American Institute of Mathematical Sciences

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April  2017, 13(2): 1125-1147. doi: 10.3934/jimo.2016065

Pricing and remanufacturing decisions for two substitutable products with a common retailer

Jing Zhao 1, , Jie Wei 2,, and  Yongjian Li 3,

1. 

School of Science, Tianjin Polytechnic University, Tianjin 300387, China
2. 

School of Management, Tianjin University of Technology, Tianjin 300384, China
3. 

Business School, Nankai University, Tianjin 300071, China

* Corresponding author: Jie Wei

Received  June 2015 Published  October 2016

Fund Project: The authors wish to express their sincerest thanks to the editors and anonymous referees for their constructive comments and suggestions on the paper. We gratefully acknowledge the support of (ⅰ) National Natural Science Foundation of China (NSFC), Research Fund Nos. 71301116,71302112 for J. Zhao; (ⅱ) National Natural Science Foundation of China, Research Fund Nos. 71371186,71202162 for J. Wei; (ⅲ) National Natural Science Foundation of China (NSFC), Research Fund No. 71372100, and the Major Program of the National Social Science Fund of China(Grant No. 13 & ZD147) for Y.J., Li.

This paper studies pricing and remanufacturing decisions for two substitutable products in a supply chain with two manufacturers and one common retailer. The two manufacturers produce two substitutable products and sell them to the retailer. Specifically, the first manufacturer is a traditional manufacturer who produces the new product directly from raw material, while the second manufacturer has incorporated a remanufacturing process for used product into his original production system, so that he can manufacture a new product directly from raw material, or remanufacture part or whole of a returned unit into a new product. We establish seven game models by considering the chain members' horizontal and vertical competitions, and obtain the corresponding closed-form expressions for equilibrium solution. Then, the equilibrium characteristics with respect to the second manufacturer's remanufacturing decision and all channel members' pricing decisions are explored, the sensitivity analysis of equilibrium solution is conducted for some model parameters, and the maximal profits and equilibrium solutions obtained in different game models are compared by numerical analyses. Based on these results, some interesting and valuable economic and managerial insights are established.

Keywords: Supply chain management, game theory, pricing, remanufacturings.
Mathematics Subject Classification: Primary: 90B60; Secondary: 90B50.
Citation: Jing Zhao, Jie Wei, Yongjian Li. Pricing and remanufacturing decisions for two substitutable products with a common retailer. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1125-1147. doi: 10.3934/jimo.2016065
References:
[1]

S. Choi, Price competition in a channel structure with common retailer, Marketing Science, 10 (1991), 271-296.  doi: 10.1287/mksc.10.4.271.  Google Scholar

[2]

S. Choi, Price competition in a duopoly common retailer channel, Journal of Retailing, 72 (1996), 117-134.  doi: 10.1016/S0022-4359(96)90010-X.  Google Scholar

[3]

T. Choi, Y. Li and L. Xu, Channel leadership, performance and coordination in closed loop supply chains, International Journal of Production Economics, 146 (2013), 371-380.  doi: 10.1016/j.ijpe.2013.08.002.  Google Scholar

[4]

X. Hong, X. Wang, D. Wang and H. Zhang, Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection, The International Journal of Advanced Manufacturing Technology, 68 (2013), 1851-1865.  doi: 10.1007/s00170-013-4982-1.  Google Scholar

[5]

E. Lee and R. Staelin, Vertical strategic interaction: Implications for channel pricing strategy, Marketing Science, 16 (1997), 185-207.  doi: 10.1287/mksc.16.3.185.  Google Scholar

[6]

X. Li, Y. Li and S. Saghafian, A Hybrid Manufacturing/Remanufacturing System with Random Remanufacturing Yield and Market-Driven Product Acquisition, IEEE Transactions on Engineering Management, 60 (2013), 424-437.  doi: 10.1109/TEM.2012.2215873.  Google Scholar

[7]

T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-192.   Google Scholar

[8]

S. Mitraa and S. Webster, Competition in remanufacturing and the effects of government subsidies, International Journal of Production Economics, 111 (2008), 287-298.  doi: 10.1016/j.ijpe.2007.02.042.  Google Scholar

[9]

B. Mishra and S. Raghunathan, Retail-vs. vendor-managed inventory and brand competition, Management Science, 50 (2004), 445-457.   Google Scholar

[10]

S. Netessine and N. Rudi, Centralized and competitive inventory models with demand substitution, Operations Research, 51 (2003), 329-335.  doi: 10.1287/opre.51.2.329.12788.  Google Scholar

[11]

B. Pasternack and Z. Drezner, Optimal inventory policies for substitutable commodities with stochastic demand, Naval Research Logistics, 38 (1991), 221-240.  doi: 10.1002/1520-6750(199104)38:2<221::AID-NAV3220380208>3.0.CO;2-7.  Google Scholar

[12]

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

[13]

R. Savaskan and L. Van Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar

[14]

E. Stavrulaki, Inventory decisions for substitutable products with stock-dependent demand, International Journal of Production Economics, 129 (2011), 65-78.  doi: 10.1016/j.ijpe.2010.09.002.  Google Scholar

[15]

X. Sun, Y. Li and K. Govindan, Integrating dynamic acquisition pricing and remanufacturing decisions under random price-sensitive returns, The International Journal of Advanced Manufacturing Technology, 68 (2013), 933-947.  doi: 10.1007/s00170-013-4954-5.  Google Scholar

[16]

C. Tang and R. Yin, Joint ordering and pricing strategies for managing substitutable products, Production and Operations Management, 16 (2007), 138-153.  doi: 10.1111/j.1937-5956.2007.tb00171.x.  Google Scholar

[17]

M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896.  Google Scholar

[18]

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

[19]

C. Wu, C. Chen and C. Hsieh, Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274.  doi: 10.1016/j.ijpe.2011.07.020.  Google Scholar

[20]

Y. Xia, Competitive strategies and market segmentation for suppliers with substitutable products, European Journal of Operational Research, 210 (2011), 194-203.  doi: 10.1016/j.ejor.2010.09.028.  Google Scholar

[21]

X. Zhao and D. Atkins, Newsvendors under simultaneous price and inventory competition, Manufacturing and Service Operations Management, 10 (2008), 539-546.  doi: 10.1287/msom.1070.0186.  Google Scholar

[22]

J. Zhao, W. Tang and J. Wei, Pricing decision for substitutable products with retail competition in a fuzzy environment, International Journal of Production Economics, 135 (2012), 144-153.  doi: 10.1016/j.ijpe.2010.12.024.  Google Scholar

show all references

References:
[1]

S. Choi, Price competition in a channel structure with common retailer, Marketing Science, 10 (1991), 271-296.  doi: 10.1287/mksc.10.4.271.  Google Scholar

[2]

S. Choi, Price competition in a duopoly common retailer channel, Journal of Retailing, 72 (1996), 117-134.  doi: 10.1016/S0022-4359(96)90010-X.  Google Scholar

[3]

T. Choi, Y. Li and L. Xu, Channel leadership, performance and coordination in closed loop supply chains, International Journal of Production Economics, 146 (2013), 371-380.  doi: 10.1016/j.ijpe.2013.08.002.  Google Scholar

[4]

X. Hong, X. Wang, D. Wang and H. Zhang, Decision models of closed-loop supply chain with remanufacturing under hybrid dual-channel collection, The International Journal of Advanced Manufacturing Technology, 68 (2013), 1851-1865.  doi: 10.1007/s00170-013-4982-1.  Google Scholar

[5]

E. Lee and R. Staelin, Vertical strategic interaction: Implications for channel pricing strategy, Marketing Science, 16 (1997), 185-207.  doi: 10.1287/mksc.16.3.185.  Google Scholar

[6]

X. Li, Y. Li and S. Saghafian, A Hybrid Manufacturing/Remanufacturing System with Random Remanufacturing Yield and Market-Driven Product Acquisition, IEEE Transactions on Engineering Management, 60 (2013), 424-437.  doi: 10.1109/TEM.2012.2215873.  Google Scholar

[7]

T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-192.   Google Scholar

[8]

S. Mitraa and S. Webster, Competition in remanufacturing and the effects of government subsidies, International Journal of Production Economics, 111 (2008), 287-298.  doi: 10.1016/j.ijpe.2007.02.042.  Google Scholar

[9]

B. Mishra and S. Raghunathan, Retail-vs. vendor-managed inventory and brand competition, Management Science, 50 (2004), 445-457.   Google Scholar

[10]

S. Netessine and N. Rudi, Centralized and competitive inventory models with demand substitution, Operations Research, 51 (2003), 329-335.  doi: 10.1287/opre.51.2.329.12788.  Google Scholar

[11]

B. Pasternack and Z. Drezner, Optimal inventory policies for substitutable commodities with stochastic demand, Naval Research Logistics, 38 (1991), 221-240.  doi: 10.1002/1520-6750(199104)38:2<221::AID-NAV3220380208>3.0.CO;2-7.  Google Scholar

[12]

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

[13]

R. Savaskan and L. Van Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar

[14]

E. Stavrulaki, Inventory decisions for substitutable products with stock-dependent demand, International Journal of Production Economics, 129 (2011), 65-78.  doi: 10.1016/j.ijpe.2010.09.002.  Google Scholar

[15]

X. Sun, Y. Li and K. Govindan, Integrating dynamic acquisition pricing and remanufacturing decisions under random price-sensitive returns, The International Journal of Advanced Manufacturing Technology, 68 (2013), 933-947.  doi: 10.1007/s00170-013-4954-5.  Google Scholar

[16]

C. Tang and R. Yin, Joint ordering and pricing strategies for managing substitutable products, Production and Operations Management, 16 (2007), 138-153.  doi: 10.1111/j.1937-5956.2007.tb00171.x.  Google Scholar

[17]

M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896.  Google Scholar

[18]

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

[19]

C. Wu, C. Chen and C. Hsieh, Competitive pricing decisions in a two-echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274.  doi: 10.1016/j.ijpe.2011.07.020.  Google Scholar

[20]

Y. Xia, Competitive strategies and market segmentation for suppliers with substitutable products, European Journal of Operational Research, 210 (2011), 194-203.  doi: 10.1016/j.ejor.2010.09.028.  Google Scholar

[21]

X. Zhao and D. Atkins, Newsvendors under simultaneous price and inventory competition, Manufacturing and Service Operations Management, 10 (2008), 539-546.  doi: 10.1287/msom.1070.0186.  Google Scholar

[22]

J. Zhao, W. Tang and J. Wei, Pricing decision for substitutable products with retail competition in a fuzzy environment, International Journal of Production Economics, 135 (2012), 144-153.  doi: 10.1016/j.ijpe.2010.12.024.  Google Scholar

Figure 1.  changes of optimal prices with β in MSM model
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Figure 2.  changes of optimal remanufacturing effort with β in MSM model
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Figure 3.  changes of optimal profits with β in MSM model
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Figure 4.  changes of optimal prices with γ in MSM model
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Figure 5.  changes of optimal remanufacturing effort with γ in MSM model
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Figure 6.  changes of optimal profits with γ in MSM model
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Figure 7.  changes of optimal prices with a in MSM model
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Figure 8.  changes of optimal remanufacturing effort with a in MSM model
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Figure 9.  changes of optimal profits with a in MSM model
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Figure 10.  changes of optimal prices with B in MSM model
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Figure 11.  changes of optimal remanufacturing effort with B in MSM model
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Figure 12.  changes of optimal profits with B in MSM model
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Figure 13.  changes of optimal prices with δ in MSM model
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Figure 14.  changes of optimal remanufacturing effort with δ in MSM model
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Figure 15.  changes of optimal profits with δ in MSM model
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Table 1.  Chain members' maximum profits in different decision models
Scenario$\pi_{m1}+\pi_{m2}+\pi_{r}$$\pi_{m1}$$\pi_{m2}$$\pi_{r}$
MSB13549.72701.42713.68134.7
MSM13361.22744.02976.97640.3
MSR13357.52966.42756.97634.2
RSB13553.51351.71353.810848.0
RSM13066.11332.41672.710061.0
RSR13047.61667.61343.010037.0
NG13082.64103.74124.04854.9
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Scenario$\pi_{m1}+\pi_{m2}+\pi_{r}$$\pi_{m1}$$\pi_{m2}$$\pi_{r}$
MSB13549.72701.42713.68134.7
MSM13361.22744.02976.97640.3
MSR13357.52966.42756.97634.2
RSB13553.51351.71353.810848.0
RSM13066.11332.41672.710061.0
RSR13047.61667.61343.010037.0
NG13082.64103.74124.04854.9
Table 2.  Optimal prices and remanufacturing effort in different decision models
Scenario$p_1^*$$w_1^*$$p_2^*$$w_2^*$$\tau^*$
MSB257.45114.89257.34114.680.28575
MSM264.20128.40259.58119.170.29929
MSR259.72119.44264.16128.320.25393
RSB257.3967.54257.1866.970.28650
RSM272.9282.92262.3272.320.31775
RSR262.7272.72273.1683.160.21194
NG151.35102.70151.08102.160.49893
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Scenario$p_1^*$$w_1^*$$p_2^*$$w_2^*$$\tau^*$
MSB257.45114.89257.34114.680.28575
MSM264.20128.40259.58119.170.29929
MSR259.72119.44264.16128.320.25393
RSB257.3967.54257.1866.970.28650
RSM272.9282.92262.3272.320.31775
RSR262.7272.72273.1683.160.21194
NG151.35102.70151.08102.160.49893
Table 3.  Notations used in the Problem Description
SymbolDescription
$p_i$unit retail price of product $i,~i=1,2,$
$w_i$unit wholesale price of product $i,$
$c_{mi}$unit manufacturing cost of product $i,~i=1,2$
$c_{r}$unit remanufacturing cost of product $2$
$\beta$self-price sensitivity of a product's demand to its own price
$\gamma$cross-price sensitivity of one product's demand to the other product's price
$D_i$the demand for product $i,~i=1,2$
$\tau$the manufacturer 2's remanufacturing effort
$B$scaling parameter of the manufacturer 2's recycling process
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SymbolDescription
$p_i$unit retail price of product $i,~i=1,2,$
$w_i$unit wholesale price of product $i,$
$c_{mi}$unit manufacturing cost of product $i,~i=1,2$
$c_{r}$unit remanufacturing cost of product $2$
$\beta$self-price sensitivity of a product's demand to its own price
$\gamma$cross-price sensitivity of one product's demand to the other product's price
$D_i$the demand for product $i,~i=1,2$
$\tau$the manufacturer 2's remanufacturing effort
$B$scaling parameter of the manufacturer 2's recycling process
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