# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2018152

## Pricing and modularity decisions under competition

 a. Department of Management Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China b. Shanghai University of International Business and Economics, Gubei Road, 200336, Shanghai, China c. Shanghai Wage Intelligent Technology Co., Ltd d. College of Economics, Shenzhen University, Shenzhen, China e. International Business School, Shaanxi Normal University, Xian, China

* Corresponding author: Hao Shao

Received  October 2017 Revised  May 2018 Published  September 2018

This paper considers price and modularity of competition between two firms with deterministic demand, in which demand is dependent on both the prices and the modularity levels determined by two firms. Bertrand competition and Stackelberg competition are formulated to derive the equilibrium solutions analytically. Because of the complexity, an intensive numerical study is conducted to investigate the impact of the sensitive parameters on equilibrium prices and modularity levels, as well as optimal profits of the two firms. An important and interesting finding is that optimal profits of the two firms under both types of competition are decreasing with the modularity cost when the price and modularity sensitivities are low, where both firms are worse-off due to decrease of the modularity levels; but they are increasing when the price and modularity sensitivities are high, where both firms are better-off at the expense of modular design. Our research reveals that Stackelberg game improves the modularity levels in most of the cases, though both firms perform better in Bertrand competition in these cases when jointly deciding the prices and modularity levels in the two firms.

Citation: Feng Tao, Hao Shao, KinKeung Lai. Pricing and modularity decisions under competition. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018152
##### References:
 [1] B. Agard and S. Bassetto, Modular design of product families for quality and cost, International Journal of Production Research, 51 (2013), 1648-1667. doi: 10.1080/00207543.2012.693963. Google Scholar [2] R. D. Banker, I. Khosla and K. K. Sinha, Quality and competition, Management Science, 44 (1998), 1179-1192. doi: 10.1287/mnsc.44.9.1179. Google Scholar [3] L. M. Barbosa, D. P. Lacerda, F. A. S. Piran and A. Dresch, Exploratory analysis of the variables prevailing on the effects of product modularization on production volume and efficiency, International Journal of Production Economics, 193 (2017), 677-690. doi: 10.1016/j.ijpe.2017.08.028. Google Scholar [4] L. M. B. Cabral and M. Villas-Boas, Bertrand supertraps, Management Science, 51 (2005), 519-678. doi: 10.1287/mnsc.1040.0313. Google Scholar [5] S. Y. Chang and T. Y. Yeh, Optimal order quantity and product modularity for a two-echelon returnable supply chain, International Journal of Production Research, 51 (2013), 5210-5220. doi: 10.1080/00207543.2013.802051. Google Scholar [6] S. C. Choi, W. S. Desarbo and P. T. Harker, Product positioning under price competition, Management Science, 36 (1990), 123-246. doi: 10.1287/mnsc.36.2.175. Google Scholar [7] P. Danese and R. Filippini, Direct and mediated effects of product modularity on development time and product performance, 2010 IEEE International Conference on Management of Innovation & Technology, (2010). doi: 10.1109/ICMIT.2010.5492779. Google Scholar [8] A. Gamba and N. Fusari, Valuing modularity as a real option, Management Science, 55 (2009), 1877-1896. doi: 10.1287/mnsc.1090.1070. Google Scholar [9] J. Gualandris and M. Kalchschmidt, Product and process modularity: Improving flexibility and reducing supplier failure risk, International Journal of Production Research, 51 (2013), 5757-5770. doi: 10.1080/00207543.2013.793430. Google Scholar [10] M. E. Ketzenberg and R. A. Zuidwijk, Optimal pricing, ordering, and return policies for consumer goods, Production and Operations Management, 18 (2009), 344-360. doi: 10.1111/j.1937-5956.2009.01017.x. Google Scholar [11] A. Lamas and P. Chevalier, Joint dynamic pricing and lot-sizing under competition, European Journal of Operational Research, 266 (2018), 864-876. doi: 10.1016/j.ejor.2017.10.026. Google Scholar [12] J. F. Lampon, P. Cabanelas and J. Gonzalez-Benito, The impact of modular platforms on automobile manufacturing networks, Production Planning & Control, 28 (2017), 335-348. doi: 10.1080/09537287.2017.1287442. Google Scholar [13] W. Li and J. Chen, Pricing and quality competition in a brand-differentiated supply chain, International Journal of Production Economics, 202 (2018), 97-108. doi: 10.1016/j.ijpe.2018.04.026. Google Scholar [14] N. Matsubayashi and Y. Yamada, A note on price and quality competition between asymmetric firms, European Journal of Operational Research, 187 (2008), 571-581. doi: 10.1016/j.ejor.2007.03.021. Google Scholar [15] S. K. Mukhopadhyay and R. Setoputro, Optimal return policy and modular design for build-to-order products, Journal of Operations Management, 23 (2005), 496-506. doi: 10.1016/j.jom.2004.10.012. Google Scholar [16] S. K. Mukhopadhyay and R. Setaputra, Return policy in product reuse under uncertainty, International Journal of Production Research, 49 (2011), 5317-5332. doi: 10.1080/00207543.2010.523723. Google Scholar [17] M. Pero, M. StöBlein and R. Cigolini, Linking product modularity to supply chain integration in the construction and shipbuilding industries, International Journal of Production Economics, 170 (2015), 602-615. doi: 10.1016/j.ijpe.2015.05.011. Google Scholar [18] C. Raduly-Baka and O. S. Nevalainen, The modular tool switching problem, European Journal of Operational Research, 242 (2015), 100-106. doi: 10.1016/j.ejor.2014.09.052. Google Scholar [19] J. S. Raju and A. Roy, Market information and firm performance, Management Science, 46 (2000), 1013-1169. doi: 10.1287/mnsc.46.8.1075.12024. Google Scholar [20] A. Roy, D. M. Hanssens and J. S. Raju, Competitive pricing by a price leader, Management Science, 40 (1994), 809-945. doi: 10.1287/mnsc.40.7.809. Google Scholar [21] F. Salvador, C. Forza and M. Rungtusanatham, Modularity, product variety, production volume, and component sourcing: Theorizing beyond generic prescriptions, Journal of Operations Management, 20 (2002), 549-575. doi: 10.1016/S0272-6963(02)00027-X. Google Scholar [22] M. Seifbarghy, K. Nouhi and A. Mahmoudi, Contract design in a supply chain considering price and quality dependent demand with customer segmentation, International Journal of Production Economics, 167 (2015), 108-118. doi: 10.1016/j.ijpe.2015.05.004. Google Scholar [23] J. D. Shulman and X. Geng, Add-on pricing by asymmetric firms, Management Science, 59 (2013), 899-917. doi: 10.1287/mnsc.1120.1603. Google Scholar [24] Q. Tu, M. A. Ragu-Nathan, T. S. Vonderembse and B. Ragu-Nathan, Measuring modularity-based manufacturing practices and their impact on mass customization capability: a customer-driven perspective, Decision Sciences, 35 (2004), 147-168. doi: 10.1111/j.00117315.2004.02663.x. Google Scholar [25] D. G. Tyndall, Welfare pricing and transport costs, Management Science, 5 (1959), 169-178. doi: 10.1287/mnsc.5.2.169. Google Scholar [26] S. K. Vickery, S. D. Bolumole, M. J. Castel and R. F. Calantone, The effects of product modularity on launch speed, European Journal of Operational Research, 53 (2015), 5369-5381. doi: 10.1080/00207543.2015.1047972. Google Scholar [27] S. Wang, Q. Hu and W. Liu, Price and quality-based competition and channel structure with consumer loyalty, European Journal of Operational Research, 262 (2017), 563-574. doi: 10.1016/j.ejor.2017.03.052. Google Scholar [28] S. X. Xu, Q. Lu and Z. Li, Optimal modular production strategies under market uncertainty: A real options perspective, International Journal of Production Economics, 139 (2012), 266-274. doi: 10.1016/j.ijpe.2012.05.009. Google Scholar [29] M. Zhang, H. Guo, B. Huo, X. Zhao and J. Huang, Linking supply chain quality integration with mass customization and product modularity, International Journal of Production Economics, 2017. doi: 10.1016/j.ijpe.2017.01.011. Google Scholar [30] Q. Zhang, D. Wu, C. Fu, C. Baron and Z. Peng, A new method for measuring process flexibility of product design, International Transactions in Operational Research, 24 (2017), 821-838. doi: 10.1111/itor.12299. Google Scholar

show all references

##### References:
 [1] B. Agard and S. Bassetto, Modular design of product families for quality and cost, International Journal of Production Research, 51 (2013), 1648-1667. doi: 10.1080/00207543.2012.693963. Google Scholar [2] R. D. Banker, I. Khosla and K. K. Sinha, Quality and competition, Management Science, 44 (1998), 1179-1192. doi: 10.1287/mnsc.44.9.1179. Google Scholar [3] L. M. Barbosa, D. P. Lacerda, F. A. S. Piran and A. Dresch, Exploratory analysis of the variables prevailing on the effects of product modularization on production volume and efficiency, International Journal of Production Economics, 193 (2017), 677-690. doi: 10.1016/j.ijpe.2017.08.028. Google Scholar [4] L. M. B. Cabral and M. Villas-Boas, Bertrand supertraps, Management Science, 51 (2005), 519-678. doi: 10.1287/mnsc.1040.0313. Google Scholar [5] S. Y. Chang and T. Y. Yeh, Optimal order quantity and product modularity for a two-echelon returnable supply chain, International Journal of Production Research, 51 (2013), 5210-5220. doi: 10.1080/00207543.2013.802051. Google Scholar [6] S. C. Choi, W. S. Desarbo and P. T. Harker, Product positioning under price competition, Management Science, 36 (1990), 123-246. doi: 10.1287/mnsc.36.2.175. Google Scholar [7] P. Danese and R. Filippini, Direct and mediated effects of product modularity on development time and product performance, 2010 IEEE International Conference on Management of Innovation & Technology, (2010). doi: 10.1109/ICMIT.2010.5492779. Google Scholar [8] A. Gamba and N. Fusari, Valuing modularity as a real option, Management Science, 55 (2009), 1877-1896. doi: 10.1287/mnsc.1090.1070. Google Scholar [9] J. Gualandris and M. Kalchschmidt, Product and process modularity: Improving flexibility and reducing supplier failure risk, International Journal of Production Research, 51 (2013), 5757-5770. doi: 10.1080/00207543.2013.793430. Google Scholar [10] M. E. Ketzenberg and R. A. Zuidwijk, Optimal pricing, ordering, and return policies for consumer goods, Production and Operations Management, 18 (2009), 344-360. doi: 10.1111/j.1937-5956.2009.01017.x. Google Scholar [11] A. Lamas and P. Chevalier, Joint dynamic pricing and lot-sizing under competition, European Journal of Operational Research, 266 (2018), 864-876. doi: 10.1016/j.ejor.2017.10.026. Google Scholar [12] J. F. Lampon, P. Cabanelas and J. Gonzalez-Benito, The impact of modular platforms on automobile manufacturing networks, Production Planning & Control, 28 (2017), 335-348. doi: 10.1080/09537287.2017.1287442. Google Scholar [13] W. Li and J. Chen, Pricing and quality competition in a brand-differentiated supply chain, International Journal of Production Economics, 202 (2018), 97-108. doi: 10.1016/j.ijpe.2018.04.026. Google Scholar [14] N. Matsubayashi and Y. Yamada, A note on price and quality competition between asymmetric firms, European Journal of Operational Research, 187 (2008), 571-581. doi: 10.1016/j.ejor.2007.03.021. Google Scholar [15] S. K. Mukhopadhyay and R. Setoputro, Optimal return policy and modular design for build-to-order products, Journal of Operations Management, 23 (2005), 496-506. doi: 10.1016/j.jom.2004.10.012. Google Scholar [16] S. K. Mukhopadhyay and R. Setaputra, Return policy in product reuse under uncertainty, International Journal of Production Research, 49 (2011), 5317-5332. doi: 10.1080/00207543.2010.523723. Google Scholar [17] M. Pero, M. StöBlein and R. Cigolini, Linking product modularity to supply chain integration in the construction and shipbuilding industries, International Journal of Production Economics, 170 (2015), 602-615. doi: 10.1016/j.ijpe.2015.05.011. Google Scholar [18] C. Raduly-Baka and O. S. Nevalainen, The modular tool switching problem, European Journal of Operational Research, 242 (2015), 100-106. doi: 10.1016/j.ejor.2014.09.052. Google Scholar [19] J. S. Raju and A. Roy, Market information and firm performance, Management Science, 46 (2000), 1013-1169. doi: 10.1287/mnsc.46.8.1075.12024. Google Scholar [20] A. Roy, D. M. Hanssens and J. S. Raju, Competitive pricing by a price leader, Management Science, 40 (1994), 809-945. doi: 10.1287/mnsc.40.7.809. Google Scholar [21] F. Salvador, C. Forza and M. Rungtusanatham, Modularity, product variety, production volume, and component sourcing: Theorizing beyond generic prescriptions, Journal of Operations Management, 20 (2002), 549-575. doi: 10.1016/S0272-6963(02)00027-X. Google Scholar [22] M. Seifbarghy, K. Nouhi and A. Mahmoudi, Contract design in a supply chain considering price and quality dependent demand with customer segmentation, International Journal of Production Economics, 167 (2015), 108-118. doi: 10.1016/j.ijpe.2015.05.004. Google Scholar [23] J. D. Shulman and X. Geng, Add-on pricing by asymmetric firms, Management Science, 59 (2013), 899-917. doi: 10.1287/mnsc.1120.1603. Google Scholar [24] Q. Tu, M. A. Ragu-Nathan, T. S. Vonderembse and B. Ragu-Nathan, Measuring modularity-based manufacturing practices and their impact on mass customization capability: a customer-driven perspective, Decision Sciences, 35 (2004), 147-168. doi: 10.1111/j.00117315.2004.02663.x. Google Scholar [25] D. G. Tyndall, Welfare pricing and transport costs, Management Science, 5 (1959), 169-178. doi: 10.1287/mnsc.5.2.169. Google Scholar [26] S. K. Vickery, S. D. Bolumole, M. J. Castel and R. F. Calantone, The effects of product modularity on launch speed, European Journal of Operational Research, 53 (2015), 5369-5381. doi: 10.1080/00207543.2015.1047972. Google Scholar [27] S. Wang, Q. Hu and W. Liu, Price and quality-based competition and channel structure with consumer loyalty, European Journal of Operational Research, 262 (2017), 563-574. doi: 10.1016/j.ejor.2017.03.052. Google Scholar [28] S. X. Xu, Q. Lu and Z. Li, Optimal modular production strategies under market uncertainty: A real options perspective, International Journal of Production Economics, 139 (2012), 266-274. doi: 10.1016/j.ijpe.2012.05.009. Google Scholar [29] M. Zhang, H. Guo, B. Huo, X. Zhao and J. Huang, Linking supply chain quality integration with mass customization and product modularity, International Journal of Production Economics, 2017. doi: 10.1016/j.ijpe.2017.01.011. Google Scholar [30] Q. Zhang, D. Wu, C. Fu, C. Baron and Z. Peng, A new method for measuring process flexibility of product design, International Transactions in Operational Research, 24 (2017), 821-838. doi: 10.1111/itor.12299. Google Scholar
Effect of own price sensitivity
Effect of competitor's price sensitivity
Effect of own modularity sensitivity
Effect of competitor's modularity sensitivity
Effect of competitor's modularity sensitivity
Effect of competitor's modularity sensitivity
Effect of competitor's modularity sensitivity
Effect of competitor's modularity sensitivity
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