0.000
C	1	0.0000	0.0000	0.01	0.920
D	1	0.0001	0.0001	0.25	0.669
E	1	0.9655	0.9655	3708.69	0.000
Error	2	0.0005	0.0003	-	-
Total	7	2.3891	-	-	-

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2020 Impact Factor: 1.801

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2020 Impact Factor: 1.801

American Institute of Mathematical Sciences

Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

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Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

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