# American Institute of Mathematical Sciences

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

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

 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.

Citation: 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
##### 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. [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. [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. [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. [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. [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. [7] T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-192. [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. [9] B. Mishra and S. Raghunathan, Retail-vs. vendor-managed inventory and brand competition, Management Science, 50 (2004), 445-457. [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. [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. [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. [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. [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. [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. [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. [17] M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896. [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. [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. [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. [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. [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.

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##### 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. [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. [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. [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. [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. [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. [7] T. W. McGuire and R. Staelin, An industry equilibrium analysis of downstream vertical integration, Marketing Science, 2 (1983), 161-192. [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. [9] B. Mishra and S. Raghunathan, Retail-vs. vendor-managed inventory and brand competition, Management Science, 50 (2004), 445-457. [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. [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. [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. [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. [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. [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. [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. [17] M. Trivedi, Distribution channels: An extension of exclusive retailership, Management Science, 44 (1998), 896-909.  doi: 10.1287/mnsc.44.7.896. [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. [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. [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. [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. [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.
changes of optimal prices with β in MSM model
changes of optimal remanufacturing effort with β in MSM model
changes of optimal profits with β in MSM model
changes of optimal prices with γ in MSM model
changes of optimal remanufacturing effort with γ in MSM model
changes of optimal profits with γ in MSM model
changes of optimal prices with a in MSM model
changes of optimal remanufacturing effort with a in MSM model
changes of optimal profits with a in MSM model
changes of optimal prices with B in MSM model
changes of optimal remanufacturing effort with B in MSM model
changes of optimal profits with B in MSM model
changes of optimal prices with δ in MSM model
changes of optimal remanufacturing effort with δ in MSM model
changes of optimal profits with δ in MSM model
Chain members' maximum profits in different decision models
 Scenario $\pi_{m1}+\pi_{m2}+\pi_{r}$ $\pi_{m1}$ $\pi_{m2}$ $\pi_{r}$ MSB 13549.7 2701.4 2713.6 8134.7 MSM 13361.2 2744.0 2976.9 7640.3 MSR 13357.5 2966.4 2756.9 7634.2 RSB 13553.5 1351.7 1353.8 10848.0 RSM 13066.1 1332.4 1672.7 10061.0 RSR 13047.6 1667.6 1343.0 10037.0 NG 13082.6 4103.7 4124.0 4854.9
 Scenario $\pi_{m1}+\pi_{m2}+\pi_{r}$ $\pi_{m1}$ $\pi_{m2}$ $\pi_{r}$ MSB 13549.7 2701.4 2713.6 8134.7 MSM 13361.2 2744.0 2976.9 7640.3 MSR 13357.5 2966.4 2756.9 7634.2 RSB 13553.5 1351.7 1353.8 10848.0 RSM 13066.1 1332.4 1672.7 10061.0 RSR 13047.6 1667.6 1343.0 10037.0 NG 13082.6 4103.7 4124.0 4854.9
Optimal prices and remanufacturing effort in different decision models
 Scenario $p_1^*$ $w_1^*$ $p_2^*$ $w_2^*$ $\tau^*$ MSB 257.45 114.89 257.34 114.68 0.28575 MSM 264.20 128.40 259.58 119.17 0.29929 MSR 259.72 119.44 264.16 128.32 0.25393 RSB 257.39 67.54 257.18 66.97 0.28650 RSM 272.92 82.92 262.32 72.32 0.31775 RSR 262.72 72.72 273.16 83.16 0.21194 NG 151.35 102.70 151.08 102.16 0.49893
 Scenario $p_1^*$ $w_1^*$ $p_2^*$ $w_2^*$ $\tau^*$ MSB 257.45 114.89 257.34 114.68 0.28575 MSM 264.20 128.40 259.58 119.17 0.29929 MSR 259.72 119.44 264.16 128.32 0.25393 RSB 257.39 67.54 257.18 66.97 0.28650 RSM 272.92 82.92 262.32 72.32 0.31775 RSR 262.72 72.72 273.16 83.16 0.21194 NG 151.35 102.70 151.08 102.16 0.49893
Notations used in the Problem Description
 Symbol Description $p_i$ 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
 Symbol Description $p_i$ 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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