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doi: 10.3934/jimo.2021033

Pricing and energy efficiency decisions by manufacturer under channel coordination

1. 

Coordinated Innovation Center for Computable Modelling in Management Science, Yango University, Fujian 350015, China

2. 

Coordinated Innovation Center for Computable Modelling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China

3. 

School of Mathematical Sciences, Sunway University, Malaysia

* Corresponding author: Shuhua Chang

Received  September 2020 Revised  November 2020 Published  February 2021

Fund Project: The first author is supported by the National Basic Research Program (2012CB955804), the Major Research Plan of the National Natural Science Foundation of China (91430108), the National Natural Science Foundation of China (11771322), and the Major Program of Tianjin University of Finance and Economics (ZD1302). The third author is supported by the Humanities and Social Science Research Program of the Ministry of Education of China (19YJCZH174)

The profit level of the green supply chain under two decision modes is explored in cooperative and non-cooperative games, where the variable decision timing in direct channel and retail channel within the manufacturer management is studied based on the theory of observable delay game. This paper discusses how the total profit of the green supply chain can realize the profit of the inferior copy of the superior under the two decision-making modes. In the existing literature, it is usually assumed that the pricing decisions of the manufacturers and retailers are made simultaneously. In this study, our model takes into account not only the decision on the pricing, but also on the product innovation. Decision makers can choose the levels of the decision variables as well as the decision times. The observable delay game theory is applied to the study of the decision-making of price levels and energy efficiency levels in multi-channel supply chains. Early pricing decisions can be extended to the study of the product development process. This is more in line with the development of the market in reality. The results of our model show that: (a) an increase of the product efficiency innovation by the manufacturers will lead to

Citation: Shuhua Chang, Yameng Wang, Xinyu Wang, Kok Lay Teo. Pricing and energy efficiency decisions by manufacturer under channel coordination. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021033
References:
[1]

D. Atkins and L. Liang, A note on competitive supply chains with generalised supply costs, European Journal of Operational Research, 207 (2010), 1316-1320.  doi: 10.1016/j.ejor.2010.07.012.  Google Scholar

[2]

S. R. Bhaskaran and V. Krishnan, Effort, revenue, and cost sharing mechanisms for collaborative new product development, Management Science, 55 (2009), 1152-1169.  doi: 10.1287/mnsc.1090.1010.  Google Scholar

[3]

F. E. BowenP. D. CousinsR. C. LamminG and A. C. Farukt, The role of supply management capabilities in green supply, Production and Operations Management, 10 (2001), 174-189.  doi: 10.1111/j.1937-5956.2001.tb00077.x.  Google Scholar

[4]

G. P. Cachon and A. G. Kök, Competing Manufacturers in a Retail Supply Chain: On Contractual Form and Coordination, Management Science, 56 (2010), 571-589.  doi: 10.1287/mnsc.1090.1122.  Google Scholar

[5]

G. P. Cachón and M. A. Lariviere, Supply chain coordination with revenue sharing contracts: Strengths and limitations, Marketing Science, 51 (2005), 30-44.  doi: 10.1287/mnsc.1040.0215.  Google Scholar

[6]

G. CaiY. Dai and S. X. Zhou, Exclusive channels and revenue sharing in a complementary goods market, Marketing Science, 31 (2012), 172-187.  doi: 10.1287/mksc.1110.0688.  Google Scholar

[7]

J. CaoK. C. So and S. Yin, Impact of an "online-to-store" channel on demand allocation, pricing and profitability, European Journal of Operational Research, 248 (2016), 234-245.  doi: 10.1016/j.ejor.2015.07.014.  Google Scholar

[8]

J. ChemamaM. C. CohenR. Lobel and G. Perakis, Consumer Subsidies with a Strategic Supplier: Commitment vs. Flexibility, Management Science, 65 (2018), 1-33.   Google Scholar

[9]

M. C. CohenR. Lobel and G. Perakis, The impact of demand uncertainty on consumer subsidies for green technology adoption, Management Science, 62 (2016), 1235-1258.  doi: 10.1287/mnsc.2015.2173.  Google Scholar

[10]

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.  Google Scholar

[11]

J. J. CroninJ. S. SmithM. R. GleimE. Ramirez and J. D. Martinez, Green marketing strategies: an examination of stakeholders and the opportunities they present, Journal of the Academy of Marketing Science, 39 (2011), 158-174.  doi: 10.1007/s11747-010-0227-0.  Google Scholar

[12]

S. Dutta and A. M. Weiss, The relationship between a firm's level of technological innovativeness and its pattern of partnership agreements, Marketing Science, 43 (1997), 343-356.  doi: 10.1287/mnsc.43.3.343.  Google Scholar

[13]

Ø. ForosK. P. Hagen and H. J. Kind, Price-dependent profit sharing as a channel coordination device, Management Science, 55 (2009), 1280-1291.  doi: 10.1287/mnsc.1090.1019.  Google Scholar

[14]

E. Gal-Or, First mover and second mover advantages, International Economic Review, 26 (1985), 649-653.  doi: 10.2307/2526710.  Google Scholar

[15]

S. M. Gilbert and V. Cvsa, Strategic commitment to price to stimulate downstream innovation in a supply chain, European Journal of Operational Research, 150 (2003), 617-639.  doi: 10.1016/S0377-2217(02)00590-8.  Google Scholar

[16]

D. Granot and S. Yin, Price and order postponement in a decentralized newsvendor model with multiplicative and price-dependent demand, Operations Research, 56 (2008), 121-139.  doi: 10.1287/opre.1070.0430.  Google Scholar

[17]

J. H. Hamilton and S. M. Slutsky, Endogenous timing in duopoly games: Stackelberg or Cournot equilibria, Games and Economic Behavior, 2 (1990), 29-46.  doi: 10.1016/0899-8256(90)90012-J.  Google Scholar

[18]

A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272.  doi: 10.1287/mksc.2.3.239.  Google Scholar

[19]

D. KrassT. Nedorezov and A. Ovchinnikov, Environmental taxes and the choice of green technology, Production and Operations Management, 22 (2013), 1035-1055.  doi: 10.1111/poms.12023.  Google Scholar

[20]

D. Kuksov and A. Pazgal, Research Note–The effects of cost and competition on slotting allowances, Marketing Science, 26 (2007), 259-267.  doi: 10.1287/mksc.1060.0206.  Google Scholar

[21]

T. LevinaY. LevinJ. McGill and M. Nediak, Strategic consumer cooperation in a name-your-own-price channel, Production and Operations Management, 24 (2015), 1883-1900.  doi: 10.1111/poms.12412.  Google Scholar

[22]

T. LiS. P. Sethi and X. He, Dynamic Pricing, Production, and Channel Coordination with Stochastic Learning, Production and Operations Management, 24 (2015), 857-882.  doi: 10.1111/poms.12320.  Google Scholar

[23]

Z. 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.  Google Scholar

[24]

L. LuoP. K. Kannan and B. T. Ratchford, New product development under channel acceptance, Management Science, 26 (2007), 149-163.  doi: 10.1287/mksc.1060.0240.  Google Scholar

[25]

K. Matsui, When should a manufacturer set its direct price and wholesale price in dual-channel supply chains, European Journal of Operational Research, 258 (2017), 501-511.  doi: 10.1016/j.ejor.2016.08.048.  Google Scholar

[26]

T. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-191.   Google Scholar

[27]

J. Nash, Non-cooperative games, Annals of Mathematics, 54 (1951), 286-295.  doi: 10.2307/1969529.  Google Scholar

[28]

J. Raju and Z. J. Zhang, Channel coordination in the presence of a dominant retailer, Marketing Science, 24 (2005), 254-262.  doi: 10.1287/mksc.1040.0081.  Google Scholar

[29]

V. K. RanganA. A. Zoltners and R. J. Becker, The channel intermediary selection decision: A model and an application, Management Science, 32 (1986), 1114-1122.  doi: 10.1287/mnsc.32.9.1114.  Google Scholar

[30]

B. Rodríguez and G. Aydín, Pricing and assortment decisions for a manufacturer selling through dual channels, European Journal of Operational Research, 242 (2015), 901-909.  doi: 10.1016/j.ejor.2014.10.047.  Google Scholar

[31]

M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896.  Google Scholar

[32]

A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2004), 9-110.   Google Scholar

[33]

D.-Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, Omega, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.  Google Scholar

[34]

A. Yenipazarli, To collaborate or not to collaborate: Prompting upstream eco-efficient innovation in a supply chain, European Journal of Operational Research, 260 (2017), 571-587.  doi: 10.1016/j.ejor.2016.12.035.  Google Scholar

[35]

J. ZhangQ. GouL. Liang and Z. Huang, Supply chain coordination through cooperative advertising with reference price effect, Omega, 41 (2013), 345-353.  doi: 10.1016/j.omega.2012.03.009.  Google Scholar

[36]

L. ZhangJ. Wang and J. You, Consumer environmental awareness and channel coordination with two substitutable products, European Journal of Operational Research, 241 (2015), 63-73.  doi: 10.1016/j.ejor.2014.07.043.  Google Scholar

[37]

W. Zhu and Y. He, Green product design in supply chains under competition, European Journal of Operational Research, 258 (2017), 165-180.  doi: 10.1016/j.ejor.2016.08.053.  Google Scholar

show all references

References:
[1]

D. Atkins and L. Liang, A note on competitive supply chains with generalised supply costs, European Journal of Operational Research, 207 (2010), 1316-1320.  doi: 10.1016/j.ejor.2010.07.012.  Google Scholar

[2]

S. R. Bhaskaran and V. Krishnan, Effort, revenue, and cost sharing mechanisms for collaborative new product development, Management Science, 55 (2009), 1152-1169.  doi: 10.1287/mnsc.1090.1010.  Google Scholar

[3]

F. E. BowenP. D. CousinsR. C. LamminG and A. C. Farukt, The role of supply management capabilities in green supply, Production and Operations Management, 10 (2001), 174-189.  doi: 10.1111/j.1937-5956.2001.tb00077.x.  Google Scholar

[4]

G. P. Cachon and A. G. Kök, Competing Manufacturers in a Retail Supply Chain: On Contractual Form and Coordination, Management Science, 56 (2010), 571-589.  doi: 10.1287/mnsc.1090.1122.  Google Scholar

[5]

G. P. Cachón and M. A. Lariviere, Supply chain coordination with revenue sharing contracts: Strengths and limitations, Marketing Science, 51 (2005), 30-44.  doi: 10.1287/mnsc.1040.0215.  Google Scholar

[6]

G. CaiY. Dai and S. X. Zhou, Exclusive channels and revenue sharing in a complementary goods market, Marketing Science, 31 (2012), 172-187.  doi: 10.1287/mksc.1110.0688.  Google Scholar

[7]

J. CaoK. C. So and S. Yin, Impact of an "online-to-store" channel on demand allocation, pricing and profitability, European Journal of Operational Research, 248 (2016), 234-245.  doi: 10.1016/j.ejor.2015.07.014.  Google Scholar

[8]

J. ChemamaM. C. CohenR. Lobel and G. Perakis, Consumer Subsidies with a Strategic Supplier: Commitment vs. Flexibility, Management Science, 65 (2018), 1-33.   Google Scholar

[9]

M. C. CohenR. Lobel and G. Perakis, The impact of demand uncertainty on consumer subsidies for green technology adoption, Management Science, 62 (2016), 1235-1258.  doi: 10.1287/mnsc.2015.2173.  Google Scholar

[10]

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.  Google Scholar

[11]

J. J. CroninJ. S. SmithM. R. GleimE. Ramirez and J. D. Martinez, Green marketing strategies: an examination of stakeholders and the opportunities they present, Journal of the Academy of Marketing Science, 39 (2011), 158-174.  doi: 10.1007/s11747-010-0227-0.  Google Scholar

[12]

S. Dutta and A. M. Weiss, The relationship between a firm's level of technological innovativeness and its pattern of partnership agreements, Marketing Science, 43 (1997), 343-356.  doi: 10.1287/mnsc.43.3.343.  Google Scholar

[13]

Ø. ForosK. P. Hagen and H. J. Kind, Price-dependent profit sharing as a channel coordination device, Management Science, 55 (2009), 1280-1291.  doi: 10.1287/mnsc.1090.1019.  Google Scholar

[14]

E. Gal-Or, First mover and second mover advantages, International Economic Review, 26 (1985), 649-653.  doi: 10.2307/2526710.  Google Scholar

[15]

S. M. Gilbert and V. Cvsa, Strategic commitment to price to stimulate downstream innovation in a supply chain, European Journal of Operational Research, 150 (2003), 617-639.  doi: 10.1016/S0377-2217(02)00590-8.  Google Scholar

[16]

D. Granot and S. Yin, Price and order postponement in a decentralized newsvendor model with multiplicative and price-dependent demand, Operations Research, 56 (2008), 121-139.  doi: 10.1287/opre.1070.0430.  Google Scholar

[17]

J. H. Hamilton and S. M. Slutsky, Endogenous timing in duopoly games: Stackelberg or Cournot equilibria, Games and Economic Behavior, 2 (1990), 29-46.  doi: 10.1016/0899-8256(90)90012-J.  Google Scholar

[18]

A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272.  doi: 10.1287/mksc.2.3.239.  Google Scholar

[19]

D. KrassT. Nedorezov and A. Ovchinnikov, Environmental taxes and the choice of green technology, Production and Operations Management, 22 (2013), 1035-1055.  doi: 10.1111/poms.12023.  Google Scholar

[20]

D. Kuksov and A. Pazgal, Research Note–The effects of cost and competition on slotting allowances, Marketing Science, 26 (2007), 259-267.  doi: 10.1287/mksc.1060.0206.  Google Scholar

[21]

T. LevinaY. LevinJ. McGill and M. Nediak, Strategic consumer cooperation in a name-your-own-price channel, Production and Operations Management, 24 (2015), 1883-1900.  doi: 10.1111/poms.12412.  Google Scholar

[22]

T. LiS. P. Sethi and X. He, Dynamic Pricing, Production, and Channel Coordination with Stochastic Learning, Production and Operations Management, 24 (2015), 857-882.  doi: 10.1111/poms.12320.  Google Scholar

[23]

Z. 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.  Google Scholar

[24]

L. LuoP. K. Kannan and B. T. Ratchford, New product development under channel acceptance, Management Science, 26 (2007), 149-163.  doi: 10.1287/mksc.1060.0240.  Google Scholar

[25]

K. Matsui, When should a manufacturer set its direct price and wholesale price in dual-channel supply chains, European Journal of Operational Research, 258 (2017), 501-511.  doi: 10.1016/j.ejor.2016.08.048.  Google Scholar

[26]

T. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-191.   Google Scholar

[27]

J. Nash, Non-cooperative games, Annals of Mathematics, 54 (1951), 286-295.  doi: 10.2307/1969529.  Google Scholar

[28]

J. Raju and Z. J. Zhang, Channel coordination in the presence of a dominant retailer, Marketing Science, 24 (2005), 254-262.  doi: 10.1287/mksc.1040.0081.  Google Scholar

[29]

V. K. RanganA. A. Zoltners and R. J. Becker, The channel intermediary selection decision: A model and an application, Management Science, 32 (1986), 1114-1122.  doi: 10.1287/mnsc.32.9.1114.  Google Scholar

[30]

B. Rodríguez and G. Aydín, Pricing and assortment decisions for a manufacturer selling through dual channels, European Journal of Operational Research, 242 (2015), 901-909.  doi: 10.1016/j.ejor.2014.10.047.  Google Scholar

[31]

M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896.  Google Scholar

[32]

A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2004), 9-110.   Google Scholar

[33]

D.-Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, Omega, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.  Google Scholar

[34]

A. Yenipazarli, To collaborate or not to collaborate: Prompting upstream eco-efficient innovation in a supply chain, European Journal of Operational Research, 260 (2017), 571-587.  doi: 10.1016/j.ejor.2016.12.035.  Google Scholar

[35]

J. ZhangQ. GouL. Liang and Z. Huang, Supply chain coordination through cooperative advertising with reference price effect, Omega, 41 (2013), 345-353.  doi: 10.1016/j.omega.2012.03.009.  Google Scholar

[36]

L. ZhangJ. Wang and J. You, Consumer environmental awareness and channel coordination with two substitutable products, European Journal of Operational Research, 241 (2015), 63-73.  doi: 10.1016/j.ejor.2014.07.043.  Google Scholar

[37]

W. Zhu and Y. He, Green product design in supply chains under competition, European Journal of Operational Research, 258 (2017), 165-180.  doi: 10.1016/j.ejor.2016.08.053.  Google Scholar

Figure 1.  Channels describe
Figure 2.  The equilibrium matrix
Figure 3.  Effect of $ g $ on $ \pi^{d} $ and $ \pi^{c} $
Figure 4.  Effect of $ g $ on $ q_{M} $ and $ q_{R} $
Figure 5.  Effects of $ g $ and $ \theta $ on $ \pi^{d} $
Figure 6.  Effects of $ g $ and $ \theta $ on $ \pi^{c} $
Figure 7.  Effects of $ g $ and $ \theta $ on $ q_{M} $ and $ q_{R} $
Figure 8.  Effects of $ g $ and $ \theta $ on $ \pi^{D} $
Table 1.  Notations
$ p_M $ Direct price
$ p_R $ Retail price
$ c $ Marginal cost
$ c_1 $ Wholesale price
$ x $ Level of energy efficiency
$ g $ Sensitivity of energy efficiency levels to demand
$ \theta $ Cross-price sensitivity between the channels
$ a_M $ Intercept of the demand function for the direct channel
$ a_R $ Intercept of the demand function for the retail channel
$ b_M $ Sensitivity of demand in the direct channel to the direct channel price
$ b_R $ Sensitivity of demand in the retail channel to the retail channel price
$ q_M $ The demand at the direct end
$ q_R $ The demand at the retail end
$ t_{c1} $ Period when the manufacturer chooses the wholesale price
$ t_{p_M} $ Period when the manufacturer chooses the direct channel price
$ t_{p_R} $ Period when the retailer chooses the retail channel price
$ t_x $ Period when the manufacture chooses the level of energy efficiency
$ E $ Manufacturer precede retailer in setting direct price
$ S $ Manufacturer and retailer setting the order of direct price at the same time
$ L $ Manufacturer setting the order of direct price later than retailer
$ \pi_M $ Profit for the manufacture under decentralized decision-making
$ \pi_R $ Profit for the retailer under decentralized decision-making
$ \pi_V $ Profit of the whole supply chain under centralized decision-making
$ p_M $ Direct price
$ p_R $ Retail price
$ c $ Marginal cost
$ c_1 $ Wholesale price
$ x $ Level of energy efficiency
$ g $ Sensitivity of energy efficiency levels to demand
$ \theta $ Cross-price sensitivity between the channels
$ a_M $ Intercept of the demand function for the direct channel
$ a_R $ Intercept of the demand function for the retail channel
$ b_M $ Sensitivity of demand in the direct channel to the direct channel price
$ b_R $ Sensitivity of demand in the retail channel to the retail channel price
$ q_M $ The demand at the direct end
$ q_R $ The demand at the retail end
$ t_{c1} $ Period when the manufacturer chooses the wholesale price
$ t_{p_M} $ Period when the manufacturer chooses the direct channel price
$ t_{p_R} $ Period when the retailer chooses the retail channel price
$ t_x $ Period when the manufacture chooses the level of energy efficiency
$ E $ Manufacturer precede retailer in setting direct price
$ S $ Manufacturer and retailer setting the order of direct price at the same time
$ L $ Manufacturer setting the order of direct price later than retailer
$ \pi_M $ Profit for the manufacture under decentralized decision-making
$ \pi_R $ Profit for the retailer under decentralized decision-making
$ \pi_V $ Profit of the whole supply chain under centralized decision-making
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