doi: 10.3934/jimo.2021043
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Pricing new and remanufactured products based on customer purchasing behavior

1. 

School of Management, Hefei University of Technology, Hefei, China

2. 

Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, China

3. 

Research Center of Industrial Transfer and Innovation Development, Hefei University of Technology, Hefei, China

* Corresponding author: Tao Zhou

Received  May 2020 Revised  September 2020 Early access March 2021

Fund Project: The first author is supported by National Natural Science Foundation of China under grants 71871076, 71690235, 71521001

Firms' pricing strategies are largely influenced by customer purchasing behavior. By considering whether to invest in customer purchasing behavior analysis, firms can choose a discriminatory or a non-discriminatory pricing model. This paper presents a two-period duopoly that the original material supplier (OS) supplying new products faces a competition of an independent material supplier (IS) providing remanufactured products to analyze each party's competitive strategy under each pricing model. We also identify situations under which the firms would obtain more profits and cause less environmental impact under the model with price discrimination compared with the model without price discrimination. A numerical study is provided to illustrate the performance of the model. A sensitivity analysis with respect to primary parameters is used to assess the stability of the model. The proposed model could be applied in many industrial fields where the managers have the full awareness of extended producer responsibility, and they are willing to engage in the project related to remanufacturing.

Citation: Kai Li, Tao Zhou, Bohai Liu. Pricing new and remanufactured products based on customer purchasing behavior. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021043
References:
[1]

J. D. Abbey and J. D. Blackburn, Optimal pricing for new and remanufactured products, J. Oper. Manag., 36 (2015), 130-146.  doi: 10.1016/j.jom.2015.03.007.  Google Scholar

[2]

J. D. AbbeyR. KleberG. C. Souza and G. Voigt, The role of perceived quality risk in pricing remanufactured products, Prod. Oper. Manag., 26 (2017), 100-115.  doi: 10.1111/poms.12628.  Google Scholar

[3]

V. V. AgrawalA. Atasu and K. V. Ittersum, Remanufacturing, third-party competition, and consumers' perceived value of new products, Manage. Sci., 61 (2015), 60-72.   Google Scholar

[4]

R. AnB. YuR. Li and Y. Wei, Potential of energy savings and $CO_{2}$ emission reduction in China's iron and steel industry, Appl. Energ., 226 (2018), 862-880.   Google Scholar

[5]

A. AtasuM. Sarvary and L. N. Van Wassenhove, Remanufacturing as a marketing strategy, Manag. Sci., 54 (2008), 1731-1746.  doi: 10.1287/mnsc.1080.0893.  Google Scholar

[6]

A. AtasuV. D. R. Guide Jr. and L.N. Van Wassenhove, So what if remanufacturing cannibalizes my new product sales?, Calif. Manage. Rev., 52 (2010), 56-76.  doi: 10.1525/cmr.2010.52.2.56.  Google Scholar

[7]

A. Atasu and G. C. Souza, How does product recovery affect quality choice?, Prod. Oper. Manag., 22 (2013), 991-1010.  doi: 10.1111/j.1937-5956.2011.01290.x.  Google Scholar

[8]

H. Barman, M. Pervin, S. K. Roy and G. W. Weber, Back-ordered inventory model with inflation in a cloudy-fuzzy environment, J. Ind. Manag. Optim., 13(5) (2020). Google Scholar

[9]

G. Bitran and R. Caldentey, An overview of pricing models for revenue management, M & SOM-Manuf. Serv. Op., 5 (2003), 203-229.   Google Scholar

[10]

L. G. DeboL. B. Toktay and L. N. Van Wassenhove, Market segmentation and product technology selection for remanufacturable products, Manage. Sci., 51 (2005), 1193-1205.  doi: 10.1287/mnsc.1050.0369.  Google Scholar

[11]

M. E. Ferguson and L. B. Toktay, The effect of competition on recovery strategies, Prod. Oper. Manag., 15 (2006), 351-368.  doi: 10.1111/j.1937-5956.2006.tb00250.x.  Google Scholar

[12]

G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Manage. Sci., 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465.  Google Scholar

[13]

D. A. Garvin, What does "product quality" really mean?, Sloan. Manage. Rev., 26 (1984), 25-43.   Google Scholar

[14]

R. GeyerL. N. Van Wassenhove and A. Atasu, The economics of remanufacturing under limited component durability and finite product life cycles, Manag. Sci., 53 (2007), 88-100.  doi: 10.1287/mnsc.1060.0600.  Google Scholar

[15]

V. D. R. Guide Jr.R. H. Teunter and L. N. Van Wassenhove, Matching demand and supply to maximize profits from remanufacturing, M & SOM-Manuf. Serv. Op., 5 (2003), 303-316.   Google Scholar

[16]

V. D. R. Guide Jr. and L. N. Van Wassenhove, Closed-loop supply chains, Quantitative approaches to distribution logistics and supply chain management, (2002), 47–60. Google Scholar

[17]

T. G. GutowskiS. SahniA. Boustani and and S. C. Gravesa, Remanufacturing and energy savings, Environ. Sci. Technol., 45 (2011), 4540-4547.  doi: 10.1021/es102598b.  Google Scholar

[18]

I. Hendel and A. Lizzeri, Interfering with secondary markets, RAND. J. Econ., 30 (1999), 1-21.   Google Scholar

[19]

N. KaraliT. Xu and J. Sathaye, Reducing energy consumption and $CO_{2}$ emissions by energy efficiency measures and international trading: a bottom-up modeling for the US iron and steel sector, Appl. Energ., 120 (2014), 133-146.   Google Scholar

[20]

R. LotfiG. W. WeberS. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, J. Ind. Manag. Optim., 16 (2020), 117-140.  doi: 10.3934/jimo.2018143.  Google Scholar

[21]

R. LotfiM. NayeriS. M. Sajadifar and N. Mardani, Determination of start times and ordering plans for two-period projects with interdependent demand in project-oriented organizations: A case study on molding industry, J. Proj. Manag., 2(4) (2017), 119-142.  doi: 10.5267/j.jpm.2017.9.001.  Google Scholar

[22]

MarkLines, China-Flash report, Sales volume, 2018, 2018. https://www.marklines.com/en/statistics/flash_sales/salesfig_china_2018. Google Scholar

[23]

K.S. Moorthy, Product and price competition in a duopoly, Market. Sci., 7 (1988), 141-168.  doi: 10.1287/mksc.7.2.141.  Google Scholar

[24]

National Laws, Circular Economy Promotion Law of the People's Republic of China, 2008. Google Scholar

[25]

A. ÖrsdemirE. Kemahlıoǧlu-Ziya and A. K. Parlaktürk, Competitive quality choice and remanufacturing, Prod. Oper. Manag., 23 (2014), 48-64.   Google Scholar

[26]

A. Ovchinnikov, Revenue and cost management for remanufactured products, Prod. Oper. Manag., 20 (2011), 824-840.  doi: 10.1111/j.1937-5956.2010.01214.x.  Google Scholar

[27]

A. Ovchinnikovv. Blass and G. Raz, Economic and environmental assessment of remanufacturing strategies for product+service firms, Prod. Oper. Manag., 23 (2014), 744-761.  doi: 10.1111/poms.12070.  Google Scholar

[28]

M. PervinS. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Ann. Oper. Res, 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.  Google Scholar

[29]

M. PervinS. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.  Google Scholar

[30]

M. PervinS. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price-and stock-sensitive demand, J. Ind. Manag. Optim., 16 (2020), 1585-1612.  doi: 10.3934/jimo.2019019.  Google Scholar

[31]

M. Pranab and G. Harry, Competition in remanufacturing, Prod. Oper. Manag., 10 (2001), 125-141.   Google Scholar

[32]

S. K. RoyM. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, J. Ind. Manag. Optim., 16 (2020), 553-578.  doi: 10.3934/jimo.2018167.  Google Scholar

[33]

R. C. SavaskanS. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manag. Sci., 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[34]

G. C. Souza, Closed-loop supply chains with remanufacturing, State-of-the-Art Decision-Making Tools in the Information-Intensive Age, Informs, (2014), 130-153. doi: 10.1287/educ. 1080.0040.  Google Scholar

[35]

State Legislation, Electronics Take-Back Coalition, 2010. Google Scholar

[36]

R. SubramanianM. E. Ferguson and L. B. Toktay, Remanufacturing and the Component Commonality Decision, Prod. Oper. Manag., 22 (2013), 36-53.   Google Scholar

[37]

M. ThierryM. SalomonJ. Van Nunen and L. N. Van Wassenhove, Strategic issues in product recovery management, Calif. Manage. Rev., 37 (1995), 114-135.  doi: 10.2307/41165792.  Google Scholar

[38]

V. Thomas, The environmental potential of reuse: an application to used books, Sustain. Sci., 6 (2011), 109-116.   Google Scholar

[39]

B. K. Thorn and P. Rogerson, Take it back, IIE Solutions., 34 (2002), 34-40.   Google Scholar

[40]

N. Tojo, Extended producer responsibility as a driver for design change-utopia or reality? IIIEE Dissertations, Lund University, (2004). Google Scholar

[41]

J. Vorasayan and S. M. Ryan, Optimal price and quantity of refurbished products, Prod. Oper. Manag., 15 (2009), 369-383.  doi: 10.1111/j.1937-5956.2006.tb00251.x.  Google Scholar

[42]

L. WangG. CaiA. A. Tsay and A. J. Vakharia, Design of the reverse channel for remanufacturing: must profit-maximization harm the environment?, Prod. Oper. Manag., 26 (2017), 1585-1603.  doi: 10.1111/poms.12709.  Google Scholar

[43]

WEEE Forum, 2012 Annual Report, European Association of Electric and Electronic Waste Take-Back Systems, 2013. Available from: Google Scholar

[44]

X. YanX. ChaoY. Lu and S. X. Zhou, Optimal policies for selling new and remanufactured products, Prod. Oper. Manag., 26 (2017), 1746-1759.  doi: 10.1111/poms.12724.  Google Scholar

[45]

R. Yin and C. S. Tang, Optimal temporal customer purchasing decisions under trade-in programs with up-front fees, Decision. Sci., 45 (2014), 373-400.  doi: 10.1111/deci.12081.  Google Scholar

show all references

References:
[1]

J. D. Abbey and J. D. Blackburn, Optimal pricing for new and remanufactured products, J. Oper. Manag., 36 (2015), 130-146.  doi: 10.1016/j.jom.2015.03.007.  Google Scholar

[2]

J. D. AbbeyR. KleberG. C. Souza and G. Voigt, The role of perceived quality risk in pricing remanufactured products, Prod. Oper. Manag., 26 (2017), 100-115.  doi: 10.1111/poms.12628.  Google Scholar

[3]

V. V. AgrawalA. Atasu and K. V. Ittersum, Remanufacturing, third-party competition, and consumers' perceived value of new products, Manage. Sci., 61 (2015), 60-72.   Google Scholar

[4]

R. AnB. YuR. Li and Y. Wei, Potential of energy savings and $CO_{2}$ emission reduction in China's iron and steel industry, Appl. Energ., 226 (2018), 862-880.   Google Scholar

[5]

A. AtasuM. Sarvary and L. N. Van Wassenhove, Remanufacturing as a marketing strategy, Manag. Sci., 54 (2008), 1731-1746.  doi: 10.1287/mnsc.1080.0893.  Google Scholar

[6]

A. AtasuV. D. R. Guide Jr. and L.N. Van Wassenhove, So what if remanufacturing cannibalizes my new product sales?, Calif. Manage. Rev., 52 (2010), 56-76.  doi: 10.1525/cmr.2010.52.2.56.  Google Scholar

[7]

A. Atasu and G. C. Souza, How does product recovery affect quality choice?, Prod. Oper. Manag., 22 (2013), 991-1010.  doi: 10.1111/j.1937-5956.2011.01290.x.  Google Scholar

[8]

H. Barman, M. Pervin, S. K. Roy and G. W. Weber, Back-ordered inventory model with inflation in a cloudy-fuzzy environment, J. Ind. Manag. Optim., 13(5) (2020). Google Scholar

[9]

G. Bitran and R. Caldentey, An overview of pricing models for revenue management, M & SOM-Manuf. Serv. Op., 5 (2003), 203-229.   Google Scholar

[10]

L. G. DeboL. B. Toktay and L. N. Van Wassenhove, Market segmentation and product technology selection for remanufacturable products, Manage. Sci., 51 (2005), 1193-1205.  doi: 10.1287/mnsc.1050.0369.  Google Scholar

[11]

M. E. Ferguson and L. B. Toktay, The effect of competition on recovery strategies, Prod. Oper. Manag., 15 (2006), 351-368.  doi: 10.1111/j.1937-5956.2006.tb00250.x.  Google Scholar

[12]

G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Manage. Sci., 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465.  Google Scholar

[13]

D. A. Garvin, What does "product quality" really mean?, Sloan. Manage. Rev., 26 (1984), 25-43.   Google Scholar

[14]

R. GeyerL. N. Van Wassenhove and A. Atasu, The economics of remanufacturing under limited component durability and finite product life cycles, Manag. Sci., 53 (2007), 88-100.  doi: 10.1287/mnsc.1060.0600.  Google Scholar

[15]

V. D. R. Guide Jr.R. H. Teunter and L. N. Van Wassenhove, Matching demand and supply to maximize profits from remanufacturing, M & SOM-Manuf. Serv. Op., 5 (2003), 303-316.   Google Scholar

[16]

V. D. R. Guide Jr. and L. N. Van Wassenhove, Closed-loop supply chains, Quantitative approaches to distribution logistics and supply chain management, (2002), 47–60. Google Scholar

[17]

T. G. GutowskiS. SahniA. Boustani and and S. C. Gravesa, Remanufacturing and energy savings, Environ. Sci. Technol., 45 (2011), 4540-4547.  doi: 10.1021/es102598b.  Google Scholar

[18]

I. Hendel and A. Lizzeri, Interfering with secondary markets, RAND. J. Econ., 30 (1999), 1-21.   Google Scholar

[19]

N. KaraliT. Xu and J. Sathaye, Reducing energy consumption and $CO_{2}$ emissions by energy efficiency measures and international trading: a bottom-up modeling for the US iron and steel sector, Appl. Energ., 120 (2014), 133-146.   Google Scholar

[20]

R. LotfiG. W. WeberS. M. Sajadifar and N. Mardani, Interdependent demand in the two-period newsvendor problem, J. Ind. Manag. Optim., 16 (2020), 117-140.  doi: 10.3934/jimo.2018143.  Google Scholar

[21]

R. LotfiM. NayeriS. M. Sajadifar and N. Mardani, Determination of start times and ordering plans for two-period projects with interdependent demand in project-oriented organizations: A case study on molding industry, J. Proj. Manag., 2(4) (2017), 119-142.  doi: 10.5267/j.jpm.2017.9.001.  Google Scholar

[22]

MarkLines, China-Flash report, Sales volume, 2018, 2018. https://www.marklines.com/en/statistics/flash_sales/salesfig_china_2018. Google Scholar

[23]

K.S. Moorthy, Product and price competition in a duopoly, Market. Sci., 7 (1988), 141-168.  doi: 10.1287/mksc.7.2.141.  Google Scholar

[24]

National Laws, Circular Economy Promotion Law of the People's Republic of China, 2008. Google Scholar

[25]

A. ÖrsdemirE. Kemahlıoǧlu-Ziya and A. K. Parlaktürk, Competitive quality choice and remanufacturing, Prod. Oper. Manag., 23 (2014), 48-64.   Google Scholar

[26]

A. Ovchinnikov, Revenue and cost management for remanufactured products, Prod. Oper. Manag., 20 (2011), 824-840.  doi: 10.1111/j.1937-5956.2010.01214.x.  Google Scholar

[27]

A. Ovchinnikovv. Blass and G. Raz, Economic and environmental assessment of remanufacturing strategies for product+service firms, Prod. Oper. Manag., 23 (2014), 744-761.  doi: 10.1111/poms.12070.  Google Scholar

[28]

M. PervinS. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Ann. Oper. Res, 260 (2018), 437-460.  doi: 10.1007/s10479-016-2355-5.  Google Scholar

[29]

M. PervinS. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy, J. Ind. Manag. Optim., 15 (2019), 1345-1373.  doi: 10.3934/jimo.2018098.  Google Scholar

[30]

M. PervinS. K. Roy and G. W. Weber, Deteriorating inventory with preservation technology under price-and stock-sensitive demand, J. Ind. Manag. Optim., 16 (2020), 1585-1612.  doi: 10.3934/jimo.2019019.  Google Scholar

[31]

M. Pranab and G. Harry, Competition in remanufacturing, Prod. Oper. Manag., 10 (2001), 125-141.   Google Scholar

[32]

S. K. RoyM. Pervin and G. W. Weber, A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy, J. Ind. Manag. Optim., 16 (2020), 553-578.  doi: 10.3934/jimo.2018167.  Google Scholar

[33]

R. C. SavaskanS. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manag. Sci., 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[34]

G. C. Souza, Closed-loop supply chains with remanufacturing, State-of-the-Art Decision-Making Tools in the Information-Intensive Age, Informs, (2014), 130-153. doi: 10.1287/educ. 1080.0040.  Google Scholar

[35]

State Legislation, Electronics Take-Back Coalition, 2010. Google Scholar

[36]

R. SubramanianM. E. Ferguson and L. B. Toktay, Remanufacturing and the Component Commonality Decision, Prod. Oper. Manag., 22 (2013), 36-53.   Google Scholar

[37]

M. ThierryM. SalomonJ. Van Nunen and L. N. Van Wassenhove, Strategic issues in product recovery management, Calif. Manage. Rev., 37 (1995), 114-135.  doi: 10.2307/41165792.  Google Scholar

[38]

V. Thomas, The environmental potential of reuse: an application to used books, Sustain. Sci., 6 (2011), 109-116.   Google Scholar

[39]

B. K. Thorn and P. Rogerson, Take it back, IIE Solutions., 34 (2002), 34-40.   Google Scholar

[40]

N. Tojo, Extended producer responsibility as a driver for design change-utopia or reality? IIIEE Dissertations, Lund University, (2004). Google Scholar

[41]

J. Vorasayan and S. M. Ryan, Optimal price and quantity of refurbished products, Prod. Oper. Manag., 15 (2009), 369-383.  doi: 10.1111/j.1937-5956.2006.tb00251.x.  Google Scholar

[42]

L. WangG. CaiA. A. Tsay and A. J. Vakharia, Design of the reverse channel for remanufacturing: must profit-maximization harm the environment?, Prod. Oper. Manag., 26 (2017), 1585-1603.  doi: 10.1111/poms.12709.  Google Scholar

[43]

WEEE Forum, 2012 Annual Report, European Association of Electric and Electronic Waste Take-Back Systems, 2013. Available from: Google Scholar

[44]

X. YanX. ChaoY. Lu and S. X. Zhou, Optimal policies for selling new and remanufactured products, Prod. Oper. Manag., 26 (2017), 1746-1759.  doi: 10.1111/poms.12724.  Google Scholar

[45]

R. Yin and C. S. Tang, Optimal temporal customer purchasing decisions under trade-in programs with up-front fees, Decision. Sci., 45 (2014), 373-400.  doi: 10.1111/deci.12081.  Google Scholar

Figure 1.  Pricing new and remanufactured products without or with price discrimination
Figure 2.  The difference between Model B and Model A with respect to the firms' profits and environmental impact
Figure 3.  Optimal prices as a function of $ \alpha $
Figure 4.  Optimal demands as a function of $ \alpha $
Figure 5.  Optimal profits as a function of $ \alpha $
Figure 6.  Optimal environment impacts as a function of $ \alpha $
Figure 7.  Optimal prices as a function of $ C_{s} $
Figure 8.  Optimal demands as a function of $ C_{s} $
Figure 9.  Optimal profits as a function of $ C_{s} $
Figure 10.  Optimal environment impacts as a function of $ C_{s} $
Table 1.  Some Key Literature on Remanufacturing and Pricing Strategies
Reference Production planning Inventory management Market competition Consumer behavior
Component remanufacturing Material remanufacturing Discount No discount Internal External WTP Switching
Ferrer and Swaminathan [12] $ \surd $ $ \surd $ $ \surd $
Subramanian et al. [36] $ \surd $ $ \surd $ $ \surd $
Pranab and Harry [31] $ \surd $ $ \surd $
Lotfi et al. [20] $ \surd $
Lotfi et al. [21] $ \surd $
Pervin et al. [28] $ \surd $
Pervin et al. [29] $ \surd $
Roy et al. [32] $ \surd $
Pervin et al. [30] $ \surd $
Barman et al. [8] $ \surd $
Ferguson and Toktay [11] $ \surd $ $ \surd $ $ \surd $
Örsdemir et al. [25] $ \surd $ $ \surd $
Ovchinnikov [26] $ \surd $ $ \surd $ $ \surd $
Yan et al. [44] $ \surd $ $ \surd $ $ \surd $
Agrawal et al. [3] $ \surd $ $ \surd $ $ \surd $
Vorasayan and Ryan [41] $ \surd $ $ \surd $ $ \surd $
Wang et al. [42] $ \surd $ $ \surd $ $ \surd $ $ \surd $
Abbey et al. [2] $ \surd $ $ \surd $ $ \surd $
Abbey et al. [1] $ \surd $ $ \surd $ $ \surd $ $ \surd $
Atasu et al. [5] $ \surd $ $ \surd $ $ \surd $ $ \surd $
This paper $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
Reference Production planning Inventory management Market competition Consumer behavior
Component remanufacturing Material remanufacturing Discount No discount Internal External WTP Switching
Ferrer and Swaminathan [12] $ \surd $ $ \surd $ $ \surd $
Subramanian et al. [36] $ \surd $ $ \surd $ $ \surd $
Pranab and Harry [31] $ \surd $ $ \surd $
Lotfi et al. [20] $ \surd $
Lotfi et al. [21] $ \surd $
Pervin et al. [28] $ \surd $
Pervin et al. [29] $ \surd $
Roy et al. [32] $ \surd $
Pervin et al. [30] $ \surd $
Barman et al. [8] $ \surd $
Ferguson and Toktay [11] $ \surd $ $ \surd $ $ \surd $
Örsdemir et al. [25] $ \surd $ $ \surd $
Ovchinnikov [26] $ \surd $ $ \surd $ $ \surd $
Yan et al. [44] $ \surd $ $ \surd $ $ \surd $
Agrawal et al. [3] $ \surd $ $ \surd $ $ \surd $
Vorasayan and Ryan [41] $ \surd $ $ \surd $ $ \surd $
Wang et al. [42] $ \surd $ $ \surd $ $ \surd $ $ \surd $
Abbey et al. [2] $ \surd $ $ \surd $ $ \surd $
Abbey et al. [1] $ \surd $ $ \surd $ $ \surd $ $ \surd $
Atasu et al. [5] $ \surd $ $ \surd $ $ \surd $ $ \surd $
This paper $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
Table 2.  Parameter settings
Parameter Parameter values
$ C_{s} $ 0.15 (low); 0.35 (medium); 0.55 (high)
$ \alpha $ 0.25 (low); 0.45 (medium); 0.65 (high)
$ C_{n} $ 0.65
$ e_{n} $ 0.05
$ e_{r} $ 0.01
Parameter Parameter values
$ C_{s} $ 0.15 (low); 0.35 (medium); 0.55 (high)
$ \alpha $ 0.25 (low); 0.45 (medium); 0.65 (high)
$ C_{n} $ 0.65
$ e_{n} $ 0.05
$ e_{r} $ 0.01
Table 3.  The optimal solution and comparison of profit
OS's total profits IS's total profits Comparison between OS & IS
$ \pi^{B\ast}_{o} $ $ \pi^{A\ast}_{o} $ $ \pi^{B\ast}_{o}-\pi^{A\ast}_{o} $ $ \pi^{B\ast}_{i} $ $ \pi^{A\ast}_{i} $ $ \pi^{B\ast}_{i}-\pi^{A\ast}_{i} $ $ \pi^{B\ast}_{o}-\pi^{B\ast}_{i} $ $ \pi^{A\ast}_{o}-\pi^{A\ast}_{i} $
$ C_{s}=0.15 $ $ \alpha=0.25 $ 0.4919 0.54 -0.0481 0.2481 0.24 +0.0081 +0.2438 +0.3
$ \alpha=0.45 $ 0.3341 0.3646 -0.0305 0.1987 0.198 +0.0007 +0.1354 +0.1666
$ \alpha=0.65 $ 0.1792 0.1921 -0.0129 0.1522 0.1587 -0.0065 +0.0270 +0.0334
$ C_{s}=0.35 $ $ \alpha=0.25 $ 0.3679 0.3919 -0.024 0.3408 0.3585 -0.0177 +0.0271 +0.0334
$ \alpha=0.45 $ 0.2215 0.2273 -0.0058 0.3027 0.3273 -0.0246 -0.0812 -0.1
$ \alpha=0.65 $ 0.091 0.0778 +0.0132 0.2806 0.3111 -0.0305 -0.1896 -0.2333
$ C_{s}=0.55 $ $ \alpha=0.25 $ 0.2689 0.2674 +0.0015 0.4585 0.5007 -0.0422 -0.1896 -0.2333
$ \alpha=0.45 $ 0.143 0.1222 +0.0208 0.4409 0.4889 -0.048 -0.2979 -0.3667
$ \alpha=0.65 $ 0.0563 0.0143 +0.042 0.4626 0.5143 -0.0517 -0.4063 -0.5
OS's total profits IS's total profits Comparison between OS & IS
$ \pi^{B\ast}_{o} $ $ \pi^{A\ast}_{o} $ $ \pi^{B\ast}_{o}-\pi^{A\ast}_{o} $ $ \pi^{B\ast}_{i} $ $ \pi^{A\ast}_{i} $ $ \pi^{B\ast}_{i}-\pi^{A\ast}_{i} $ $ \pi^{B\ast}_{o}-\pi^{B\ast}_{i} $ $ \pi^{A\ast}_{o}-\pi^{A\ast}_{i} $
$ C_{s}=0.15 $ $ \alpha=0.25 $ 0.4919 0.54 -0.0481 0.2481 0.24 +0.0081 +0.2438 +0.3
$ \alpha=0.45 $ 0.3341 0.3646 -0.0305 0.1987 0.198 +0.0007 +0.1354 +0.1666
$ \alpha=0.65 $ 0.1792 0.1921 -0.0129 0.1522 0.1587 -0.0065 +0.0270 +0.0334
$ C_{s}=0.35 $ $ \alpha=0.25 $ 0.3679 0.3919 -0.024 0.3408 0.3585 -0.0177 +0.0271 +0.0334
$ \alpha=0.45 $ 0.2215 0.2273 -0.0058 0.3027 0.3273 -0.0246 -0.0812 -0.1
$ \alpha=0.65 $ 0.091 0.0778 +0.0132 0.2806 0.3111 -0.0305 -0.1896 -0.2333
$ C_{s}=0.55 $ $ \alpha=0.25 $ 0.2689 0.2674 +0.0015 0.4585 0.5007 -0.0422 -0.1896 -0.2333
$ \alpha=0.45 $ 0.143 0.1222 +0.0208 0.4409 0.4889 -0.048 -0.2979 -0.3667
$ \alpha=0.65 $ 0.0563 0.0143 +0.042 0.4626 0.5143 -0.0517 -0.4063 -0.5
Table 4.  The optimal solution and comparison of environment impact
OS's environment impact IS's environment impact Comparison between OS & IS
$ E^{B\ast}_{o} $ $ E^{A\ast}_{o} $ $ E^{B\ast}_{o}-E^{A\ast}_{o} $ $ E^{B\ast}_{i} $ $ E^{A\ast}_{i} $ $ E^{B\ast}_{i}-E^{A\ast}_{i} $ $ E^{B\ast}_{o}-E^{B\ast}_{i} $ $ E^{A\ast}_{o}-E^{A\ast}_{i} $
$ C_{s}=0.15 $ $ \alpha=0.25 $ 0.0612 0.06 +0.0012 0.0078 0.008 -0.0002 +0.0534 +0.052
$ \alpha=0.45 $ 0.0585 0.0576 +0.0009 0.0083 0.0085 -0.0002 +0.0502 +0.0491
$ \alpha=0.65 $ 0.0527 0.0524 +0.0003 0.0095 0.0095 0 +0.0432 +0.0429
$ C_{s}=0.35 $ $ \alpha=0.25 $ 0.0512 0.0511 +0.0001 0.0098 0.0098 0 +0.0414 +0.0413
$ \alpha=0.45 $ 0.0449 0.0455 -0.0006 0.011 0.0109 +0.0001 +0.0339 +0.0346
$ \alpha=0.65 $ 0.0313 0.0333 -0.002 0.0138 0.0133 +0.0005 +0.0175 +0.02
$ C_{s}=0.55 $ $ \alpha=0.25 $ 0.0412 0.0422 -0.001 0.0118 0.0116 +0.0002 +0.0294 +0.0306
$ \alpha=0.45 $ 0.0312 0.0333 -0.0021 0.0138 0.0133 +0.0005 +0.0174 +0.02
$ \alpha=0.65 $ 0.0098 0.0143 -0.0045 0.018 0.0171 +0.0009 –0.0082 -0.0028
OS's environment impact IS's environment impact Comparison between OS & IS
$ E^{B\ast}_{o} $ $ E^{A\ast}_{o} $ $ E^{B\ast}_{o}-E^{A\ast}_{o} $ $ E^{B\ast}_{i} $ $ E^{A\ast}_{i} $ $ E^{B\ast}_{i}-E^{A\ast}_{i} $ $ E^{B\ast}_{o}-E^{B\ast}_{i} $ $ E^{A\ast}_{o}-E^{A\ast}_{i} $
$ C_{s}=0.15 $ $ \alpha=0.25 $ 0.0612 0.06 +0.0012 0.0078 0.008 -0.0002 +0.0534 +0.052
$ \alpha=0.45 $ 0.0585 0.0576 +0.0009 0.0083 0.0085 -0.0002 +0.0502 +0.0491
$ \alpha=0.65 $ 0.0527 0.0524 +0.0003 0.0095 0.0095 0 +0.0432 +0.0429
$ C_{s}=0.35 $ $ \alpha=0.25 $ 0.0512 0.0511 +0.0001 0.0098 0.0098 0 +0.0414 +0.0413
$ \alpha=0.45 $ 0.0449 0.0455 -0.0006 0.011 0.0109 +0.0001 +0.0339 +0.0346
$ \alpha=0.65 $ 0.0313 0.0333 -0.002 0.0138 0.0133 +0.0005 +0.0175 +0.02
$ C_{s}=0.55 $ $ \alpha=0.25 $ 0.0412 0.0422 -0.001 0.0118 0.0116 +0.0002 +0.0294 +0.0306
$ \alpha=0.45 $ 0.0312 0.0333 -0.0021 0.0138 0.0133 +0.0005 +0.0174 +0.02
$ \alpha=0.65 $ 0.0098 0.0143 -0.0045 0.018 0.0171 +0.0009 –0.0082 -0.0028
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