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September  2022, 18(5): 3187-3214. doi: 10.3934/jimo.2021108

Competitive strategies in the presence of consumers' expected service and product returns

1. 

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

2. 

Yango University, Fujian 350015, China

3. 

School of Mathematical Sciences, Sunway University, Malaysia

* Corresponding author: Shuhua Chang

Received  February 2021 Revised  March 2021 Published  September 2022 Early access  June 2021

Fund Project: This project was supported in part by the Major Research Plan of the National Natural Science Foundation of China (91430108), the National Natural Science Foundation of China (11771322), the National Social Science Foundation of China (19CGL002), Tianjin Social Science Planning Project (TJGLQN20-002), and the Russian Science Foundation (20-61-46017)

This paper investigates the optimal strategies and profits of dual channel with product returns in the presence of customers' expected service. Customers' expected service is related to advertising effort and price. We build a two-stage decision making process to analyze the impact of expected services of customers. In addition, we analyze the parameter sensitivity and compare the competitive equilibrium strategies. The results show that the manufacturer will give a lower wholesale price to the retailer in some case. Furthermore, the dual-channel product returns will discourage advertising effort and the service level of the retailer, but it will enable the manufacturer to provide a higher service level. Thus, for managers, the survey of the expected service of customers is very important for the optimal strategies making, and it should not always blindly exploit the retailer's profit for the manufacturer. Finally, when the physical store allows unconditional return of goods, the service level of the online channel will be more considerate.

Citation: Ting Zhang, Shuhua Chang, Yan Dong, Jingyi Yue, Kok Lay Teo. Competitive strategies in the presence of consumers' expected service and product returns. Journal of Industrial and Management Optimization, 2022, 18 (5) : 3187-3214. doi: 10.3934/jimo.2021108
References:
[1]

S. M. AliM. H. RahmanT. J. TumpaA. A. M. Rifat and S. K. Paul, Examining price and service competition among retailers in a supply chain under potential demand disruption, Journal of Retailing & Consumer Services, 40 (2018), 40-47.  doi: 10.1016/j.jretconser.2017.08.025.

[2]

R. E. Anderson, Consumer dissatisfaction: The effect of disconfirmed expectancy on perceived product performance, Journal of Marketing Research, 10 (1973), 38-44.  doi: 10.1177/002224377301000106.

[3]

P. D. BergerJ. Lee and B. D. Weinberg, Optimal cooperative advertising integration strategy for organizations adding a direct online channel, Journal of the Operational Research Society, 57 (2006), 920-927.  doi: 10.1057/palgrave.jors.2602069.

[4]

J. Chen and P. C. Bell, The impact of customer returns on pricing and order decisions, European Journal of Operational Research, 195 (2009), 280-295.  doi: 10.1016/j.ejor.2008.01.030.

[5]

K-Y. ChenM. Kaya and Ö. Özer, Dual sales channel management with service competition, Manufacturing & Service Operations Management, 10 (2008), 654-675.  doi: 10.1287/msom.1070.0177.

[6]

I. J. Chen and K. Popovich, Understanding customer relationship management (CRM): People, process and technology, Business Process Management Journal, 9 (2003), 672-688.  doi: 10.1108/14637150310496758.

[7]

B. DanZ. J. QuC. LiuX. M. Zhang and H. Y. Zhang, Price and service competition in the supply chain with both pure play internet and strong bricks-and-mortar retailers, Journal of Applied Research & Technology, 12 (2014), 212-222.  doi: 10.1016/S1665-6423(14)72337-5.

[8]

Y. DingX. GaoC. HuangJ. Shu and D. Yang, Service competition in an online duopoly market, Omega, 77 (2018), 58-72.  doi: 10.1016/j.omega.2017.05.007.

[9]

A. DumrongsiriM. FanA. Jain and K. Moinzadeh, A supply chain model with direct and retail channels, European Journal of Operational Research, 187 (2008), 691-718.  doi: 10.1016/j.ejor.2006.05.044.

[10]

F. Gao and X. M. Su, Online and Offline Information for Omnichannel Retailing., Manufacturing & Service Operations Management, 19 (2009), 84-98. 

[11]

J. Green, Still pulling the strings, but locally, too, Brandweek, 41 (2000), 34-42. 

[12]

J. A. GuajardoM. A. Cohen and S. Netessine, Service competition and product quality in the U.S. automobile industry, Management Science, 62 (2016), 1860-1877.  doi: 10.1287/mnsc.2015.2195.

[13]

X. Hu, Z. Wan and N. N. Murthy, Dynamic pricing of limited inventories with product returns, Manufacturing & Service Operations Management, (2018), 1–18.

[14]

M. Jahre, Household waste collection as a reverse channel, International Journal of Physical Distribution & Logistics Management, 25 (1995), 39-55. 

[15]

S. K. Jena and P. L. Meena, Price and service competition in a tourism supply chain, Service Science, 11 (2019). doi: 10.1287/serv.2019.0240.

[16]

S. K. Jena and S. P. Sarmah, Price and service co-opetiton under uncertain demand and condition of used items in a remanufacturing system, International Journal of Production Economics, 173 (2016), 1-21.  doi: 10.1016/j.ijpe.2015.11.019.

[17]

M. KiesslingS. Kurz and J. Rambau, The integrated size and price optimization problem, Numerical Algebra Control & Optimization, 2 (2017), 669-693.  doi: 10.3934/naco.2012.2.669.

[18]

J. A. P. Kumar, Are product returns a necessary evil? Antecedents and consequences, Journal of Retailing, 73 (2009), 35-51. 

[19]

Y. LiL. Xu and D. Li., Examining relationships between the return policy, product quality, and pricing strategy in online direct selling, International Journal of Production Economics, 144 (2013), 451-460.  doi: 10.1016/j.ijpe.2013.03.013.

[20]

A. MinnemaT. H. A. BijmoltS. Gensler and T. Wiesel, To keep or not to keep: effects of online customer reviews on product returns, Journal of Retailing, 92 (2016), 253-267.  doi: 10.1016/j.jretai.2016.03.001.

[21]

J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36 (1950), 48-49.  doi: 10.1073/pnas.36.1.48.

[22]

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

[23]

E. OfekZ. Katona and M. Sarvary, "Bricks and clicks": The impact of product returns on the strategies of multichannel retailers, Marketing Science, 30 (2011), 42-60.  doi: 10.1287/mksc.1100.0588.

[24]

L. PaoloP. Morteza and H. Terry, The impact of consumer returns on the multichannel sales strategies of manufacturers, Production and Operations Management, 27 (2017), 323-349.  doi: 10.1111/poms.12799.

[25]

A. ParasuramanL. L. Berry and V. A. Zeithamal, Understanding customer expectations of service, Sloan Management Review, 32 (1991), 39-48. 

[26]

A. ParasuramanV. A. Zeithaml and L. L. Berry, Servqual: A multiple-item scale for measuring consumer perceptions of service quality, Journal of Retailing, 64 (1988), 12-40. 

[27]

J. A. Petersen and V. Kumar, Can product returns make you money?, Sloan Management Review, 51 (2010), 84-91. 

[28]

L. Ren, Y. He and H. Song, Price and service competition of dual-channel supply chain with consumer returns, Discrete Dynamics in Nature and Society, 2014 (2014), Art. ID 565603, 10 pp. doi: 10.1155/2014/565603.

[29]

D. Renner, Customer relationship management: A new weapon in your competitive arsenal, Siebel Magazine, 1 (2000).

[30]

R. T. RustJ. J. InmanJ. Jia and A. Zahorik, What you don't know about customer-perceived quality: the role of customer expectation distribution, Marketing Science, 18 (1999), 77-92.  doi: 10.1287/mksc.18.1.77.

[31]

A. ShahC. ZeisH. Regassa and A. Ahmadian, Expected service quality as perceived by potential customers of an educational institution, Journal of Marketing for Higher Education, 9 (2000), 49-72.  doi: 10.1300/J050v09n03_05.

[32]

A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-ommerce age, Production and Operations Management, 13 (2004), 93-110.  doi: 10.1111/j.1937-5956.2004.tb00147.x.

[33]

A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing & Service Operations Management, 2 (2000), 372-391.  doi: 10.1287/msom.2.4.372.12342.

[34]

W. Wang, Cooperative advertising in a dual channel, 2009 International Conference on Business Intelligence and Financial Engineering, (2009). doi: 10.1109/BIFE.2009.137.

[35]

D. WeathersS. Sharma and S. L. Wood, Effects of online communication practices on consumer perceptions of performance uncertainty for search and experience goods, Journal of Retailing, 83 (2007), 393-401.  doi: 10.1016/j.jretai.2007.03.009.

[36]

Y. Xia and S. M. Gilbert, Strategic interactions between channel structure and demand enhancing services, European Journal of Operational Research, 181 (2007), 252-265.  doi: 10.1016/j.ejor.2006.06.027.

[37]

Y. XiaT. Xiao and G. P. Zhang, The impact of product returns and retailer's service investment on manufacturer's channel strategies, Decision Sciences, 48 (2016), 918-955.  doi: 10.1111/deci.12241.

[38]

Y. Xia, T. Xiao and G. P. Zhang, Service investment and channel structure decisions in competing supply chains, Service Science, 11 (2019). doi: 10.1287/serv.2018.0235.

[39]

L. XuY. LiK. Govindan and X. Yue, Return policy and supply chain coordination with network-externality effect, International Journal of Production Research, 3 (2018), 3714-3732.  doi: 10.1080/00207543.2017.1421786.

[40]

R. Yan, S. Ghose and A. Bhatnagar, Cooperative advertising in a dual channel supply chain, International Journal of Electronic Marketing and Retailing, 1(2006), 99. doi: 10.1504/IJEMR.2006.011028.

[41]

W. S. Yoo and E. Lee, Internet channel entry: A strategic analysis of mixed channel structures, Marketing Science, 30 (2011), 29-41.  doi: 10.1287/mksc.1100.0586.

[42]

V. A. ZeithamlL. L. Berry and A. Parasuraman, The behavioral consequences of service quality, Journal of Marketing, 60 (1996), 31-46.  doi: 10.1177/002224299606000203.

[43]

G. Zhang, G. Dai, H. Sun, G. Zhang and Z. Yang, Equilibrium in supply chain network with competition and service level between channels considering consumers' channel preferences, Journal of Retailing and Consumer Services, 57 (2020), 102199. doi: 10.1016/j.jretconser.2020.102199.

[44]

Z. P. ZhouX. B. LiuJ. PeiP. M. Pardalos and H. Cheng, Competition of pricing and service investment between Iot-based and traditional manufacturers, Journal of Industrial and Management Optimization, 14 (2018), 1203-1218.  doi: 10.3934/jimo.2018006.

show all references

References:
[1]

S. M. AliM. H. RahmanT. J. TumpaA. A. M. Rifat and S. K. Paul, Examining price and service competition among retailers in a supply chain under potential demand disruption, Journal of Retailing & Consumer Services, 40 (2018), 40-47.  doi: 10.1016/j.jretconser.2017.08.025.

[2]

R. E. Anderson, Consumer dissatisfaction: The effect of disconfirmed expectancy on perceived product performance, Journal of Marketing Research, 10 (1973), 38-44.  doi: 10.1177/002224377301000106.

[3]

P. D. BergerJ. Lee and B. D. Weinberg, Optimal cooperative advertising integration strategy for organizations adding a direct online channel, Journal of the Operational Research Society, 57 (2006), 920-927.  doi: 10.1057/palgrave.jors.2602069.

[4]

J. Chen and P. C. Bell, The impact of customer returns on pricing and order decisions, European Journal of Operational Research, 195 (2009), 280-295.  doi: 10.1016/j.ejor.2008.01.030.

[5]

K-Y. ChenM. Kaya and Ö. Özer, Dual sales channel management with service competition, Manufacturing & Service Operations Management, 10 (2008), 654-675.  doi: 10.1287/msom.1070.0177.

[6]

I. J. Chen and K. Popovich, Understanding customer relationship management (CRM): People, process and technology, Business Process Management Journal, 9 (2003), 672-688.  doi: 10.1108/14637150310496758.

[7]

B. DanZ. J. QuC. LiuX. M. Zhang and H. Y. Zhang, Price and service competition in the supply chain with both pure play internet and strong bricks-and-mortar retailers, Journal of Applied Research & Technology, 12 (2014), 212-222.  doi: 10.1016/S1665-6423(14)72337-5.

[8]

Y. DingX. GaoC. HuangJ. Shu and D. Yang, Service competition in an online duopoly market, Omega, 77 (2018), 58-72.  doi: 10.1016/j.omega.2017.05.007.

[9]

A. DumrongsiriM. FanA. Jain and K. Moinzadeh, A supply chain model with direct and retail channels, European Journal of Operational Research, 187 (2008), 691-718.  doi: 10.1016/j.ejor.2006.05.044.

[10]

F. Gao and X. M. Su, Online and Offline Information for Omnichannel Retailing., Manufacturing & Service Operations Management, 19 (2009), 84-98. 

[11]

J. Green, Still pulling the strings, but locally, too, Brandweek, 41 (2000), 34-42. 

[12]

J. A. GuajardoM. A. Cohen and S. Netessine, Service competition and product quality in the U.S. automobile industry, Management Science, 62 (2016), 1860-1877.  doi: 10.1287/mnsc.2015.2195.

[13]

X. Hu, Z. Wan and N. N. Murthy, Dynamic pricing of limited inventories with product returns, Manufacturing & Service Operations Management, (2018), 1–18.

[14]

M. Jahre, Household waste collection as a reverse channel, International Journal of Physical Distribution & Logistics Management, 25 (1995), 39-55. 

[15]

S. K. Jena and P. L. Meena, Price and service competition in a tourism supply chain, Service Science, 11 (2019). doi: 10.1287/serv.2019.0240.

[16]

S. K. Jena and S. P. Sarmah, Price and service co-opetiton under uncertain demand and condition of used items in a remanufacturing system, International Journal of Production Economics, 173 (2016), 1-21.  doi: 10.1016/j.ijpe.2015.11.019.

[17]

M. KiesslingS. Kurz and J. Rambau, The integrated size and price optimization problem, Numerical Algebra Control & Optimization, 2 (2017), 669-693.  doi: 10.3934/naco.2012.2.669.

[18]

J. A. P. Kumar, Are product returns a necessary evil? Antecedents and consequences, Journal of Retailing, 73 (2009), 35-51. 

[19]

Y. LiL. Xu and D. Li., Examining relationships between the return policy, product quality, and pricing strategy in online direct selling, International Journal of Production Economics, 144 (2013), 451-460.  doi: 10.1016/j.ijpe.2013.03.013.

[20]

A. MinnemaT. H. A. BijmoltS. Gensler and T. Wiesel, To keep or not to keep: effects of online customer reviews on product returns, Journal of Retailing, 92 (2016), 253-267.  doi: 10.1016/j.jretai.2016.03.001.

[21]

J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sciences, 36 (1950), 48-49.  doi: 10.1073/pnas.36.1.48.

[22]

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

[23]

E. OfekZ. Katona and M. Sarvary, "Bricks and clicks": The impact of product returns on the strategies of multichannel retailers, Marketing Science, 30 (2011), 42-60.  doi: 10.1287/mksc.1100.0588.

[24]

L. PaoloP. Morteza and H. Terry, The impact of consumer returns on the multichannel sales strategies of manufacturers, Production and Operations Management, 27 (2017), 323-349.  doi: 10.1111/poms.12799.

[25]

A. ParasuramanL. L. Berry and V. A. Zeithamal, Understanding customer expectations of service, Sloan Management Review, 32 (1991), 39-48. 

[26]

A. ParasuramanV. A. Zeithaml and L. L. Berry, Servqual: A multiple-item scale for measuring consumer perceptions of service quality, Journal of Retailing, 64 (1988), 12-40. 

[27]

J. A. Petersen and V. Kumar, Can product returns make you money?, Sloan Management Review, 51 (2010), 84-91. 

[28]

L. Ren, Y. He and H. Song, Price and service competition of dual-channel supply chain with consumer returns, Discrete Dynamics in Nature and Society, 2014 (2014), Art. ID 565603, 10 pp. doi: 10.1155/2014/565603.

[29]

D. Renner, Customer relationship management: A new weapon in your competitive arsenal, Siebel Magazine, 1 (2000).

[30]

R. T. RustJ. J. InmanJ. Jia and A. Zahorik, What you don't know about customer-perceived quality: the role of customer expectation distribution, Marketing Science, 18 (1999), 77-92.  doi: 10.1287/mksc.18.1.77.

[31]

A. ShahC. ZeisH. Regassa and A. Ahmadian, Expected service quality as perceived by potential customers of an educational institution, Journal of Marketing for Higher Education, 9 (2000), 49-72.  doi: 10.1300/J050v09n03_05.

[32]

A. A. Tsay and N. Agrawal, Channel conflict and coordination in the e-ommerce age, Production and Operations Management, 13 (2004), 93-110.  doi: 10.1111/j.1937-5956.2004.tb00147.x.

[33]

A. A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing & Service Operations Management, 2 (2000), 372-391.  doi: 10.1287/msom.2.4.372.12342.

[34]

W. Wang, Cooperative advertising in a dual channel, 2009 International Conference on Business Intelligence and Financial Engineering, (2009). doi: 10.1109/BIFE.2009.137.

[35]

D. WeathersS. Sharma and S. L. Wood, Effects of online communication practices on consumer perceptions of performance uncertainty for search and experience goods, Journal of Retailing, 83 (2007), 393-401.  doi: 10.1016/j.jretai.2007.03.009.

[36]

Y. Xia and S. M. Gilbert, Strategic interactions between channel structure and demand enhancing services, European Journal of Operational Research, 181 (2007), 252-265.  doi: 10.1016/j.ejor.2006.06.027.

[37]

Y. XiaT. Xiao and G. P. Zhang, The impact of product returns and retailer's service investment on manufacturer's channel strategies, Decision Sciences, 48 (2016), 918-955.  doi: 10.1111/deci.12241.

[38]

Y. Xia, T. Xiao and G. P. Zhang, Service investment and channel structure decisions in competing supply chains, Service Science, 11 (2019). doi: 10.1287/serv.2018.0235.

[39]

L. XuY. LiK. Govindan and X. Yue, Return policy and supply chain coordination with network-externality effect, International Journal of Production Research, 3 (2018), 3714-3732.  doi: 10.1080/00207543.2017.1421786.

[40]

R. Yan, S. Ghose and A. Bhatnagar, Cooperative advertising in a dual channel supply chain, International Journal of Electronic Marketing and Retailing, 1(2006), 99. doi: 10.1504/IJEMR.2006.011028.

[41]

W. S. Yoo and E. Lee, Internet channel entry: A strategic analysis of mixed channel structures, Marketing Science, 30 (2011), 29-41.  doi: 10.1287/mksc.1100.0586.

[42]

V. A. ZeithamlL. L. Berry and A. Parasuraman, The behavioral consequences of service quality, Journal of Marketing, 60 (1996), 31-46.  doi: 10.1177/002224299606000203.

[43]

G. Zhang, G. Dai, H. Sun, G. Zhang and Z. Yang, Equilibrium in supply chain network with competition and service level between channels considering consumers' channel preferences, Journal of Retailing and Consumer Services, 57 (2020), 102199. doi: 10.1016/j.jretconser.2020.102199.

[44]

Z. P. ZhouX. B. LiuJ. PeiP. M. Pardalos and H. Cheng, Competition of pricing and service investment between Iot-based and traditional manufacturers, Journal of Industrial and Management Optimization, 14 (2018), 1203-1218.  doi: 10.3934/jimo.2018006.

Table 1.  The impact of the expected service
$ \omega $ $ S_d $ $ S_r $ $ A $ $ Q_d $ $ Q_r $ $ \pi_m $ $ \pi_r $
$ a=b=0 $ 6.0174 2.1878 1.5861 2.8323 3.6562 6.7535 67.2808 10.7280
$ a\neq0,b\neq0 $ 6.1059 2.1259 1.5153 2.4894 2.7451 5.8292 55.5396 8.8085
change $ + $ $ - $ $ - $ $ - $ $ - $ $ - $ $ - $ $ - $
$ \omega $ $ S_d $ $ S_r $ $ A $ $ Q_d $ $ Q_r $ $ \pi_m $ $ \pi_r $
$ a=b=0 $ 6.0174 2.1878 1.5861 2.8323 3.6562 6.7535 67.2808 10.7280
$ a\neq0,b\neq0 $ 6.1059 2.1259 1.5153 2.4894 2.7451 5.8292 55.5396 8.8085
change $ + $ $ - $ $ - $ $ - $ $ - $ $ - $ $ - $ $ - $
Table 2.  Sensitivity analysis
$ A $ $ \omega $ $ S_d $ $ S_r $ $ Q_d $ $ Q_r $ $ \pi_d $ $ \pi_m $ $ \pi_r $
$ \tau $ $ \nearrow $ $ \searrow\nearrow $ $ \nearrow\searrow $ $ \nearrow\searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow\searrow $
$ \delta $ $ \nearrow $ $ \searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \searrow $ $ \nearrow $ $ \nearrow $ $ \searrow $
$ \mu $ $ \nearrow $ $ \searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow\searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $
$ g $ $ \searrow $ $ \nearrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow\nearrow $ $ \searrow $ $ \searrow $ $ \searrow $
$ \gamma $ $ \nearrow $ $ \searrow\nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $
$ a $ $ \searrow $ $ \nearrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $
$ r $ $ \searrow $ $ \nearrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \nearrow\searrow $ $ \nearrow $
* Some parameters are analyzed only within ranges.
$ A $ $ \omega $ $ S_d $ $ S_r $ $ Q_d $ $ Q_r $ $ \pi_d $ $ \pi_m $ $ \pi_r $
$ \tau $ $ \nearrow $ $ \searrow\nearrow $ $ \nearrow\searrow $ $ \nearrow\searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow\searrow $
$ \delta $ $ \nearrow $ $ \searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \searrow $ $ \nearrow $ $ \nearrow $ $ \searrow $
$ \mu $ $ \nearrow $ $ \searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow\searrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $
$ g $ $ \searrow $ $ \nearrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow\nearrow $ $ \searrow $ $ \searrow $ $ \searrow $
$ \gamma $ $ \nearrow $ $ \searrow\nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $ $ \nearrow $
$ a $ $ \searrow $ $ \nearrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $
$ r $ $ \searrow $ $ \nearrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \searrow $ $ \nearrow\searrow $ $ \nearrow $
* Some parameters are analyzed only within ranges.
Table 3.  Decision changes influenced by parameters
$ g $ $ \gamma $ $ \phi $ $ \delta $ $ \tau $ $ \mu $ $ a $
$ B $ $ +\rightarrow - $ $ -\rightarrow + $ $ -\rightarrow + $ $ +\rightarrow - $ $ -\rightarrow + $ $ +\rightarrow - $ $ +\rightarrow - $
$ E $ $ +\rightarrow - $ $ -\rightarrow + $ $ -\rightarrow + $ $ +\rightarrow - $ $ -\rightarrow + $ $ - $ $ - $
$ F $ $ - $ $ - $ $ -\rightarrow + $ $ +\rightarrow - $ $ - $ $ - $ $ - $
* See Appendix Table 1 for details.
$ g $ $ \gamma $ $ \phi $ $ \delta $ $ \tau $ $ \mu $ $ a $
$ B $ $ +\rightarrow - $ $ -\rightarrow + $ $ -\rightarrow + $ $ +\rightarrow - $ $ -\rightarrow + $ $ +\rightarrow - $ $ +\rightarrow - $
$ E $ $ +\rightarrow - $ $ -\rightarrow + $ $ -\rightarrow + $ $ +\rightarrow - $ $ -\rightarrow + $ $ - $ $ - $
$ F $ $ - $ $ - $ $ -\rightarrow + $ $ +\rightarrow - $ $ - $ $ - $ $ - $
* See Appendix Table 1 for details.
Table 4.  The impact of the expected service
$ \omega $ $ S_d $ $ S_r $ $ A $ $ P $ $ \pi_m $ $ \pi_r $
$ a=b=0 $ 7.2135 7.5698 3.0290 5.4090 10.9997 47.9312 1.7613
$ a\neq0,b\neq0 $ 6.4174 6.7444 2.5324 4.1064 9.5829 38.4156 2.5834
change $ - $ $ - $ $ - $ $ - $ $ - $ $ - $ $ + $
$ \omega $ $ S_d $ $ S_r $ $ A $ $ P $ $ \pi_m $ $ \pi_r $
$ a=b=0 $ 7.2135 7.5698 3.0290 5.4090 10.9997 47.9312 1.7613
$ a\neq0,b\neq0 $ 6.4174 6.7444 2.5324 4.1064 9.5829 38.4156 2.5834
change $ - $ $ - $ $ - $ $ - $ $ - $ $ - $ $ + $
Table 1.  The changes of decision due to the influence of the parameters
$ g $ $ \gamma $ $ \phi $ $ \delta $ $ \tau $ $ \mu $ $ a $
B $<0.69 $ $>0.69 $ $<0.53 $ $>0.53 $ $<0.2 $ $>0.2 $ $<0.2 $ $>0.2 $ $<0.66 $ $>0.66 $ $<0.6 $ $>0.6 $ $<0.018 $ $>0.018 $
$>0 $ $<0 $ $<0 $ $>0 $ $<0 $ $>0 $ $>0 $ $<0 $ $<0 $ $>0 $ $>0 $ $<0 $ $>0 $ $<0 $
E $<0.3 $ $>0.3 $ $<0.65 $ $>0.65 $ $<0.49 $ $>0.49 $ $<0.09 $ $>0.09 $ $<0.85 $ $>0.85 $ $<0 $ $<0 $
$>0 $ $<0 $ $<0 $ $>0 $ $<0 $ $>0 $ $>0 $ $<0 $ $<0 $ $>0 $
F $<0 $ $<0 $ $<0.25 $ $>0.25 $ $<0.17 $ $>0.17 $ $<0 $ $<0 $ $<0 $
$<0 $ $>0 $ $>0 $ $<0 $
$ g $ $ \gamma $ $ \phi $ $ \delta $ $ \tau $ $ \mu $ $ a $
B $<0.69 $ $>0.69 $ $<0.53 $ $>0.53 $ $<0.2 $ $>0.2 $ $<0.2 $ $>0.2 $ $<0.66 $ $>0.66 $ $<0.6 $ $>0.6 $ $<0.018 $ $>0.018 $
$>0 $ $<0 $ $<0 $ $>0 $ $<0 $ $>0 $ $>0 $ $<0 $ $<0 $ $>0 $ $>0 $ $<0 $ $>0 $ $<0 $
E $<0.3 $ $>0.3 $ $<0.65 $ $>0.65 $ $<0.49 $ $>0.49 $ $<0.09 $ $>0.09 $ $<0.85 $ $>0.85 $ $<0 $ $<0 $
$>0 $ $<0 $ $<0 $ $>0 $ $<0 $ $>0 $ $>0 $ $<0 $ $<0 $ $>0 $
F $<0 $ $<0 $ $<0.25 $ $>0.25 $ $<0.17 $ $>0.17 $ $<0 $ $<0 $ $<0 $
$<0 $ $>0 $ $>0 $ $<0 $
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