# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2022086
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## Strategic service investment by retailers confronted by manufacturer encroachment

 1 School of Management and Economics, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China 2 School of Management and Economics; Center for Digital Culture and Media Studies, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China

*Corresponding author: Junwu Chai

Received  July 2021 Revised  April 2022 Early access June 2022

Fund Project: The authors thank the National Natural Science Foundation of China (71872028) and the Digital Culture and Media Research Fund of Philosophy and Social Sciences Research Base in Sichuan Province (19CDCM03)

This study investigates the service strategies of retailers confronted by manufacturer encroachment and explores the influences of retail services on profitability under different channel structures. In contrast to previous studies, this paper differentiates between channel costs and considers retail service. First, it is demonstrated that retail services are profitable for supply chain members under certain circumstances, regardless of whether the retail service effort is endogenous or exogenous. In particular, when the service effort is endogenous, the retailer can optimize its service effort to influence sales and profit outcomes. Second, this study finds that a service strategy can cause harm to manufacturers while benefiting retailers, which can help retailers regain market dominance and make manufacturers less competitive. The findings also suggest that there can be a "lose-lose" outcome due to service inefficiencies and intense competition. Third, the results indicate that a retailer would prefer to improve their service effort if market competition is less intense or the retail channel has obvious cost advantages. As the service effort increases, a manufacturer has little incentive to encroach on the market. Finally, consumer surplus and service spillovers are discussed.

Citation: Hengyu Li, Junwu Chai. Strategic service investment by retailers confronted by manufacturer encroachment. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022086
##### References:
 [1] A. Arya, B. Mittendorf and D. E. M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659. [2] W. Y. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Science, 49 (2003), 1-20. [3] B. Dan, G. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. [4] A. Ha, X. Long and J. Nasiry, Quality in supply chain encroachment, Manufacturing & Service Operations Management, 18 (2016), 280-298. [5] S. Huang, X. G. Guan and Y. J. Chen, Retailer information sharing with supplier encroachment, Production and Operations Management, 27 (2018), 1089-1101. [6] Y. Liu, S. Gupta and Z. J. Zhang, Note on self-restraint as an online entry-deterrence strategy, Management Science, 52 (2006), 1799-1809. [7] Z. Li, S. M. Gilbert and G. Lai, Supplier encroachment under asymmetric information, Management Science, 60 (2014), 449-462. [8] T. Li, J. Xie and X. Zhao, Supplier encroachment in competitive supply chains, International Journal of Production Economics, 165 (2015), 120-131. [9] L. Luo and J. Sun, New product design under channel acceptance: Brick-and-mortar, online-exclusive, or brick-and-click, Production and Operation Management, 25 (2016), 2014-2034. [10] Y. Xiong, W. Yan and K. Fernandes, 'Bricks vs. clicks': The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, European Journal of Operational Research, 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012. [11] R. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, Journal of Retailing and Consumer Services, 16 (2009), 306-314. [12] D.-H. Yoon, Supplier encroachment and investment spillovers, Production and Operations Management, 25 (2016), 1839-1854. [13] S. Zhang, J. Zhang and G. Zhu, Retail service investing: an anti-encroachment strategy in a retailer-led supply chain, Omega, 84 (2016), 212-231. [14] X. Guan, B. Liu, Y. Chen and H. Wang, Inducing supply chain transparency through supplier encroachment, Production and Operations Management, 29 (2020), 725-749. [15] S. Zheng and Y. Yu, Manufacturer encroachment with equal pricing strategy, Transportation Research Part E: Logistics and Transportation Review, 152 (2021), 102346. [16] P. Hotkar and S. M. Gilbert, Supplier Encroachment in a Nonexclusive Reselling Channel, Management Science, 67 (2021), 5821-5837. [17] J. Zhang, Q. Cao and X. He, Manufacturer encroachment with advertising, Omega, 91 (2020), 102013. [18] T. Zhang, X. Feng and N. Wang, Manufacturer encroachment and product assortment under vertical differentiation, European Journal of Operational Research, 293 (2021), 120-132.  doi: 10.1016/j.ejor.2020.11.044. [19] X. Wu, J. Zhao and M. Wang, Managing cost reduction efforts in supplier encroachment, Mathematical Problems in Engineering, (2021), 1–6. doi: 10.1155/2021/6638830. [20] B. Liu, X. Guan and Y. Wang, Supplier encroachment with multiple retailers, Production and Operations Management, (2021). doi: 10.1111/poms.13447. [21] H. Yang, J. Luo and Q. Zhang, Supplier encroachment under nonlinear pricing with imperfect substitutes: Bargaining power versus revenue-sharing, European Journal of Operational Research, 267 (2018), 1089-1101.  doi: 10.1016/j.ejor.2017.12.027. [22] K. Matsui, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, European Journal of Operational Research, 287 (2020), 225-236.  doi: 10.1016/j.ejor.2020.05.004. [23] L. H. Zhang and C. Zhang, Manufacturer encroachment with capital-constrained competitive retailers, European Journal of Operational Research, 296 (2022), 1067-1083.  doi: 10.1016/j.ejor.2021.05.027. [24] S. Zhang, Y. Yao and J. Zhang, Consumer showrooming with supplier encroachment and omnichannel retail, Decision Sciences, (2021). doi: 10.1111/deci.12539. [25] J. Li, L. Yi, V. Shi and X. Chen, Supplier encroachment strategy in the presence of retail strategic inventory: Centralization or decentralization?, Omega, 98 (2021), 102213. [26] H. Guan, H. Gurnani, X. Geng and Y. Luo, Strategic inventory and supplier encroachment, Manufacturing & Service Operations Management, 21 (2019), 536-555. [27] L. H. Zhang, J. Yao and L. Xu, Emission reduction and market encroachment: Whether the manufacturer opens a direct channel or not?, Journal of Cleaner Production, 269 (2020), 121932. [28] J. Li, J. Liang, V. Shi and J. Zhu, The benefit of manufacturer encroachment considering consumer's environmental awareness and product competition, Annals of Operations Research, (2021), 1–21. [29] W. Hu and Y. Li, Retail service for mixed retail and E-tail channels, Annals of Operations Research, 192 (2012), 151-171.  doi: 10.1007/s10479-010-0818-7. [30] G. Li, L. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E: Logistics and Transportation Review, 126 (2019), 32-48. [31] L. Zhao, J. You and S. C. Fang, A dual-channel supply chain problem with resource-utilization penalty: Who can benefit from sales effort?, Journal of Industrial & Management Optimization, 17 (2021), 2837.  doi: 10.3934/jimo.2020097. [32] X. Chen, X. Wang and X. Jiang, The impact of power structure on the retail service supply chain with an O2O mixed channel, Journal of the Operational Research Society, 67 (2016), 294-301. [33] C. Dong, L. Yang and C. T. Ng, Quantity leadership for a dual-channel supply chain with retail service, Asia-Pacific Journal of Operational Research, 37 (2020), 2050005.  doi: 10.1142/S0217595920500050. [34] W. Zhao, C. Ye and X. Ding, Preferred service investment in the dual-channel supply chain: Leader-follower relationships and product characteristics, Mathematical Problems in Engineering, (2020). doi: 10.1155/2020/1656094. [35] Y. Jiang, L. Liu and A. Lim, Optimal pricing decisions for an omni-channel supply chain with retail service, International Transactions in Operational Research, 27 (2020), 2927-2948.  doi: 10.1111/itor.12784. [36] J. Guo, Y. Zhou and B. Li, The optimal pricing and service strategies of a dual-channel retailer under free riding, Journal of Industrial & Management Optimization, (2021). doi: 10.3934/jimo.2021056. [37] L. Chai, Y. Duan and J. Huo, Pricing strategies for O2O business model considering service spillover and power structures, International Transactions in Operational Research, 28 (2021), 1978-2001.  doi: 10.1111/itor.12863. [38] J. Hamamura and Y. Zennyo, Retailer voluntary investment against a threat of manufacturer encroachment, Marketing Letters, (2021), 1–17. [39] N. Wang and Z. Li, Supplier encroachment with a dual-purpose retailer, Production and Operations Management, (2021). doi: 10.1111/poms.13400. [40] J. Nie, Q. Wang, C. Shi and Y. Zhou, The dark side of bilateral encroachment within a supply chain, Journal of the Operational Research Society, (2021), 1–11. [41] Z. Zhang, H. Song, X. Gu, V. Shi and J. Zhu, How to compete with a supply chain partner: Retailer's store brand vs. manufacturer's encroachment, Omega, 103 (2021), 102412. [42] Z. Pei and R. Yan, Do channel members value supportive retail services? Why?, Journal of Business Research, 68 (2015), 1350-1358. [43] J. Xia and W. Niu, Adding clicks to bricks: An analysis of supplier encroachment under service spillovers, Electronic Commerce Research and Applications, 37 (2019), 100876. [44] Z. Cao and J. Min, Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain, Journal of Industrial & Management Optimization, (2020). doi: 10.3934/jimo.2020167. [45] S. Feng, J. Liu and X. Hu, Presale strategy for a dual-channel retailer considering sales effort, IEEE Access, 9 (2021), 40318-40335. [46] M. Tu, An exploratory study of internet of things (IoT) adoption intention in logistics and supply chain management: A mixed research approach, The International Journal of Logistics Management, 29 (2018), 131-151. [47] K. Govindan, T. C. E. Cheng, N. Mishra and N. Shukla, Big data analytics and application for logistics and supply chain management, Transportation Research Part E: Logistics and Transportation Review, (2018), 343–349. [48] A. Rey, E. Panetti, R. Maglio and M. Ferretti, Determinants in adopting the internet of things in the transport and logistics industry, Journal of Business Research, 131 (2021), 584-590. [49] J. Sarkis, L. M. Meade and S. Talluri, E-logistics and the natural environment, Supply Chain Management: An International Journal, 9 (2004), 303-312. [50] S. P. Daly and L. X. Cui, E-logistics in China: Basic problems, manageable concerns and intractable solutions, Industrial Marketing Management, 32 (2003), 235-242. [51] C. W. Hsu and C. C. Yeh, Understanding the factors affecting the adoption of the internet of things, Technology Analysis & Strategic Management, 29 (2017), 1089-1102. [52] H. Zhou and W. C. Benton Jr, Supply chain practice and information sharing, Journal of Operations management, 25 (2007), 1348-1365. [53] B. Hu, Y. Mai and S. Pekec, Managing innovation spillover in outsourcing, Production and Operations Management, 29 (2020), 2252-2267. [54] X. Zhang and W. Hou, The impacts of e-tailer's private label on the sales mode selection: From the perspectives of economic and environmental sustainability, European Journal of Operational Research, 296 (2022), 601-614.  doi: 10.1016/j.ejor.2021.04.009.

show all references

##### References:
 [1] A. Arya, B. Mittendorf and D. E. M. Sappington, The bright side of supplier encroachment, Marketing Science, 26 (2007), 651-659. [2] W. Y. K. Chiang, D. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Science, 49 (2003), 1-20. [3] B. Dan, G. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. [4] A. Ha, X. Long and J. Nasiry, Quality in supply chain encroachment, Manufacturing & Service Operations Management, 18 (2016), 280-298. [5] S. Huang, X. G. Guan and Y. J. Chen, Retailer information sharing with supplier encroachment, Production and Operations Management, 27 (2018), 1089-1101. [6] Y. Liu, S. Gupta and Z. J. Zhang, Note on self-restraint as an online entry-deterrence strategy, Management Science, 52 (2006), 1799-1809. [7] Z. Li, S. M. Gilbert and G. Lai, Supplier encroachment under asymmetric information, Management Science, 60 (2014), 449-462. [8] T. Li, J. Xie and X. Zhao, Supplier encroachment in competitive supply chains, International Journal of Production Economics, 165 (2015), 120-131. [9] L. Luo and J. Sun, New product design under channel acceptance: Brick-and-mortar, online-exclusive, or brick-and-click, Production and Operation Management, 25 (2016), 2014-2034. [10] Y. Xiong, W. Yan and K. Fernandes, 'Bricks vs. clicks': The impact of manufacturer encroachment with a dealer leasing and selling of durable goods, European Journal of Operational Research, 217 (2012), 75-83.  doi: 10.1016/j.ejor.2011.08.012. [11] R. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, Journal of Retailing and Consumer Services, 16 (2009), 306-314. [12] D.-H. Yoon, Supplier encroachment and investment spillovers, Production and Operations Management, 25 (2016), 1839-1854. [13] S. Zhang, J. Zhang and G. Zhu, Retail service investing: an anti-encroachment strategy in a retailer-led supply chain, Omega, 84 (2016), 212-231. [14] X. Guan, B. Liu, Y. Chen and H. Wang, Inducing supply chain transparency through supplier encroachment, Production and Operations Management, 29 (2020), 725-749. [15] S. Zheng and Y. Yu, Manufacturer encroachment with equal pricing strategy, Transportation Research Part E: Logistics and Transportation Review, 152 (2021), 102346. [16] P. Hotkar and S. M. Gilbert, Supplier Encroachment in a Nonexclusive Reselling Channel, Management Science, 67 (2021), 5821-5837. [17] J. Zhang, Q. Cao and X. He, Manufacturer encroachment with advertising, Omega, 91 (2020), 102013. [18] T. Zhang, X. Feng and N. Wang, Manufacturer encroachment and product assortment under vertical differentiation, European Journal of Operational Research, 293 (2021), 120-132.  doi: 10.1016/j.ejor.2020.11.044. [19] X. Wu, J. Zhao and M. Wang, Managing cost reduction efforts in supplier encroachment, Mathematical Problems in Engineering, (2021), 1–6. doi: 10.1155/2021/6638830. [20] B. Liu, X. Guan and Y. Wang, Supplier encroachment with multiple retailers, Production and Operations Management, (2021). doi: 10.1111/poms.13447. [21] H. Yang, J. Luo and Q. Zhang, Supplier encroachment under nonlinear pricing with imperfect substitutes: Bargaining power versus revenue-sharing, European Journal of Operational Research, 267 (2018), 1089-1101.  doi: 10.1016/j.ejor.2017.12.027. [22] K. Matsui, Optimal bargaining timing of a wholesale price for a manufacturer with a retailer in a dual-channel supply chain, European Journal of Operational Research, 287 (2020), 225-236.  doi: 10.1016/j.ejor.2020.05.004. [23] L. H. Zhang and C. Zhang, Manufacturer encroachment with capital-constrained competitive retailers, European Journal of Operational Research, 296 (2022), 1067-1083.  doi: 10.1016/j.ejor.2021.05.027. [24] S. Zhang, Y. Yao and J. Zhang, Consumer showrooming with supplier encroachment and omnichannel retail, Decision Sciences, (2021). doi: 10.1111/deci.12539. [25] J. Li, L. Yi, V. Shi and X. Chen, Supplier encroachment strategy in the presence of retail strategic inventory: Centralization or decentralization?, Omega, 98 (2021), 102213. [26] H. Guan, H. Gurnani, X. Geng and Y. Luo, Strategic inventory and supplier encroachment, Manufacturing & Service Operations Management, 21 (2019), 536-555. [27] L. H. Zhang, J. Yao and L. Xu, Emission reduction and market encroachment: Whether the manufacturer opens a direct channel or not?, Journal of Cleaner Production, 269 (2020), 121932. [28] J. Li, J. Liang, V. Shi and J. Zhu, The benefit of manufacturer encroachment considering consumer's environmental awareness and product competition, Annals of Operations Research, (2021), 1–21. [29] W. Hu and Y. Li, Retail service for mixed retail and E-tail channels, Annals of Operations Research, 192 (2012), 151-171.  doi: 10.1007/s10479-010-0818-7. [30] G. Li, L. Li and J. Sun, Pricing and service effort strategy in a dual-channel supply chain with showrooming effect, Transportation Research Part E: Logistics and Transportation Review, 126 (2019), 32-48. [31] L. Zhao, J. You and S. C. Fang, A dual-channel supply chain problem with resource-utilization penalty: Who can benefit from sales effort?, Journal of Industrial & Management Optimization, 17 (2021), 2837.  doi: 10.3934/jimo.2020097. [32] X. Chen, X. Wang and X. Jiang, The impact of power structure on the retail service supply chain with an O2O mixed channel, Journal of the Operational Research Society, 67 (2016), 294-301. [33] C. Dong, L. Yang and C. T. Ng, Quantity leadership for a dual-channel supply chain with retail service, Asia-Pacific Journal of Operational Research, 37 (2020), 2050005.  doi: 10.1142/S0217595920500050. [34] W. Zhao, C. Ye and X. Ding, Preferred service investment in the dual-channel supply chain: Leader-follower relationships and product characteristics, Mathematical Problems in Engineering, (2020). doi: 10.1155/2020/1656094. [35] Y. Jiang, L. Liu and A. Lim, Optimal pricing decisions for an omni-channel supply chain with retail service, International Transactions in Operational Research, 27 (2020), 2927-2948.  doi: 10.1111/itor.12784. [36] J. Guo, Y. Zhou and B. Li, The optimal pricing and service strategies of a dual-channel retailer under free riding, Journal of Industrial & Management Optimization, (2021). doi: 10.3934/jimo.2021056. [37] L. Chai, Y. Duan and J. Huo, Pricing strategies for O2O business model considering service spillover and power structures, International Transactions in Operational Research, 28 (2021), 1978-2001.  doi: 10.1111/itor.12863. [38] J. Hamamura and Y. Zennyo, Retailer voluntary investment against a threat of manufacturer encroachment, Marketing Letters, (2021), 1–17. [39] N. Wang and Z. Li, Supplier encroachment with a dual-purpose retailer, Production and Operations Management, (2021). doi: 10.1111/poms.13400. [40] J. Nie, Q. Wang, C. Shi and Y. Zhou, The dark side of bilateral encroachment within a supply chain, Journal of the Operational Research Society, (2021), 1–11. [41] Z. Zhang, H. Song, X. Gu, V. Shi and J. Zhu, How to compete with a supply chain partner: Retailer's store brand vs. manufacturer's encroachment, Omega, 103 (2021), 102412. [42] Z. Pei and R. Yan, Do channel members value supportive retail services? Why?, Journal of Business Research, 68 (2015), 1350-1358. [43] J. Xia and W. Niu, Adding clicks to bricks: An analysis of supplier encroachment under service spillovers, Electronic Commerce Research and Applications, 37 (2019), 100876. [44] Z. Cao and J. Min, Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain, Journal of Industrial & Management Optimization, (2020). doi: 10.3934/jimo.2020167. [45] S. Feng, J. Liu and X. Hu, Presale strategy for a dual-channel retailer considering sales effort, IEEE Access, 9 (2021), 40318-40335. [46] M. Tu, An exploratory study of internet of things (IoT) adoption intention in logistics and supply chain management: A mixed research approach, The International Journal of Logistics Management, 29 (2018), 131-151. [47] K. Govindan, T. C. E. Cheng, N. Mishra and N. Shukla, Big data analytics and application for logistics and supply chain management, Transportation Research Part E: Logistics and Transportation Review, (2018), 343–349. [48] A. Rey, E. Panetti, R. Maglio and M. Ferretti, Determinants in adopting the internet of things in the transport and logistics industry, Journal of Business Research, 131 (2021), 584-590. [49] J. Sarkis, L. M. Meade and S. Talluri, E-logistics and the natural environment, Supply Chain Management: An International Journal, 9 (2004), 303-312. [50] S. P. Daly and L. X. Cui, E-logistics in China: Basic problems, manageable concerns and intractable solutions, Industrial Marketing Management, 32 (2003), 235-242. [51] C. W. Hsu and C. C. Yeh, Understanding the factors affecting the adoption of the internet of things, Technology Analysis & Strategic Management, 29 (2017), 1089-1102. [52] H. Zhou and W. C. Benton Jr, Supply chain practice and information sharing, Journal of Operations management, 25 (2007), 1348-1365. [53] B. Hu, Y. Mai and S. Pekec, Managing innovation spillover in outsourcing, Production and Operations Management, 29 (2020), 2252-2267. [54] X. Zhang and W. Hou, The impacts of e-tailer's private label on the sales mode selection: From the perspectives of economic and environmental sustainability, European Journal of Operational Research, 296 (2022), 601-614.  doi: 10.1016/j.ejor.2021.04.009.
The supply chain structure
The game theory flowchart
Impact of encroachment without service ($d = 0.5$)
Impact of encroachment with retail services ($d = 0.5$ $s = 1$ $n = 1$)
The retailer's service strategy ($d = 0.8$ $n = 1$ $c = 0.4$)
The impact of service on the manufacturer encroachment threshold ($n = 1$)
Regions with the introduction of service ($d = 0.8$ $n = 1$ $c = 0.4$)
Optimal service effort under different channel structure with variations in $k$, $d$, $c$, $n$
The impact of endogenous service on retailer and total supply chain. ($d = 0.8$ $n = 2$)
The impact of exogenous service on retailer and total supply chain. ($b = 0.8$ $n = 1$ $c = 0.4$)
The impact of endogenous service on retailer and total supply chain. ($b = 0.8$ $n = 2$)
Recently published works
 Literature Channel preference Retail cost Service cost Direct cost Situations Research issues Chen et al. [32] No Yes No Yes Market share, pricing strategy Impact of power structure Pei et al. [42] Yes No Yes No Product compatibility Impact of service Xia et al. [43] Yes No Yes Yes Dominant power structure Impact of encroachment Zhang et al. [13] Yes No Yes Yes Effect of information Impact of service Cao et al. [44] No No Yes Yes Different decision sequences Encroachment and service Wang et al. [39] No No No Yes Consumer surplus and profit Dual-purpose retailer on encroachment Guo et al. [36] Yes No Yes No Degree of free riding Impact of free riding Zhao et al. [31] Yes Yes Yes No Cost-sharing proportion resource-utilization and service impact This study Yes Yes Yes Yes Extra channel and service cost Endogenous and exogenous service strategy
 Literature Channel preference Retail cost Service cost Direct cost Situations Research issues Chen et al. [32] No Yes No Yes Market share, pricing strategy Impact of power structure Pei et al. [42] Yes No Yes No Product compatibility Impact of service Xia et al. [43] Yes No Yes Yes Dominant power structure Impact of encroachment Zhang et al. [13] Yes No Yes Yes Effect of information Impact of service Cao et al. [44] No No Yes Yes Different decision sequences Encroachment and service Wang et al. [39] No No No Yes Consumer surplus and profit Dual-purpose retailer on encroachment Guo et al. [36] Yes No Yes No Degree of free riding Impact of free riding Zhao et al. [31] Yes Yes Yes No Cost-sharing proportion resource-utilization and service impact This study Yes Yes Yes Yes Extra channel and service cost Endogenous and exogenous service strategy
Description of notations
 Indices Description $m, r$ Subscript, represents the manufacturer and the retailer. $i$ Superscript, represents Model N, S, E respectively. Parameters $k$ Unit marginal cost to open the direct channel. $c$ Unit marginal cost to off-line retailing activity. $d$ The degree of consumer acceptance of direct channel. $n$ The cost-effectiveness of the retail service. $v$ The consumer utility on product. $U_m/U_r$ The consumer's willingness-to-pay through direct/retail channel. Independent Variables $q_m^i /q_r^i$ Sales volume via the direct/tradition channel in Model $i$. $s$ The service effort offered by the retailer. $w^i$ Manufacturer's unit wholesale price in Model $i$. Dependent Variables $p_m^i /p_r^i$ Unit market price from the direct/tradition channel in Model $i$. $\pi _m^i /\pi _r^i$ Profit for the manufacturer/retailer in Model $i$.
 Indices Description $m, r$ Subscript, represents the manufacturer and the retailer. $i$ Superscript, represents Model N, S, E respectively. Parameters $k$ Unit marginal cost to open the direct channel. $c$ Unit marginal cost to off-line retailing activity. $d$ The degree of consumer acceptance of direct channel. $n$ The cost-effectiveness of the retail service. $v$ The consumer utility on product. $U_m/U_r$ The consumer's willingness-to-pay through direct/retail channel. Independent Variables $q_m^i /q_r^i$ Sales volume via the direct/tradition channel in Model $i$. $s$ The service effort offered by the retailer. $w^i$ Manufacturer's unit wholesale price in Model $i$. Dependent Variables $p_m^i /p_r^i$ Unit market price from the direct/tradition channel in Model $i$. $\pi _m^i /\pi _r^i$ Profit for the manufacturer/retailer in Model $i$.
Equilibrium outcomes under no services
 Strategy N Direct channel (NM) $k < k_m$ Dual channel (ND) $k_m < k < k_r$ Retail channel (NR) $k>k_r$ $N/A$ $w^{ND} = \frac{{8c + 4d - 4cd + dk - d^2 - 8}}{{6d - 16}}$ $w^{NR} = \frac{1}{2} - \frac{c}{2}$ $N/A$ $q_r^{ND} = \frac{{2c + 2d - 2k - 2}}{{3d - 8}}$ $q_r^{NR} = \frac{1}{4} - \frac{c}{4}$ $q_m^{NM} = \frac{{d - k}}{{2d}}$ $q_m^{ND} = \frac{{ - (6d - 8k + 2cd + dk - d^2 )}}{{2d(3d - 8)}}$ $N/A$ $\pi _m^{NM} = \frac{{(d - k)^2 }}{{4d}}$ $\pi _m^{ND} = \frac{{4c^2 d + 8cd^2 - 8cdk - 8cd + d^3 - 2d^2 k + dk^2 - 8dk + 4d + 8k^2 }}{{ - 4d(3d - 8)}}$ $\pi _m^{NR} = \frac{{(c - 1)^2 }}{8}$ $N/A$ $\pi _r^{ND} = \frac{{4(c + d - k - 1)^2 }}{{(3d - 8)^2 }}$ $\pi _r^{NR} = \frac{{(c - 1)^2 }}{{16}}$
 Strategy N Direct channel (NM) $k < k_m$ Dual channel (ND) $k_m < k < k_r$ Retail channel (NR) $k>k_r$ $N/A$ $w^{ND} = \frac{{8c + 4d - 4cd + dk - d^2 - 8}}{{6d - 16}}$ $w^{NR} = \frac{1}{2} - \frac{c}{2}$ $N/A$ $q_r^{ND} = \frac{{2c + 2d - 2k - 2}}{{3d - 8}}$ $q_r^{NR} = \frac{1}{4} - \frac{c}{4}$ $q_m^{NM} = \frac{{d - k}}{{2d}}$ $q_m^{ND} = \frac{{ - (6d - 8k + 2cd + dk - d^2 )}}{{2d(3d - 8)}}$ $N/A$ $\pi _m^{NM} = \frac{{(d - k)^2 }}{{4d}}$ $\pi _m^{ND} = \frac{{4c^2 d + 8cd^2 - 8cdk - 8cd + d^3 - 2d^2 k + dk^2 - 8dk + 4d + 8k^2 }}{{ - 4d(3d - 8)}}$ $\pi _m^{NR} = \frac{{(c - 1)^2 }}{8}$ $N/A$ $\pi _r^{ND} = \frac{{4(c + d - k - 1)^2 }}{{(3d - 8)^2 }}$ $\pi _r^{NR} = \frac{{(c - 1)^2 }}{{16}}$
Equilibrium outcomes under retail services
 Strategy S Direct channel (NM) $k < k_m$ Dual channel (ND) $k_m < k < k_r$ Retail channel (NR) $k>k_r$ $N/A$ $w^{SD} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}}$ $w^{SR} = \frac{{1 + s}}{2} - \frac{{c(n + 1)}}{2}$ $N/A$ $q_r^{SD} = \frac{{2c + 2d - 2k - 2s + 2cn - 2}}{{3d - 8}}$ $q_r^{SR} = \frac{{1 - c + s - cn}}{4}$ $q_m^{SM} = \frac{{d - k}}{{2d}}$ $q_m^{SD} = \frac{{2(3d - 4k + cd - ds + cdn) + dk - d^2 }}{{ - 2d(3d - 8)}}$ $N/A$ $\pi _m^{SM} = \frac{{(d - k)^2 }}{{4d}}$ $\begin{array}{l} \pi _m^{SD} =\\ \frac{{\left[ \begin{array}{l} 4c^2 dn^2 + 8c^2 dn + 4c^2 d + 8cd^2 n + 8cd^2 \;\;\;\\ - 8cdkn - 8cdk - 8cdns - 8cdn - 8cds\;\;\;\\ - 8cd + d^3 - 2d^2 k - 8d^2 s + dk^2 + 8dks\;\;\;\\ - 8dk + 4ds^2 + 8ds + 4d + 8k^2\\ \end{array} \right]}}{{ - 4d(3d - 8)}}\\ \end{array}$ $\pi _m^{SR} = \frac{{(c - s + cn - 1)^2 }}{8}$ $N/A$ $\pi _r^{SD} = \frac{{4(c + d - k - s + cn - 1)^2 }}{{(3d - 8)^2 }}$ $\pi _r^{SR} = \frac{{(c - s + cn - 1)^2 }}{{16}}$
 Strategy S Direct channel (NM) $k < k_m$ Dual channel (ND) $k_m < k < k_r$ Retail channel (NR) $k>k_r$ $N/A$ $w^{SD} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}}$ $w^{SR} = \frac{{1 + s}}{2} - \frac{{c(n + 1)}}{2}$ $N/A$ $q_r^{SD} = \frac{{2c + 2d - 2k - 2s + 2cn - 2}}{{3d - 8}}$ $q_r^{SR} = \frac{{1 - c + s - cn}}{4}$ $q_m^{SM} = \frac{{d - k}}{{2d}}$ $q_m^{SD} = \frac{{2(3d - 4k + cd - ds + cdn) + dk - d^2 }}{{ - 2d(3d - 8)}}$ $N/A$ $\pi _m^{SM} = \frac{{(d - k)^2 }}{{4d}}$ $\begin{array}{l} \pi _m^{SD} =\\ \frac{{\left[ \begin{array}{l} 4c^2 dn^2 + 8c^2 dn + 4c^2 d + 8cd^2 n + 8cd^2 \;\;\;\\ - 8cdkn - 8cdk - 8cdns - 8cdn - 8cds\;\;\;\\ - 8cd + d^3 - 2d^2 k - 8d^2 s + dk^2 + 8dks\;\;\;\\ - 8dk + 4ds^2 + 8ds + 4d + 8k^2\\ \end{array} \right]}}{{ - 4d(3d - 8)}}\\ \end{array}$ $\pi _m^{SR} = \frac{{(c - s + cn - 1)^2 }}{8}$ $N/A$ $\pi _r^{SD} = \frac{{4(c + d - k - s + cn - 1)^2 }}{{(3d - 8)^2 }}$ $\pi _r^{SR} = \frac{{(c - s + cn - 1)^2 }}{{16}}$
The retailer's service strategy
 Strategy Service effectiveness Direct selling cost Region No service $0  Strategy Service effectiveness Direct selling cost Region No service$ 0
Impact of service on the retailer and manufacturer
 Service effort Direct selling cost $(\Delta \pi _r /\Delta \pi _m)$ Region $0s_1$ $\max \{ 0, k_{ms} (s)\}0$ $k>k_{rs}(s)$ (+, +)(win, win) SR $0  Service effort Direct selling cost$ (\Delta \pi _r /\Delta \pi _m) $Region$ 0s_1  \max \{ 0, k_{ms} (s)\}0  k>k_{rs}(s) $(+, +)(win, win) SR$ 0
Equilibrium outcomes when service effort is endogenous
 Strategy E Direct channel (NM) $k < k_m$ Dual channel (ND) $k_m < k < k_r$ Retail channel (NR) $k>k_r$ $N/A$ $w^{ED} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}}$ $w^{ER} = \frac{{4n(c + cn - 1)}}{{1 - 8n}}$ $N/A$ $s_d^{ED} = \frac{{8 - 8c - 8d + 8k - 8cn}}{{9nd^2 - 48nd + 64n - 8}}$ $s_r^{ER} = \frac{{c + cn - 1}}{{1 - 8n}}$ $N/A$ $q_r^{ED} = \frac{{2n(3d - 8)(c + d - k + cn - 1)}}{{9nd^2 - 48nd + 64n - 8}}$ $q_r^{ER} = \frac{{2n(c + cn - 1)}}{{1 - 8n}}$ $q_m^{EM} = \frac{{d - k}}{{2d}}$ $q_m^{ED} = \frac{{\left[ \begin{array}{l} 8d - 8k - 48dn + 64kn + 26d^2 n \\ - 3d^3 n + 6cd^2 n^2 - 16cdn - 32dkn \;\; \\ - 16cdn^2 + 6cd^2 n + 3d^2 kn \\ \end{array} \right]}}{{ - 2d(9nd^2 - 48nd + 64n - 8)}}$ $N/A$ $\pi _m^{EM} = \frac{{(d - k)^2 }}{{4d}}$ $\pi _m^{ED} =$ shown in appendix proof $\pi _m^{ER} = \frac{{8n^2 (c + cn - 1)^2 }}{{(8n - 1)^2 }}$ $N/A$ $\pi _r^{ED} = \frac{{4n(c + d - k + cn - 1)^2 }}{{9nd^2 - 48nd + 64n - 8}}$ $\pi _r^{ER} = \frac{{n(c + cn - 1)^2 }}{{2(8n - 1)}}$
 Strategy E Direct channel (NM) $k < k_m$ Dual channel (ND) $k_m < k < k_r$ Retail channel (NR) $k>k_r$ $N/A$ $w^{ED} = \frac{{8c + 4d - 8s - 4cd + dk + 8cn + 4ds - d^2 - 4cdn - 8}}{{6d - 16}}$ $w^{ER} = \frac{{4n(c + cn - 1)}}{{1 - 8n}}$ $N/A$ $s_d^{ED} = \frac{{8 - 8c - 8d + 8k - 8cn}}{{9nd^2 - 48nd + 64n - 8}}$ $s_r^{ER} = \frac{{c + cn - 1}}{{1 - 8n}}$ $N/A$ $q_r^{ED} = \frac{{2n(3d - 8)(c + d - k + cn - 1)}}{{9nd^2 - 48nd + 64n - 8}}$ $q_r^{ER} = \frac{{2n(c + cn - 1)}}{{1 - 8n}}$ $q_m^{EM} = \frac{{d - k}}{{2d}}$ $q_m^{ED} = \frac{{\left[ \begin{array}{l} 8d - 8k - 48dn + 64kn + 26d^2 n \\ - 3d^3 n + 6cd^2 n^2 - 16cdn - 32dkn \;\; \\ - 16cdn^2 + 6cd^2 n + 3d^2 kn \\ \end{array} \right]}}{{ - 2d(9nd^2 - 48nd + 64n - 8)}}$ $N/A$ $\pi _m^{EM} = \frac{{(d - k)^2 }}{{4d}}$ $\pi _m^{ED} =$ shown in appendix proof $\pi _m^{ER} = \frac{{8n^2 (c + cn - 1)^2 }}{{(8n - 1)^2 }}$ $N/A$ $\pi _r^{ED} = \frac{{4n(c + d - k + cn - 1)^2 }}{{9nd^2 - 48nd + 64n - 8}}$ $\pi _r^{ER} = \frac{{n(c + cn - 1)^2 }}{{2(8n - 1)}}$
results of comparison when $c<c_1$
 Comparison of retailer's profit Comparison of manufacturer's profit $k 0$ $\pi _m^{ED} - \pi _m^{ND}> 0$ $k_{re} 0$ $k>k_{r}$ if $c 0$ if $c>c_3$, $\pi _r^{ER} - \pi _r^{NR} < 0$ $\pi _m^{ER} - \pi _m^{NR}< 0$
 Comparison of retailer's profit Comparison of manufacturer's profit $k 0$ $\pi _m^{ED} - \pi _m^{ND}> 0$ $k_{re} 0$ $k>k_{r}$ if $c 0$ if $c>c_3$, $\pi _r^{ER} - \pi _r^{NR} < 0$ $\pi _m^{ER} - \pi _m^{NR}< 0$
results of comparison when $c_1<c<c_2$
 Comparison of retailer's profit Comparison of manufacturer's profit $kk_6$, $\pi _r^{ED} - \pi _r^{NR} > 0$ $\pi _m^{ED} - \pi _m^{NR}> 0$ $k>k_{re}$ $\pi _r^{ER} - \pi _r^{NR}< 0$ $\pi _m^{ER} - \pi _m^{NR}< 0$
 Comparison of retailer's profit Comparison of manufacturer's profit $kk_6$, $\pi _r^{ED} - \pi _r^{NR} > 0$ $\pi _m^{ED} - \pi _m^{NR}> 0$ $k>k_{re}$ $\pi _r^{ER} - \pi _r^{NR}< 0$ $\pi _m^{ER} - \pi _m^{NR}< 0$
results of comparison when $c>c_2$
 Comparison of retailer's profit Comparison of manufacturer's profit $kk_{re}$ $\pi _r^{ER} - \pi _r^{NR}< 0$ $\pi _m^{ER} - \pi _m^{NR}< 0$
 Comparison of retailer's profit Comparison of manufacturer's profit $kk_{re}$ $\pi _r^{ER} - \pi _r^{NR}< 0$ $\pi _m^{ER} - \pi _m^{NR}< 0$
Equilibrium outcomes when no service effort
 Strategy N Direct channel (NM) $k<\frac{{c-1+b}}{{b}}$ Dual channel (ND) $\frac{{c-1+b}}{{b}}\frac{{2b-8-2cb+b^2}}{{b^2-8}}$ $N/A$ $w^{ND} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k}}{{2( - 8 + 3b^2 )}}$ $w^{NR} = \frac{{1-c}}{{2}}$ $N/A$ $q_r^{ND} = \frac{{2n(3b - 8)(c + b - k + cn - 1)}}{{9nb^2 - 48nb + 64n - 8}}$ $q_r^{NR} = \frac{{1-c}}{{4}}$ $q_m^{NM} = \frac{{1 - k}}{{2}}$ $q_m^{ND} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k}}{{2(8 - 3b^2 )}}$ $N/A$ $\pi _m^{NM} = \frac{{(k - 1)^2 }}{{4}}$ $\pi _m^{ND} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cd + b^2 - 16k \;\;\\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 \;\;\end{array} \right]}}{{4(8 - 3b^2 )}}$ $\pi _m^{NR} = \frac{{(c - 1)^2 }}{{8}}$ $N/A$ $\pi _r^{ND} = \frac{{4(1 - c - b + bk)^2 }}{{( - 8 + 3b^2 )^2 }}$ $\pi _r^{NR} = \frac{{(c - 1)^2}}{{16}}$
 Strategy N Direct channel (NM) $k<\frac{{c-1+b}}{{b}}$ Dual channel (ND) $\frac{{c-1+b}}{{b}}\frac{{2b-8-2cb+b^2}}{{b^2-8}}$ $N/A$ $w^{ND} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k}}{{2( - 8 + 3b^2 )}}$ $w^{NR} = \frac{{1-c}}{{2}}$ $N/A$ $q_r^{ND} = \frac{{2n(3b - 8)(c + b - k + cn - 1)}}{{9nb^2 - 48nb + 64n - 8}}$ $q_r^{NR} = \frac{{1-c}}{{4}}$ $q_m^{NM} = \frac{{1 - k}}{{2}}$ $q_m^{ND} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k}}{{2(8 - 3b^2 )}}$ $N/A$ $\pi _m^{NM} = \frac{{(k - 1)^2 }}{{4}}$ $\pi _m^{ND} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cd + b^2 - 16k \;\;\\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 \;\;\end{array} \right]}}{{4(8 - 3b^2 )}}$ $\pi _m^{NR} = \frac{{(c - 1)^2 }}{{8}}$ $N/A$ $\pi _r^{ND} = \frac{{4(1 - c - b + bk)^2 }}{{( - 8 + 3b^2 )^2 }}$ $\pi _r^{NR} = \frac{{(c - 1)^2}}{{16}}$
Equilibrium outcomes when service effort is exogenous
 Strategy S Direct channel (SM) $kk_2^S$ $N/A$ $w^{SD} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k + 8cn - 4cb^2 n - 8s + 4b^2 s}}{{2(3b^2 - 8)}}$ $w^{SR} = \frac{{1-c-cn+s}}{{2}}$ $N/A$ $q_r^{SD} = \frac{{2(1 - c - b + bk - cn + s)}}{{8 - 3b^2 }}$ $q_r^{SR} = \frac{{1-c-cn+s}}{{4}}$ $q_m^{SM} = \frac{{1 - k}}{{2}}$ $q_m^{SD} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k + 2cbn - 2bs}}{{2(8 - 3b^2 )}}$ $N/A$ $\pi _m^{SM} = \frac{{(k - 1)^2 }}{{4}}$ $\pi _m^{SD} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cb + b^2 - 16k \\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 - \\ 8cn + 8c^2 n + 8cbn - 8cbkn + 4c^2 n^2 + \;\;\\ 8s - 8cs - 8bs + 8bks - 8cns + 4s^2 \end{array} \right]}}{{4(3b^2 - 8)}}$ $\pi _m^{SR} = \frac{{(c + cn - s - 1)^2 }}{{8}}$ $N/A$ $\pi _r^{SD} = \frac{{4(1 - c - b + bk - cn +s)^2 }}{{( - 8 + 3b^2 )^2 }}$ $\pi _r^{SR} = \frac{{(c + cn - s - 1)^2}}{{16}}$
 Strategy S Direct channel (SM) $kk_2^S$ $N/A$ $w^{SD} = \frac{{ - 8 + 8c + 4b^2 - 4cb^2 - b^3 + b^3 k + 8cn - 4cb^2 n - 8s + 4b^2 s}}{{2(3b^2 - 8)}}$ $w^{SR} = \frac{{1-c-cn+s}}{{2}}$ $N/A$ $q_r^{SD} = \frac{{2(1 - c - b + bk - cn + s)}}{{8 - 3b^2 }}$ $q_r^{SR} = \frac{{1-c-cn+s}}{{4}}$ $q_m^{SM} = \frac{{1 - k}}{{2}}$ $q_m^{SD} = \frac{{8 - 2b + 2cb - b^2 - 8k + b^2 k + 2cbn - 2bs}}{{2(8 - 3b^2 )}}$ $N/A$ $\pi _m^{SM} = \frac{{(k - 1)^2 }}{{4}}$ $\pi _m^{SD} = \frac{{\left[ \begin{array}{l} 12 - 8c + 4c^2 - 8b + 8cb + b^2 - 16k \\ + 8bk - 8cbk - 2b^2 k + 8k^2 + b^2 k^2 - \\ 8cn + 8c^2 n + 8cbn - 8cbkn + 4c^2 n^2 + \;\;\\ 8s - 8cs - 8bs + 8bks - 8cns + 4s^2 \end{array} \right]}}{{4(3b^2 - 8)}}$ $\pi _m^{SR} = \frac{{(c + cn - s - 1)^2 }}{{8}}$ $N/A$ $\pi _r^{SD} = \frac{{4(1 - c - b + bk - cn +s)^2 }}{{( - 8 + 3b^2 )^2 }}$ $\pi _r^{SR} = \frac{{(c + cn - s - 1)^2}}{{16}}$
Equilibrium outcomes when service effort is endogenous
 Strategy E Direct channel (EM) $k k_2^E$ $N/A$ $w^{ED} =$ shown in below $w^{ER} = \frac{{1-c-cn+s}}{{2}}$ $N/A$ $q_r^{ED} = \frac{{2n(3b^2 - 8)(c + b - bk + cn - 1)}}{{9nb^4 - 48nb^2 + 64n - 8}}$ $q_r^{ER} = \frac{{1-c-cn+s}}{{4}}$ $q_m^{EM} = \frac{{1 - k}}{{2}}$ $q_m^{ED} =$ shown in below $N/A$ $\pi _m^{EM} = \frac{{(k - 1)^2 }}{{4}}$ $\pi _m^{ED} =$ shown in below $\pi _m^{ER} = \frac{{(c + cn - s - 1)^2 }}{{8}}$ $N/A$ $\pi _r^{ED} = \frac{{4n(c + b - bk + cn -1)^2 }}{{(9nb^4 - 48nb^2 + 64n - 8)}}$ $\pi _r^{ER} = \frac{{(c + cn - s - 1)^2}}{{16}}$
 Strategy E Direct channel (EM) $k k_2^E$ $N/A$ $w^{ED} =$ shown in below $w^{ER} = \frac{{1-c-cn+s}}{{2}}$ $N/A$ $q_r^{ED} = \frac{{2n(3b^2 - 8)(c + b - bk + cn - 1)}}{{9nb^4 - 48nb^2 + 64n - 8}}$ $q_r^{ER} = \frac{{1-c-cn+s}}{{4}}$ $q_m^{EM} = \frac{{1 - k}}{{2}}$ $q_m^{ED} =$ shown in below $N/A$ $\pi _m^{EM} = \frac{{(k - 1)^2 }}{{4}}$ $\pi _m^{ED} =$ shown in below $\pi _m^{ER} = \frac{{(c + cn - s - 1)^2 }}{{8}}$ $N/A$ $\pi _r^{ED} = \frac{{4n(c + b - bk + cn -1)^2 }}{{(9nb^4 - 48nb^2 + 64n - 8)}}$ $\pi _r^{ER} = \frac{{(c + cn - s - 1)^2}}{{16}}$
 [1] Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial and Management Optimization, 2022, 18 (1) : 541-560. doi: 10.3934/jimo.2020167 [2] Jun Tu, Zijiao Sun, Min Huang. Supply chain coordination considering e-tailer's promotion effort and logistics provider's service effort. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2191-2220. doi: 10.3934/jimo.2021062 [3] Honglin Yang, Siqi Zhao, Jiawu Peng. Optimal retail price and service level in a dual-channel supply chain with reference price effect. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022115 [4] Tinghai Ren, Nengmin Zeng, Dafei Wang, Shuwei Cheng. Effects of channel encroachment on the software and service decisions in it supply chains. Journal of Industrial and Management Optimization, 2022, 18 (5) : 3787-3806. doi: 10.3934/jimo.2021136 [5] Fei Cheng, Shanlin Yang, Ram Akella, Xiaoting Tang. An integrated approach for selection of service vendors in service supply chain. Journal of Industrial and Management Optimization, 2011, 7 (4) : 907-925. doi: 10.3934/jimo.2011.7.907 [6] Tinghai Ren, Kaifu Yuan, Dafei Wang, Nengmin Zeng. Effect of service quality on software sales and coordination mechanism in IT service supply chain. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021165 [7] Suresh P. Sethi, Houmin Yan, Hanqin Zhang, Jing Zhou. Information Updated Supply Chain with Service-Level Constraints. Journal of Industrial and Management Optimization, 2005, 1 (4) : 513-531. doi: 10.3934/jimo.2005.1.513 [8] Ziyuan Zhang, Liying Yu. Research on optimal pricing decisions of the service supply chain oriented to strategic consumers. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022096 [9] Xiaohui Ren, Daofang Chang, Jin Shen. Optimization of the product service supply chain under the influence of presale services. Journal of Industrial and Management Optimization, 2022, 18 (5) : 3679-3699. doi: 10.3934/jimo.2021130 [10] Tinggui Chen, Yanhui Jiang. Research on operating mechanism for creative products supply chain based on game theory. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1103-1112. doi: 10.3934/dcdss.2015.8.1103 [11] Yadong Shu, Ying Dai, Zujun Ma. Evolutionary game theory analysis of supply chain with fairness concerns of retailers. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022098 [12] Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial and Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73 [13] Qiang Lin, Ying Peng, Ying Hu. Supplier financing service decisions for a capital-constrained supply chain: Trade credit vs. combined credit financing. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1731-1752. doi: 10.3934/jimo.2019026 [14] Jing Shi, Tiaojun Xiao. Service investment and consumer returns policy in a vendor-managed inventory supply chain. Journal of Industrial and Management Optimization, 2015, 11 (2) : 439-459. doi: 10.3934/jimo.2015.11.439 [15] Bin Dan, Huali Gao, Yang Zhang, Ru Liu, Songxuan Ma. Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints. Journal of Industrial and Management Optimization, 2018, 14 (1) : 165-182. doi: 10.3934/jimo.2017041 [16] Weihua Liu, Xinran Shen, Di Wang, Jingkun Wang. Order allocation model in logistics service supply chain with demand updating and inequity aversion: A perspective of two option contracts comparison. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3269-3295. doi: 10.3934/jimo.2020118 [17] Han Zhao, Bangdong Sun, Hui Wang, Shiji Song, Yuli Zhang, Liejun Wang. Optimization and coordination in a service-constrained supply chain with the bidirectional option contract under conditional value-at-risk. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022021 [18] Yongtao Peng, Dan Xu, Eleonora Veglianti, Elisabetta Magnaghi. A product service supply chain network equilibrium considering risk management in the context of COVID-19 pandemic. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022094 [19] Dingzhong Feng, Xiaofeng Zhang, Ye Zhang. Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition. Journal of Industrial and Management Optimization, 2022, 18 (5) : 3365-3392. doi: 10.3934/jimo.2021117 [20] Jun Wu, Shouyang Wang, Wuyi Yue. Supply contract model with service level constraint. Journal of Industrial and Management Optimization, 2005, 1 (3) : 275-287. doi: 10.3934/jimo.2005.1.275

2021 Impact Factor: 1.411