# American Institute of Mathematical Sciences

May  2022, 18(3): 1557-1582. 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  May 2022 Early access  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 an increase in the demand at the retail channel; (b) the enhancement of consumers’ awareness of the environmental protection and the improvement of the price sensitivity of the double-channel crossing have positive effect on the profit level of the general channel; (c) the manufacturers are motivated to adopt a marketing strategy that masks disadvantages with advantages. After the manufacturer determines the energy efficiency level of the product, it is found that the direct channel to increase the pricing decision time and the creation of input from a high cost are more conducive to achieving higher revenue; (d) after comparing the total profits of the two decision models, the manufacturer can obtain all the surplus profit of the retailer by coordinating the fixed fee of the two-part tariff contract. At the same time, the perfect replication of decentralized decision-making and the total profit level of centralized decisionmaking are realized. Through the coordination of the choice of variable pricing time and tariff contract, not only the perfect Nash equilibrium of non cooperative game is formed, but also the optimal variable decision-making scheme of multi-channel green supply chain is provided for manufacturers to maximize their profits.

Addendum: “The National Natural Science Foundation of China (12101447)” is added so it reads “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 National Natural Science Foundation of China (12101447), and the Humanities and Social Science Research Program of the Ministry of Education of China (19YJCZH174).”

Citation: Shuhua Chang, Yameng Wang, Xinyu Wang, Kok Lay Teo. Pricing and energy efficiency decisions by manufacturer under channel coordination. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1557-1582. 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. [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. [3] F. E. Bowen, P. D. Cousins, R. 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. [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. [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. [6] G. Cai, Y. 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. [7] J. Cao, K. 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. [8] J. Chemama, M. C. Cohen, R. Lobel and G. Perakis, Consumer Subsidies with a Strategic Supplier: Commitment vs. Flexibility, Management Science, 65 (2018), 1-33. [9] M. C. Cohen, R. 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. [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. [11] J. J. Cronin, J. S. Smith, M. R. Gleim, E. 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. [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. [13] Ø. Foros, K. 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. [14] E. Gal-Or, First mover and second mover advantages, International Economic Review, 26 (1985), 649-653.  doi: 10.2307/2526710. [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. [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. [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. [18] A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272.  doi: 10.1287/mksc.2.3.239. [19] D. Krass, T. 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. [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. [21] T. Levina, Y. Levin, J. 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. [22] T. Li, S. 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. [23] Z. Liu, T. 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. [24] L. Luo, P. K. Kannan and B. T. Ratchford, New product development under channel acceptance, Management Science, 26 (2007), 149-163.  doi: 10.1287/mksc.1060.0240. [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. [26] T. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-191. [27] J. Nash, Non-cooperative games, Annals of Mathematics, 54 (1951), 286-295.  doi: 10.2307/1969529. [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. [29] V. K. Rangan, A. 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. [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. [31] M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896. [32] A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2004), 9-110. [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. [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. [35] J. Zhang, Q. Gou, L. 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. [36] L. Zhang, J. 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. [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.

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. [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. [3] F. E. Bowen, P. D. Cousins, R. 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. [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. [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. [6] G. Cai, Y. 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. [7] J. Cao, K. 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. [8] J. Chemama, M. C. Cohen, R. Lobel and G. Perakis, Consumer Subsidies with a Strategic Supplier: Commitment vs. Flexibility, Management Science, 65 (2018), 1-33. [9] M. C. Cohen, R. 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. [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. [11] J. J. Cronin, J. S. Smith, M. R. Gleim, E. 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. [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. [13] Ø. Foros, K. 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. [14] E. Gal-Or, First mover and second mover advantages, International Economic Review, 26 (1985), 649-653.  doi: 10.2307/2526710. [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. [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. [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. [18] A. P. Jeuland and S. M. Shugan, Managing channel profits, Marketing Science, 2 (1983), 239-272.  doi: 10.1287/mksc.2.3.239. [19] D. Krass, T. 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. [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. [21] T. Levina, Y. Levin, J. 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. [22] T. Li, S. 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. [23] Z. Liu, T. 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. [24] L. Luo, P. K. Kannan and B. T. Ratchford, New product development under channel acceptance, Management Science, 26 (2007), 149-163.  doi: 10.1287/mksc.1060.0240. [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. [26] T. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-191. [27] J. Nash, Non-cooperative games, Annals of Mathematics, 54 (1951), 286-295.  doi: 10.2307/1969529. [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. [29] V. K. Rangan, A. 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. [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. [31] M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896. [32] A. Tsay and N. Agrawal, Channel conflict and coordination in the e-commerce age, Production and Operations Management, 13 (2004), 9-110. [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. [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. [35] J. Zhang, Q. Gou, L. 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. [36] L. Zhang, J. 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. [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.
Channels describe
The equilibrium matrix
Effect of $g$ on $\pi^{d}$ and $\pi^{c}$
Effect of $g$ on $q_{M}$ and $q_{R}$
Effects of $g$ and $\theta$ on $\pi^{d}$
Effects of $g$ and $\theta$ on $\pi^{c}$
Effects of $g$ and $\theta$ on $q_{M}$ and $q_{R}$
Effects of $g$ and $\theta$ on $\pi^{D}$
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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