• Previous Article
    Some scheduling problems with sum of logarithm processing times based learning effect and exponential past sequence dependent delivery times
  • JIMO Home
  • This Issue
  • Next Article
    Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain
May  2022, 18(3): 1769-1794. doi: 10.3934/jimo.2021043

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 Published  May 2022 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 and Management Optimization, 2022, 18 (3) : 1769-1794. 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.

[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.

[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. 

[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. 

[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.

[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.

[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.

[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).

[9]

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

[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.

[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.

[12]

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

[13]

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

[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.

[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. 

[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.

[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.

[18]

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

[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. 

[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.

[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.

[22]

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

[23]

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

[24]

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

[25]

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

[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.

[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.

[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.

[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.

[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.

[31]

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

[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.

[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.

[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.

[35]

State Legislation, Electronics Take-Back Coalition, 2010.

[36]

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

[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.

[38]

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

[39]

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

[40]

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

[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.

[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.

[43]

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

[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.

[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.

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.

[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.

[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. 

[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. 

[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.

[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.

[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.

[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).

[9]

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

[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.

[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.

[12]

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

[13]

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

[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.

[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. 

[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.

[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.

[18]

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

[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. 

[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.

[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.

[22]

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

[23]

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

[24]

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

[25]

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

[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.

[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.

[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.

[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.

[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.

[31]

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

[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.

[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.

[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.

[35]

State Legislation, Electronics Take-Back Coalition, 2010.

[36]

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

[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.

[38]

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

[39]

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

[40]

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

[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.

[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.

[43]

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

[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.

[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.

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
[1]

Xuemei Zhang, Malin Song, Guangdong Liu. Service product pricing strategies based on time-sensitive customer choice behavior. Journal of Industrial and Management Optimization, 2017, 13 (1) : 297-312. doi: 10.3934/jimo.2016018

[2]

Gang Chen, Zaiming Liu, Jingchuan Zhang. Analysis of strategic customer behavior in fuzzy queueing systems. Journal of Industrial and Management Optimization, 2020, 16 (1) : 371-386. doi: 10.3934/jimo.2018157

[3]

Veena Goswami, Gopinath Panda. Optimal customer behavior in observable and unobservable discrete-time queues. Journal of Industrial and Management Optimization, 2021, 17 (1) : 299-316. doi: 10.3934/jimo.2019112

[4]

Sahar Vatankhah, Reza Samizadeh. Determining optimal marketing and pricing policies by considering customer lifetime network value in oligopoly markets. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021112

[5]

Maryam Ghoreishi, Abolfazl Mirzazadeh, Gerhard-Wilhelm Weber, Isa Nakhai-Kamalabadi. Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer returns. Journal of Industrial and Management Optimization, 2015, 11 (3) : 933-949. doi: 10.3934/jimo.2015.11.933

[6]

Kai Li, Yuqian Pan, Bohai Liu, Bayi Cheng. The setting and optimization of quick queue with customer loss. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1539-1553. doi: 10.3934/jimo.2019016

[7]

Mahdi Mahdiloo, Abdollah Noorizadeh, Reza Farzipoor Saen. Developing a new data envelopment analysis model for customer value analysis. Journal of Industrial and Management Optimization, 2011, 7 (3) : 531-558. doi: 10.3934/jimo.2011.7.531

[8]

Ashkan Ayough, Farbod Farhadi, Mostafa Zandieh, Parisa Rastkhadiv. Genetic algorithm for obstacle location-allocation problems with customer priorities. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1753-1769. doi: 10.3934/jimo.2020044

[9]

Kamran Jalilian, Kameleh Nasiri Pirbazari. Convex optimization without convexity of constraints on non-necessarily convex sets and its applications in customer satisfaction in automotive industry. Numerical Algebra, Control and Optimization, 2021  doi: 10.3934/naco.2021020

[10]

Zhi-tang Li, Cui-hua Zhang, Wei Kong, Ru-xia Lyu. The optimal product-line design and incentive mechanism in a supply chain with customer environmental awareness. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021204

[11]

Jing Zhao, Jie Wei, Yongjian Li. Pricing and remanufacturing decisions for two substitutable products with a common retailer. Journal of Industrial and Management Optimization, 2017, 13 (2) : 1125-1147. doi: 10.3934/jimo.2016065

[12]

Yanhua Feng, Xuhui Xia, Lei Wang, Zelin Zhang. Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2721-2748. doi: 10.3934/jimo.2021089

[13]

Dong-Sheng Ma, Hua-Ming Song. Behavior-based pricing in service differentiated industries. Journal of Dynamics and Games, 2020, 7 (4) : 351-364. doi: 10.3934/jdg.2020027

[14]

TÔn Vı$\underset{.}{\overset{\hat{\ }}{\mathop{\text{E}}}}\, $T T$\mathop {\text{A}}\limits_. $, Linhthi hoai Nguyen, Atsushi Yagi. A sustainability condition for stochastic forest model. Communications on Pure and Applied Analysis, 2017, 16 (2) : 699-718. doi: 10.3934/cpaa.2017034

[15]

William Guo, Wei Li, Roland Dodd, Ergun Gide. The trifecta for curriculum sustainability in Australian universities. STEM Education, 2021, 1 (1) : 1-16. doi: 10.3934/steme.2021001

[16]

Andrea Davini, Lin Wang. On the vanishing discount problem from the negative direction. Discrete and Continuous Dynamical Systems, 2021, 41 (5) : 2377-2389. doi: 10.3934/dcds.2020368

[17]

Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105-123. doi: 10.3934/mbe.2014.11.105

[18]

Noriaki Kawaguchi. Maximal chain continuous factor. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5915-5942. doi: 10.3934/dcds.2021101

[19]

João Correia-da-Silva, Joana Pinho. The profit-sharing rule that maximizes sustainability of cartel agreements. Journal of Dynamics and Games, 2016, 3 (2) : 143-151. doi: 10.3934/jdg.2016007

[20]

Wei Chen, Fuying Jing, Li Zhong. Coordination strategy for a dual-channel electricity supply chain with sustainability. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021139

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (576)
  • HTML views (545)
  • Cited by (0)

Other articles
by authors

[Back to Top]