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doi: 10.3934/jimo.2021220
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Analysis on the influence of retailer's introduction of store brand under manufacturer's product line strategy

1. 

Business School, Nankai University, Tianjin 300071, China

2. 

College of Management and Economics, Tianjin University, Tianjin 300072, China

* Corresponding author: Yuhang Li

Received  March 2021 Revised  August 2021 Early access December 2021

Fund Project: This work was supported by the National Natural Science Foundation of China [grant numbers 71672095

As the introduction of store brand (SB) by retailers becomes more common, national brand manufacturers (NBM) in the market often respond with a product line strategy. Then how should retailers decide their product lines under the situation that NBM adopt product line strategy? Under the manufacturer's product line strategy, this paper compares and analyzes three competitive strategies for retailers to introduce high-end SB, low-end SB and SB product line. The results show that: First, no matter what kind of competition strategy the retailer adopts, (1) the introduction of SB occupies the market share of NB; (2) the retailer gains the highest unit income from the high-end products of NB manufacturers. Second, the relationship between production cost and encroachment effects directly affects the retailer's choice of optimal competitive strategy and the manufacturer's preference for its competitive strategy choice. Finally, from the perspective of profit maximization, the optimal choice for retailers is the product line competition strategy, but this strategy is not obvious compared with the high-end competition strategy. Therefore, when retailers introduce product lines, if they are effectively threatened by national brand manufacturers (for example, NBM refuses to provide national brands to retailers), retailers may choose the suboptimal strategy, that is, to introduce store brand high-end products. When the high-end products of store brands are better than the low-end products of national brands and the production cost of products is relatively high, this strategy just meets the expectations of national brand manufacturers for retailers to introduce strategies.

Citation: Yuanyuan Jiao, Yuhang Li, Jun Du. Analysis on the influence of retailer's introduction of store brand under manufacturer's product line strategy. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021220
References:
[1]

K. L. AilawadiK. Pauwels and J. Steenkamp, Private-Label use and store loyalty, Journal of Marketing, 72 (2008), 19-30. 

[2]

K. L. Ailawadi and B. Harlam, An empirical analysis of the determinants of retail margins: The role of store-brand share, Journal of Marketing, 68 (2004), 147-165.  doi: 10.1509/jmkg.68.1.147.24027.

[3]

N. Al-MonawerM. Davoodi and L. Qi, Brand and quality effects on introduction of store brand products, Journal of Retailing and Consumer Services, 61 (2021), 102507.  doi: 10.1016/j.jretconser.2021.102507.

[4]

N. Amrouche and G. Zaccour, Shelf-space allocation of national and private brands, European Journal of Operational Research, 180 (2007), 648-663.  doi: 10.1016/j.ejor.2006.05.008.

[5]

N. Amrouche and R. Yan, Implementing online store for national brand competing against private label, Journal of Business Research, 65 (2012), 325-332.  doi: 10.1016/j.jbusres.2011.04.008.

[6]

C. ChambolleC. Christin and G. Meunier, The optimal production channel for private labels: Too much or too little innovation?, Journal of Economics Management Strategy, 24 (2015), 348-368.  doi: 10.1111/jems.12098.

[7]

L. ChenS. M. Gilbert and Y. Xia, Private labels: Facilitators or impediments to supply chain coordination, Decision Sciences, 42 (2011), 689-720.  doi: 10.1111/j.1540-5915.2011.00327.x.

[8]

R. ChengW. Ma and H. Ke, How does store-brand introduction affect a supply chain with uncertain information?, Journal of Intelligent and Fuzzy Systems, 34 (2018), 189-201.  doi: 10.3233/JIFS-171058.

[9]

C. Choi and A. T. Coughlan, Private label positioning: Quality versus feature differentiation from the national brand, Journal of Retailing, 82 (2006), 79-93. 

[10]

H. Chung and E. Lee, Store brand quality and retailer's product line design, Journal of Retailing, 93 (2017), 527-540.  doi: 10.1016/j.jretai.2017.09.002.

[11]

H. Chung and E. Lee, Effect of store brand introduction on channel price leadership: An empirical investigation, Journal of Retailing, 94 (2018), 21-32.  doi: 10.1016/j.jretai.2017.10.001.

[12]

X. FanC. Wang and Y. Liu, Positioning and channel effects of store brands under the condition of cost difference, Systems Engineering-Theory & Practice, 38 (2018), 2006-2017. 

[13]

A. Groznik and H. S. Heese, Supply chain conflict due to store brands: The value of wholesale price commitment in a retail supply chain, Decision Sciences, 41 (2010), 203-230.  doi: 10.1111/j.1540-5915.2010.00265.x.

[14]

A. Groznik and H. S. Heese, Supply chain interactions due to store-brand introductions: The impact of retail competition, European Journal of Operational Research, 203 (2010), 575-582.  doi: 10.1016/j.ejor.2009.08.014.

[15]

R. Hara and N. Matsubayashi, Premium store brand: Product development collaboration between retailers and national brand manufacturers, International Journal of Production Economics, 185 (2017), 128-138.  doi: 10.1016/j.ijpe.2016.12.024.

[16]

H. S. Heese, Competing with channel partners: Supply chain conflict when retailers introduce store brands, Naval Research Logs., 57 (2010), 441-459.  doi: 10.1002/nav.20412.

[17]

Z. Huang and T. Feng, Money-back guarantee and pricing decision with retailer's Store brand, Journal of Retailing and Consumer Services, 52 (2019), 1-12. 

[18]

G. JiD. Wang and K. H. Tan, A study on external manufacturer entering deterrence strategy in the dual-channel supply chain, Systems Engineering-Theory & Practice, 38 (2018), 2230-2241. 

[19]

H. J. JuhlL. EsbjergK. G. GrunertT. Bech-Larsen and K. Brunsø, The fight between store brands and national brands-what's the score?, Journal of Retailing and Consumer Services, 13 (2006), 331-338.  doi: 10.1016/j.jretconser.2005.10.003.

[20]

A. Kalnins, An empirical analysis of territorial encroachment within franchised and company-owned brand chains, Journal of Retailing and Consumer Services, 13 (2006), 331-338. 

[21]

S. Karray and G. Zaccour, Could co-op advertising be a manufacturer's counterstrategy to store brands?, Journal of Business Research, 59 (2006), 1008-1015.  doi: 10.1016/j.jbusres.2006.05.002.

[22]

T. Keszey and W. Biemans, Sales-marketing encroachment effects on innovation, Journal of Business Research, 69 (2016), 3698-3706.  doi: 10.1016/j.jbusres.2016.03.032.

[23]

K. LiJ. Sun and J. Yan, Analysis of effect when store brands are introduced in indirect and mixed channels, Operations Research and Management Science, 261 (2017), 103-112. 

[24]

W. LiJ. Chen and B. Chen, Supply chain coordination with customer returns and retailer's store brand product, International Journal of Production Economics, 203 (2018), 69-82.  doi: 10.1016/j.ijpe.2018.05.032.

[25]

B. LiaoC. A. Yano and M. Trivedi, Optimizing store-brand quality: Impact of choice of producer and channel price leadership, Production and Operations Management, 29 (2020), 118-137.  doi: 10.1111/poms.13084.

[26]

S. Meza and K. Sudhir, Do private labels increase retailer bargaining power?, Quantitative Marketing and Economics, 8 (2010), 333-363. 

[27]

D. E. Mills, Why retailers sell private labels, Journal of Economics & Management Strategy, 4 (1995), 509-528.  doi: 10.1111/j.1430-9134.1995.00509.x.

[28]

K. S. Moorthy, Market segmentation, self-selection, and product line design, Marketing Science, 3 (1984), 288-307.  doi: 10.1287/mksc.3.4.288.

[29]

M. Motta, Endogenous quality choice: Price vs. quantity competition, Journal of Industrial Economics, 41 (1993), 113-131.  doi: 10.2307/2950431.

[30]

M. Mussa and S. Rosem, Monopoly and product quality, Journal of Economic Theory, 18 (1978), 301-317.  doi: 10.1016/0022-0531(78)90085-6.

[31]

C. Narasimhan and R. T. Wilcox, Private labels and the channel relationship: A cross-category analysis, Journal of Business, 71 (1998), 573-600.  doi: 10.1086/209757.

[32]

S. NasserD. Turcic and C. Narasimhan, National brand's response to store brands: Throw in the towel or fight back?, Marketing Science, 32 (2013), 591-608.  doi: 10.1287/mksc.2013.0788.

[33]

J. RuR. Shi and J. Zhang, Does a store brand always hurt the manufacturer of a competing national brand?, Production and Operations Management, 24 (2015), 272-286.  doi: 10.1111/poms.12220.

[34]

J. K. RyanD. Sun and X. Zhao, Competition and coordination in online marketplaces, Production and Operations Management, 21 (2012), 997-1014.  doi: 10.1111/j.1937-5956.2012.01332.x.

[35]

R. Sethuraman, Assessing the external validity of analytical results from national brand and store brand competition models, Marketing Science, 28 (2009), 759-781.  doi: 10.1287/mksc.1080.0455.

[36]

R. L. Steiner, The nature and benefits of national brand/private label competition, Review of Industrial Organization, 24 (2004), 105-127.  doi: 10.1023/B:REIO.0000033351.66025.05.

[37]

J. M. Villas-Boas, Product line design for a distribution channel, Marketing Science, 17 (1998), 156-169.  doi: 10.1287/mksc.17.2.156.

[38]

X. Zhang and W. Hou, The impacts of e-retailer's private label on the sales mode selection: From the perspectives of economic and environmental sustainability, European Journal of Operational Research, 296 (2021), 601-614.  doi: 10.1016/j.ejor.2021.04.009.

[39]

Q. Zheng, H. Jang and X. A. Pan, Store brand introduction and multilateral contracting, Manufacturing & Service Operations Management, early access, 2021. doi: 10.1287/msom.2020.0949.

[40]

Y. ZhouT. Liu and G. Cai, Impact of in-store promotion and spillover effect on private label introduction, Service Science, 11 (2019), 96-12.  doi: 10.1287/serv.2019.0236.

show all references

References:
[1]

K. L. AilawadiK. Pauwels and J. Steenkamp, Private-Label use and store loyalty, Journal of Marketing, 72 (2008), 19-30. 

[2]

K. L. Ailawadi and B. Harlam, An empirical analysis of the determinants of retail margins: The role of store-brand share, Journal of Marketing, 68 (2004), 147-165.  doi: 10.1509/jmkg.68.1.147.24027.

[3]

N. Al-MonawerM. Davoodi and L. Qi, Brand and quality effects on introduction of store brand products, Journal of Retailing and Consumer Services, 61 (2021), 102507.  doi: 10.1016/j.jretconser.2021.102507.

[4]

N. Amrouche and G. Zaccour, Shelf-space allocation of national and private brands, European Journal of Operational Research, 180 (2007), 648-663.  doi: 10.1016/j.ejor.2006.05.008.

[5]

N. Amrouche and R. Yan, Implementing online store for national brand competing against private label, Journal of Business Research, 65 (2012), 325-332.  doi: 10.1016/j.jbusres.2011.04.008.

[6]

C. ChambolleC. Christin and G. Meunier, The optimal production channel for private labels: Too much or too little innovation?, Journal of Economics Management Strategy, 24 (2015), 348-368.  doi: 10.1111/jems.12098.

[7]

L. ChenS. M. Gilbert and Y. Xia, Private labels: Facilitators or impediments to supply chain coordination, Decision Sciences, 42 (2011), 689-720.  doi: 10.1111/j.1540-5915.2011.00327.x.

[8]

R. ChengW. Ma and H. Ke, How does store-brand introduction affect a supply chain with uncertain information?, Journal of Intelligent and Fuzzy Systems, 34 (2018), 189-201.  doi: 10.3233/JIFS-171058.

[9]

C. Choi and A. T. Coughlan, Private label positioning: Quality versus feature differentiation from the national brand, Journal of Retailing, 82 (2006), 79-93. 

[10]

H. Chung and E. Lee, Store brand quality and retailer's product line design, Journal of Retailing, 93 (2017), 527-540.  doi: 10.1016/j.jretai.2017.09.002.

[11]

H. Chung and E. Lee, Effect of store brand introduction on channel price leadership: An empirical investigation, Journal of Retailing, 94 (2018), 21-32.  doi: 10.1016/j.jretai.2017.10.001.

[12]

X. FanC. Wang and Y. Liu, Positioning and channel effects of store brands under the condition of cost difference, Systems Engineering-Theory & Practice, 38 (2018), 2006-2017. 

[13]

A. Groznik and H. S. Heese, Supply chain conflict due to store brands: The value of wholesale price commitment in a retail supply chain, Decision Sciences, 41 (2010), 203-230.  doi: 10.1111/j.1540-5915.2010.00265.x.

[14]

A. Groznik and H. S. Heese, Supply chain interactions due to store-brand introductions: The impact of retail competition, European Journal of Operational Research, 203 (2010), 575-582.  doi: 10.1016/j.ejor.2009.08.014.

[15]

R. Hara and N. Matsubayashi, Premium store brand: Product development collaboration between retailers and national brand manufacturers, International Journal of Production Economics, 185 (2017), 128-138.  doi: 10.1016/j.ijpe.2016.12.024.

[16]

H. S. Heese, Competing with channel partners: Supply chain conflict when retailers introduce store brands, Naval Research Logs., 57 (2010), 441-459.  doi: 10.1002/nav.20412.

[17]

Z. Huang and T. Feng, Money-back guarantee and pricing decision with retailer's Store brand, Journal of Retailing and Consumer Services, 52 (2019), 1-12. 

[18]

G. JiD. Wang and K. H. Tan, A study on external manufacturer entering deterrence strategy in the dual-channel supply chain, Systems Engineering-Theory & Practice, 38 (2018), 2230-2241. 

[19]

H. J. JuhlL. EsbjergK. G. GrunertT. Bech-Larsen and K. Brunsø, The fight between store brands and national brands-what's the score?, Journal of Retailing and Consumer Services, 13 (2006), 331-338.  doi: 10.1016/j.jretconser.2005.10.003.

[20]

A. Kalnins, An empirical analysis of territorial encroachment within franchised and company-owned brand chains, Journal of Retailing and Consumer Services, 13 (2006), 331-338. 

[21]

S. Karray and G. Zaccour, Could co-op advertising be a manufacturer's counterstrategy to store brands?, Journal of Business Research, 59 (2006), 1008-1015.  doi: 10.1016/j.jbusres.2006.05.002.

[22]

T. Keszey and W. Biemans, Sales-marketing encroachment effects on innovation, Journal of Business Research, 69 (2016), 3698-3706.  doi: 10.1016/j.jbusres.2016.03.032.

[23]

K. LiJ. Sun and J. Yan, Analysis of effect when store brands are introduced in indirect and mixed channels, Operations Research and Management Science, 261 (2017), 103-112. 

[24]

W. LiJ. Chen and B. Chen, Supply chain coordination with customer returns and retailer's store brand product, International Journal of Production Economics, 203 (2018), 69-82.  doi: 10.1016/j.ijpe.2018.05.032.

[25]

B. LiaoC. A. Yano and M. Trivedi, Optimizing store-brand quality: Impact of choice of producer and channel price leadership, Production and Operations Management, 29 (2020), 118-137.  doi: 10.1111/poms.13084.

[26]

S. Meza and K. Sudhir, Do private labels increase retailer bargaining power?, Quantitative Marketing and Economics, 8 (2010), 333-363. 

[27]

D. E. Mills, Why retailers sell private labels, Journal of Economics & Management Strategy, 4 (1995), 509-528.  doi: 10.1111/j.1430-9134.1995.00509.x.

[28]

K. S. Moorthy, Market segmentation, self-selection, and product line design, Marketing Science, 3 (1984), 288-307.  doi: 10.1287/mksc.3.4.288.

[29]

M. Motta, Endogenous quality choice: Price vs. quantity competition, Journal of Industrial Economics, 41 (1993), 113-131.  doi: 10.2307/2950431.

[30]

M. Mussa and S. Rosem, Monopoly and product quality, Journal of Economic Theory, 18 (1978), 301-317.  doi: 10.1016/0022-0531(78)90085-6.

[31]

C. Narasimhan and R. T. Wilcox, Private labels and the channel relationship: A cross-category analysis, Journal of Business, 71 (1998), 573-600.  doi: 10.1086/209757.

[32]

S. NasserD. Turcic and C. Narasimhan, National brand's response to store brands: Throw in the towel or fight back?, Marketing Science, 32 (2013), 591-608.  doi: 10.1287/mksc.2013.0788.

[33]

J. RuR. Shi and J. Zhang, Does a store brand always hurt the manufacturer of a competing national brand?, Production and Operations Management, 24 (2015), 272-286.  doi: 10.1111/poms.12220.

[34]

J. K. RyanD. Sun and X. Zhao, Competition and coordination in online marketplaces, Production and Operations Management, 21 (2012), 997-1014.  doi: 10.1111/j.1937-5956.2012.01332.x.

[35]

R. Sethuraman, Assessing the external validity of analytical results from national brand and store brand competition models, Marketing Science, 28 (2009), 759-781.  doi: 10.1287/mksc.1080.0455.

[36]

R. L. Steiner, The nature and benefits of national brand/private label competition, Review of Industrial Organization, 24 (2004), 105-127.  doi: 10.1023/B:REIO.0000033351.66025.05.

[37]

J. M. Villas-Boas, Product line design for a distribution channel, Marketing Science, 17 (1998), 156-169.  doi: 10.1287/mksc.17.2.156.

[38]

X. Zhang and W. Hou, The impacts of e-retailer's private label on the sales mode selection: From the perspectives of economic and environmental sustainability, European Journal of Operational Research, 296 (2021), 601-614.  doi: 10.1016/j.ejor.2021.04.009.

[39]

Q. Zheng, H. Jang and X. A. Pan, Store brand introduction and multilateral contracting, Manufacturing & Service Operations Management, early access, 2021. doi: 10.1287/msom.2020.0949.

[40]

Y. ZhouT. Liu and G. Cai, Impact of in-store promotion and spillover effect on private label introduction, Service Science, 11 (2019), 96-12.  doi: 10.1287/serv.2019.0236.

Figure 1.  Encroachment of demand under high-end competition strategy $ \left(\sigma>\theta\right) $
Figure 2.  Encroachment of demand under high-end competition strategy $ \left(\sigma<\theta\right) $
Figure 3.  Encroachment of demand under low-end competition strategy
Figure 4.  Encroachment of demand under product line competition strategy$ \left(\sigma>\theta\right) $
Figure 5.  Encroachment of demand under product line competition strategy$ \left(\sigma<\theta\right) $
Figure 6.  Profit comparison of retailer under different competitive strategies$ \left(\sigma>\theta\right) $
Figure 7.  Profit comparison of retailer under different competitive strategies$ \left(\sigma<\theta\right) $
Figure 8.  Profit comparison of NBM under different competitive strategies$ \left(\sigma>\theta\right) $
Figure 9.  Profit comparison of NBM under different competitive strategies$ \left(\sigma<\theta\right) $
Table 1.  The notations used in this paper
Notations Explanations
NB; SB National Brand; Store Brand
NH; NL;SH; SL NB high-end product; NB Low-end product; SB high-end product; SB Low-end product
$ u_{ij} $ The utility of consumers' purchasing $ j $ products of brand $ i $, where $ i={N,S};j={H,L} $
$ \theta,\sigma,\upsilon $ brand internal encroachment effect; brand external encroachment effect; Consumers' evaluation of NH
$ w_{ij},p_{ij} $ the wholesale price of $ j $ product of brand $ i $; the retail price of $ j $ product of brand $ i $
$ c_{ij},q_{ij} $ The production cost of $ j $ products of brand $ i $; The demand of $ j $ products of brand $ i $
$ \pi_{M}^{k},\pi_{R}^{k} $ Manufacturer's profit; retailer's profit; where $ k = 0,1,2,3 $ respectively indicate that there is no SB, SH competition strategy, SL competition strategy, product line competition strategy
$ \Delta_{H}^{k},\Delta_{L}^{k} $ The difference between the retailer's profit from unit SH and SL and the profit from the benchmark model
$ (x,y) $ The corresponding profit expressions for retailers under different introduction strategies, $ k=0,1,2,3 $ corresponding to $ (x, y)={(0,0),(1,0),(0,1),(1,1)} $
Notations Explanations
NB; SB National Brand; Store Brand
NH; NL;SH; SL NB high-end product; NB Low-end product; SB high-end product; SB Low-end product
$ u_{ij} $ The utility of consumers' purchasing $ j $ products of brand $ i $, where $ i={N,S};j={H,L} $
$ \theta,\sigma,\upsilon $ brand internal encroachment effect; brand external encroachment effect; Consumers' evaluation of NH
$ w_{ij},p_{ij} $ the wholesale price of $ j $ product of brand $ i $; the retail price of $ j $ product of brand $ i $
$ c_{ij},q_{ij} $ The production cost of $ j $ products of brand $ i $; The demand of $ j $ products of brand $ i $
$ \pi_{M}^{k},\pi_{R}^{k} $ Manufacturer's profit; retailer's profit; where $ k = 0,1,2,3 $ respectively indicate that there is no SB, SH competition strategy, SL competition strategy, product line competition strategy
$ \Delta_{H}^{k},\Delta_{L}^{k} $ The difference between the retailer's profit from unit SH and SL and the profit from the benchmark model
$ (x,y) $ The corresponding profit expressions for retailers under different introduction strategies, $ k=0,1,2,3 $ corresponding to $ (x, y)={(0,0),(1,0),(0,1),(1,1)} $
Table 2.  Changes in market share of national brands under different competitive strategies
strategy type Encroachment effect relationship NH's market share has encroached NL's market share has encroached Market Expansion
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ A1 B1 /
$ \sigma <\theta $ / A2 B2
Low-end competition strategy(Introduction of SL) $ \theta\sigma <\theta $ / A3 B3
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ A4 B4+A5 B5
$ \sigma <\theta $ / A6 B6+A7
Notes: The values of A1-A7 and B1-B6 are shown in Figure 1 to Figure 5.
strategy type Encroachment effect relationship NH's market share has encroached NL's market share has encroached Market Expansion
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ A1 B1 /
$ \sigma <\theta $ / A2 B2
Low-end competition strategy(Introduction of SL) $ \theta\sigma <\theta $ / A3 B3
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ A4 B4+A5 B5
$ \sigma <\theta $ / A6 B6+A7
Notes: The values of A1-A7 and B1-B6 are shown in Figure 1 to Figure 5.
Table 3.  The equilibrium price of each product under different introduction strategies of store brands
Strategy type encroachment effect relationship $ w_{NH} $ $ w_{NL} $ $ p_{NH} $ $ p_{NL} $ $ p_{SH} $ $ p_{SL} $
Benchmark Model / $ \frac{1+c_{NH}}{2} $ $ \frac{\theta+c_{NL}}{2} $ $ \frac{1+c_{NH}}{2} $ $ \frac{3\theta+c_{NL}}{4} $ / /
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\sigma c_{NL}+\theta c_{SH}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{2\theta\sigma+\sigma c_{NL}+\theta c_{SH}}{4\sigma} $ $ \frac{\sigma+c_{SH}}{2} $ /
$ \sigma <\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\theta-\sigma+c_{NL}+c_{SH}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{3\theta-\theta\sigma+c_{NL}+c_{SH}}{4} $ $ \frac{\sigma+c_{SH}}{2} $ /
Low-end competition strategy (Introduction of SL) $ \theta\sigma <\theta $ $ \frac{1-\theta\sigma+c_{NH}+c_{SL}}{2} $ $ \frac{\theta-\theta\sigma+c_{NL}+c_{SL}}{2} $ $ \frac{3-\theta\sigma+c_{NH}+c_{SL}}{4} $ $ \frac{3\theta-\theta\sigma+c_{NL}+c_{SL}}{4} $ / $ \frac{\theta\sigma+c_{SL}}{2} $
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\left( \sigma-\theta\right)c_{SL}}{2\sigma\left(1-\theta\right)}+\frac{\theta\left( 1-\sigma\right) c_{SH}}{2\sigma\left( 1-\theta\right)} +\frac{c_{NL}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{\left( \sigma-\theta\right)c_{SL}}{4\sigma\left(1-\theta\right)}+\frac{\theta\left( 1-\sigma\right) c_{SH}}{4\sigma\left( 1-\theta\right)} +\frac{c_{NL}+2\theta}{4} $ $ \frac{\sigma+c_{SH}}{2} $ $ \frac{\theta\sigma+c_{SL}}{2} $
$ \sigma <\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\theta-\sigma+c_{NL}+c_{SH}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{3\theta-\theta\sigma+c_{NL}+c_{SH}}{4} $ $ \frac{\sigma+c_{SH}}{2} $ $ \frac{\theta\sigma+c_{SL}}{2} $
Strategy type encroachment effect relationship $ w_{NH} $ $ w_{NL} $ $ p_{NH} $ $ p_{NL} $ $ p_{SH} $ $ p_{SL} $
Benchmark Model / $ \frac{1+c_{NH}}{2} $ $ \frac{\theta+c_{NL}}{2} $ $ \frac{1+c_{NH}}{2} $ $ \frac{3\theta+c_{NL}}{4} $ / /
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\sigma c_{NL}+\theta c_{SH}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{2\theta\sigma+\sigma c_{NL}+\theta c_{SH}}{4\sigma} $ $ \frac{\sigma+c_{SH}}{2} $ /
$ \sigma <\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\theta-\sigma+c_{NL}+c_{SH}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{3\theta-\theta\sigma+c_{NL}+c_{SH}}{4} $ $ \frac{\sigma+c_{SH}}{2} $ /
Low-end competition strategy (Introduction of SL) $ \theta\sigma <\theta $ $ \frac{1-\theta\sigma+c_{NH}+c_{SL}}{2} $ $ \frac{\theta-\theta\sigma+c_{NL}+c_{SL}}{2} $ $ \frac{3-\theta\sigma+c_{NH}+c_{SL}}{4} $ $ \frac{3\theta-\theta\sigma+c_{NL}+c_{SL}}{4} $ / $ \frac{\theta\sigma+c_{SL}}{2} $
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\left( \sigma-\theta\right)c_{SL}}{2\sigma\left(1-\theta\right)}+\frac{\theta\left( 1-\sigma\right) c_{SH}}{2\sigma\left( 1-\theta\right)} +\frac{c_{NL}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{\left( \sigma-\theta\right)c_{SL}}{4\sigma\left(1-\theta\right)}+\frac{\theta\left( 1-\sigma\right) c_{SH}}{4\sigma\left( 1-\theta\right)} +\frac{c_{NL}+2\theta}{4} $ $ \frac{\sigma+c_{SH}}{2} $ $ \frac{\theta\sigma+c_{SL}}{2} $
$ \sigma <\theta $ $ \frac{1-\sigma+c_{NH}+c_{SH}}{2} $ $ \frac{\theta-\sigma+c_{NL}+c_{SH}}{2} $ $ \frac{3-\sigma+c_{NH}+c_{SH}}{4} $ $ \frac{3\theta-\theta\sigma+c_{NL}+c_{SH}}{4} $ $ \frac{\sigma+c_{SH}}{2} $ $ \frac{\theta\sigma+c_{SL}}{2} $
Table 4.  The equilibrium price of each product under different introduction strategies of store brands
Strategy type $ \sigma >\theta $ $ \sigma <\theta $
High-end competition strategy (Introduction of SH) $ \Delta_{H}^{1}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{1}=\frac{\theta-\theta\sigma c}{4} $ $ \Delta_{H}^{1}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{H}^{1}=\frac{\sigma-\sigma^2 c}{4} $
Low-end competition strategy (Introduction of SL) $ \Delta_{H}^{2}=\frac{\theta\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{2}=\frac{\theta\sigma+\theta^2\sigma^2 c}{4} $ $ \Delta_{H}^{2}=\frac{\theta\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{2}=\frac{\theta\sigma+\theta^2\sigma^2 c}{4} $
Competitive strategy of product line (Introduction of SH and SL) $ \Delta_{H}^{3}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{3}=\frac{\theta-\theta c\left[ \sigma\left( 1-\sigma\right) +\theta\sigma\right]}{4} $ $ \Delta_{H}^{3}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{3}=\frac{\sigma+\sigma^2 c}{4} $
Strategy type $ \sigma >\theta $ $ \sigma <\theta $
High-end competition strategy (Introduction of SH) $ \Delta_{H}^{1}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{1}=\frac{\theta-\theta\sigma c}{4} $ $ \Delta_{H}^{1}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{H}^{1}=\frac{\sigma-\sigma^2 c}{4} $
Low-end competition strategy (Introduction of SL) $ \Delta_{H}^{2}=\frac{\theta\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{2}=\frac{\theta\sigma+\theta^2\sigma^2 c}{4} $ $ \Delta_{H}^{2}=\frac{\theta\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{2}=\frac{\theta\sigma+\theta^2\sigma^2 c}{4} $
Competitive strategy of product line (Introduction of SH and SL) $ \Delta_{H}^{3}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{3}=\frac{\theta-\theta c\left[ \sigma\left( 1-\sigma\right) +\theta\sigma\right]}{4} $ $ \Delta_{H}^{3}=\frac{\sigma-\sigma^2 c}{4} $ $ \Delta_{L}^{3}=\frac{\sigma+\sigma^2 c}{4} $
Table 5.  The impact of price encroachment under different competitive strategy
Strategy type Encroachment effect relationship $ w_{NH},p_{NH} $ $ w_{NL},p_{NL} $ $ p_{SH} $ $ p_{sL} $
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \uparrow $ $ \uparrow $ /
$ \sigma <\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \uparrow $ /
Low-end competition strategy (Introduction of SL) $ \theta\sigma <\theta $ $ \theta\sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \theta\sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \theta\sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \theta\sigma >\frac{1}{2c}\left( \downarrow\right) $ / $ \uparrow $
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \sigma <\frac{1+\theta}{2}\left(\uparrow \right) $; $ \sigma >\frac{1+\theta}{2c}\left( \downarrow\right) $ $ \uparrow $ $ \uparrow $
$ \sigma <\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \uparrow $ $ \uparrow $
Notes:"$\uparrow$" indicates that the price increases with the increase of encroachment effect, that is, the positive effect; "$\downarrow$" indicates that the price decreases with the increase of encroachment effect, that is, negative influence; "/" means not affected by encroachment effect.
Strategy type Encroachment effect relationship $ w_{NH},p_{NH} $ $ w_{NL},p_{NL} $ $ p_{SH} $ $ p_{sL} $
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \uparrow $ $ \uparrow $ /
$ \sigma <\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \uparrow $ /
Low-end competition strategy (Introduction of SL) $ \theta\sigma <\theta $ $ \theta\sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \theta\sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \theta\sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \theta\sigma >\frac{1}{2c}\left( \downarrow\right) $ / $ \uparrow $
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \sigma <\frac{1+\theta}{2}\left(\uparrow \right) $; $ \sigma >\frac{1+\theta}{2c}\left( \downarrow\right) $ $ \uparrow $ $ \uparrow $
$ \sigma <\theta $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \sigma <\frac{1}{2c}\left(\uparrow \right) $; $ \sigma >\frac{1}{2c}\left( \downarrow\right) $ $ \uparrow $ $ \uparrow $
Notes:"$\uparrow$" indicates that the price increases with the increase of encroachment effect, that is, the positive effect; "$\downarrow$" indicates that the price decreases with the increase of encroachment effect, that is, negative influence; "/" means not affected by encroachment effect.
Table 6.  The order of prices under different competition strategies
Stragegy type $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ \frac{\left( 1-\sigma\right) }{\sigma\left( 1-\theta\sigma\right) } <c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{\left( 1-\sigma\right) }{\sigma\left( 1-\theta\sigma\right) } $
$ \sigma >\theta $ $ w_{NH}^{0} >w_{NH}^{1}=w_{NH}^{3} >w_{NH}^{2} $ $ w_{NH}^{0} >w_{NH}^{2} >w_{NH}^{1}=w_{NH}^{3} $ $ w_{NL}^{0} >w_{NL}^{1} >w_{NL}^{2} >w_{NL}^{3} $ $ w_{NL}^{0} >w_{NL}^{1} >w_{NL}^{3} >w_{NL}^{2} $ $ w_{NL}^{0} >w_{NL}^{2} >w_{NL}^{1} >w_{NL}^{3} $
$ p_{NH}^{0} >p_{NH}^{1}=p_{NH}^{3} >p_{NH}^{2} $ $ p_{NH}^{0} >p_{NH}^{2} >p_{NH}^{1}=p_{NH}^{3} $ $ p_{NL}^{0} >p_{NL}^{1} >p_{NL}^{2} >p_{NL}^{3} $ $ p_{NL}^{0} >p_{NL}^{1} >p_{NL}^{3} >p_{NL}^{2} $ $ p_{NL}^{0} >p_{NL}^{2} >p_{NL}^{1} >p_{NL}^{3} $
Stragegy type $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ {} $
$ \sigma <\theta $ $ w_{NH}^{0} >w_{NH}^{1}=w_{NH}^{3} >w_{NH}^{2} $ $ w_{NH}^{0} >w_{NH}^{2} >w_{NH}^{1}=w_{NH}^{3} $ $ w_{NL}^{0} >w_{NL}^{1}+w_{NL}^{3} >w_{NL}^{2} $ $ w_{NL}^{0} >w_{NL}^{2} >w_{NL}^{1}+w_{NL}^{3} $ $ {} $
$ p_{NH}^{0} >p_{NH}^{1}=p_{NH}^{3} >p_{NH}^{2} $ $ p_{NH}^{0} >p_{NH}^{2} >p_{NH}^{1}=p_{NH}^{3} $ $ p_{NL}^{0} >p_{NL}^{1}=p_{NL}^{3} >p_{NL}^{2} $ $ p_{NL}^{0} >p_{NL}^{2} >p_{NL}^{1}=p_{NL}^{3} $ $ {} $
Stragegy type $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ \frac{\left( 1-\sigma\right) }{\sigma\left( 1-\theta\sigma\right) } <c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{\left( 1-\sigma\right) }{\sigma\left( 1-\theta\sigma\right) } $
$ \sigma >\theta $ $ w_{NH}^{0} >w_{NH}^{1}=w_{NH}^{3} >w_{NH}^{2} $ $ w_{NH}^{0} >w_{NH}^{2} >w_{NH}^{1}=w_{NH}^{3} $ $ w_{NL}^{0} >w_{NL}^{1} >w_{NL}^{2} >w_{NL}^{3} $ $ w_{NL}^{0} >w_{NL}^{1} >w_{NL}^{3} >w_{NL}^{2} $ $ w_{NL}^{0} >w_{NL}^{2} >w_{NL}^{1} >w_{NL}^{3} $
$ p_{NH}^{0} >p_{NH}^{1}=p_{NH}^{3} >p_{NH}^{2} $ $ p_{NH}^{0} >p_{NH}^{2} >p_{NH}^{1}=p_{NH}^{3} $ $ p_{NL}^{0} >p_{NL}^{1} >p_{NL}^{2} >p_{NL}^{3} $ $ p_{NL}^{0} >p_{NL}^{1} >p_{NL}^{3} >p_{NL}^{2} $ $ p_{NL}^{0} >p_{NL}^{2} >p_{NL}^{1} >p_{NL}^{3} $
Stragegy type $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ c >\frac{1}{\sigma\left( 1+\theta\right) } $ $ c <\frac{1}{\sigma\left( 1+\theta\right) } $ $ {} $
$ \sigma <\theta $ $ w_{NH}^{0} >w_{NH}^{1}=w_{NH}^{3} >w_{NH}^{2} $ $ w_{NH}^{0} >w_{NH}^{2} >w_{NH}^{1}=w_{NH}^{3} $ $ w_{NL}^{0} >w_{NL}^{1}+w_{NL}^{3} >w_{NL}^{2} $ $ w_{NL}^{0} >w_{NL}^{2} >w_{NL}^{1}+w_{NL}^{3} $ $ {} $
$ p_{NH}^{0} >p_{NH}^{1}=p_{NH}^{3} >p_{NH}^{2} $ $ p_{NH}^{0} >p_{NH}^{2} >p_{NH}^{1}=p_{NH}^{3} $ $ p_{NL}^{0} >p_{NL}^{1}=p_{NL}^{3} >p_{NL}^{2} $ $ p_{NL}^{0} >p_{NL}^{2} >p_{NL}^{1}=p_{NL}^{3} $ $ {} $
Table 7.  Optimal profit for manufacturers and retailers under different introduction strategies
Benchmark Model / $ \left\{ \begin{array}{l} \pi_{M}^{0}=\frac{1-2c+c^2 E}{8}\\ \pi_{R}^{0}=\frac{1-2c+c^2 E}{16}\end{array} \right. $
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{1}=\frac{A+c^2 B}{8} \\ \pi_{R}^{1}=\frac{D+c^2 \left( B+4\Sigma ^3\right) }{16}\end{array} \right. $
$ \sigma <\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{1}=\frac{A+\left( 1+\sigma\right) c^2 \left[ E+\sigma\left( 1+\theta+\sigma\right) \right] }{8}\\ \pi_{R}^{1}=\frac{D+c^2 \left[ E+\sigma\left( \theta^2 -\theta\sigma+3\sigma^2\right) \right] }{16}\end{array} \right. $
Low-end competition strategy (Introduction of SL) $ \theta\sigma <\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{2}=\frac{F+\left( 1-\theta\sigma\right) c^2 \left[ E+\theta\sigma\left( 1+\theta\sigma+\theta^2\right) \right] }{8} \\ \pi_{R}^{2}=\frac{G+c^2 \left[ E+\theta^3\sigma\left( 1 -\sigma+3\sigma^2\right) \right] }{16}\end{array} \right. $
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{3}=\frac{F+\left( 1-\sigma\right) c^2 \left[ 1+\sigma\left( 2-\theta^2+\theta^3\right) +E \sigma^2\right] }{8} \\ \pi_{R}^{3}=\frac{D+c^2 \left[ B+\theta^3\left( 1-\sigma\right) +\sigma^3\left( 1+3E\right) \right] }{16}\end{array} \right. $
$ \sigma <\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{3}=\frac{A+\left( 1-\sigma\right) c^2 \left[ E+\sigma\left( 1+\theta+\sigma\right) \right] }{8} \\ \pi_{R}^{3}=\frac{D+c^2 \left[ E+\theta^3\left( 1-2\theta\right) \left( 3+2\theta\right) -\theta\sigma\left( \sigma-\theta\right) \right] }{16}\end{array} \right. $
Remark / $ A=1-\sigma-2c\left( 1-2\sigma^2\right);B=1+\sigma\left( 1-\theta^2\right) -\sigma^2\left( 1-\theta\right) - \\ \sigma^3;D=1+3\sigma-2c\left( 1+3\sigma^2\right) ;E=1+\theta-\theta^2;F= \\ \left( 1-\theta\sigma\right) -2c\left( 1-\theta^2\sigma^2\right) ;G=1+3\theta\sigma-2c\left( 1+3\theta^3\sigma^3\right) $
Benchmark Model / $ \left\{ \begin{array}{l} \pi_{M}^{0}=\frac{1-2c+c^2 E}{8}\\ \pi_{R}^{0}=\frac{1-2c+c^2 E}{16}\end{array} \right. $
High-end competition strategy (Introduction of SH) $ \sigma >\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{1}=\frac{A+c^2 B}{8} \\ \pi_{R}^{1}=\frac{D+c^2 \left( B+4\Sigma ^3\right) }{16}\end{array} \right. $
$ \sigma <\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{1}=\frac{A+\left( 1+\sigma\right) c^2 \left[ E+\sigma\left( 1+\theta+\sigma\right) \right] }{8}\\ \pi_{R}^{1}=\frac{D+c^2 \left[ E+\sigma\left( \theta^2 -\theta\sigma+3\sigma^2\right) \right] }{16}\end{array} \right. $
Low-end competition strategy (Introduction of SL) $ \theta\sigma <\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{2}=\frac{F+\left( 1-\theta\sigma\right) c^2 \left[ E+\theta\sigma\left( 1+\theta\sigma+\theta^2\right) \right] }{8} \\ \pi_{R}^{2}=\frac{G+c^2 \left[ E+\theta^3\sigma\left( 1 -\sigma+3\sigma^2\right) \right] }{16}\end{array} \right. $
Competitive strategy of product line (Introduction of SH and SL) $ \sigma >\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{3}=\frac{F+\left( 1-\sigma\right) c^2 \left[ 1+\sigma\left( 2-\theta^2+\theta^3\right) +E \sigma^2\right] }{8} \\ \pi_{R}^{3}=\frac{D+c^2 \left[ B+\theta^3\left( 1-\sigma\right) +\sigma^3\left( 1+3E\right) \right] }{16}\end{array} \right. $
$ \sigma <\theta $ $ \left\{ \begin{array}{l} \pi_{M}^{3}=\frac{A+\left( 1-\sigma\right) c^2 \left[ E+\sigma\left( 1+\theta+\sigma\right) \right] }{8} \\ \pi_{R}^{3}=\frac{D+c^2 \left[ E+\theta^3\left( 1-2\theta\right) \left( 3+2\theta\right) -\theta\sigma\left( \sigma-\theta\right) \right] }{16}\end{array} \right. $
Remark / $ A=1-\sigma-2c\left( 1-2\sigma^2\right);B=1+\sigma\left( 1-\theta^2\right) -\sigma^2\left( 1-\theta\right) - \\ \sigma^3;D=1+3\sigma-2c\left( 1+3\sigma^2\right) ;E=1+\theta-\theta^2;F= \\ \left( 1-\theta\sigma\right) -2c\left( 1-\theta^2\sigma^2\right) ;G=1+3\theta\sigma-2c\left( 1+3\theta^3\sigma^3\right) $
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