# American Institute of Mathematical Sciences

• Previous Article
A performance comparison and evaluation of metaheuristics for a batch scheduling problem in a multi-hybrid cell manufacturing system with skilled workforce assignment
• JIMO Home
• This Issue
• Next Article
A threshold-based risk process with a waiting period to pay dividends
July  2018, 14(3): 1203-1218. doi: 10.3934/jimo.2018006

## Competition of pricing and service investment between iot-based and traditional manufacturers

 1 School of Management, Hefei University of Technology, Hefei 230009, China 2 Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA 3 Key Laboratory of Process Optimization, and Intelligent Decision-Making of Ministry of Education, Hefei 230009, China

* Corresponding author:Xinbao Liu, Jun Pei

Received  June 2016 Revised  September 2017 Published  July 2018 Early access  January 2018

This paper develops a multi-period product pricing and service investment model to discuss the optimal decisions of the participants in a supplier-dominant supply chain under uncertainty. The supply chain consists of a risk-neutral supplier and two risk-averse manufacturers, of which one manufacturer can provide real-time customer service based on the Internet of Things (IoT). In each period of the Stackelberg game, the supplier decides its wholesale price to maximize the profit while the manufacturers make pricing and service investment decisions to maximize their respective utility. Using the backward induction, we first investigate the effects of risk-averse coefficients and price sensitive coefficients on the optimal decisions of the manufacturers. We find that the decisions of one manufacturer are inversely proportional to both risk-averse coefficients and its own price sensitive coefficient, while proportional to the price sensitive coefficient of its rival. Then, we derive the first-best wholesale price of the supplier and analyze how relevant factors affect the results. A numerical example is conducted to verify our conclusions and demonstrate the advantages of the IoT technology in long-term competition. Finally, we summarize the main contributions of this paper and put forward some advices for further study.

Citation: Zhiping Zhou, Xinbao Liu, Jun Pei, Panos M. Pardalos, Hao Cheng. Competition of pricing and service investment between iot-based and traditional manufacturers. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1203-1218. doi: 10.3934/jimo.2018006
##### References:
 [1] M. R. Amin-Naseri and M. A. Khojasteh, Price competition between two leader-follower supply chains with risk-averse retailers under demand uncertainty, The International Journal of Advanced Manufacturing Technology, (2015), 377-393.  doi: 10.1007/s00170-014-6728-0. [2] O. Besbes and D. Saure, Product assortment and price competition under multinomial logit demand, Production and Operations Management, 25 (2016), 114-127. [3] W. Chen, Z. G. Zhang and Z. Hua, Analysis of price competition in two-tier service systems Journal of the Operational Research Society (2016). doi: 10.1057/jors.2015.123. [4] Y. Dai, X. Chao, S. C. Fang and H. L. W. Nuttle, Pricing in revenue management for multiple firms competing for customers, International Journal of Production Economics, 98 (2005), 1-16.  doi: 10.1016/j.ijpe.2004.06.056. [5] B. Dan, G. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. [6] H. Demirkan and D. Delen, Leveraging the capabilities of service-oriented decision support systems: Putting analytics and big data in cloud, Decision Support Systems, 55 (2013), 412-421.  doi: 10.1016/j.dss.2012.05.048. [7] L. Duan, J. Huang and B. Shou, Duopoly competition in dynamic spectrum leasing and pricing, IEEE Transactions on Mobile Computing, 11 (2012), 1706-1719.  doi: 10.1109/TMC.2011.213. [8] B. C. Giri and B. R. Sarker, Coordinating a two-echelon supply chain under production disruption when retailers compete with price and service level, Operational Research, 16 (2016), 71-88.  doi: 10.1007/s12351-015-0187-8. [9] D. Guinard, V. Trifa, S. Karnouskos, P. Spiess and D. Savio, Interacting with the SOA-based internet of things: discovery, query, selection, and on-demand provisioning of web services, IEEE Transactions on Services Computing, 3 (2010), 223-235.  doi: 10.1109/TSC.2010.3. [10] D. Honhon, V. Gaur and S. Seshadri, Assortment planning and inventory decisions under stockout-based substitution, Operations research, 58 (2010), 1364-1379.  doi: 10.1287/opre.1090.0805. [11] Z. Hua and S. Li, Impacts of demand uncertainty on retailer's dominance and manufacturer-retailer supply chain cooperation, Omega-International Journal of Management Science, 36 (2008), 697-714.  doi: 10.1016/j.omega.2006.02.005. [12] W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279.  doi: 10.1016/j.ejor.2007.11.041. [13] G. Jiang, B. Hu and Y. Wang, Agent-based simulation of competitive and collaborative mechanisms for mobile service chains, Information Sciences, 180 (2010), 225-240.  doi: 10.1016/j.ins.2009.09.014. [14] A. Khorana and H. Servaes, What drives market share in the mutual fund industry?, Review of Finance, 16 (2012), 81-113.  doi: 10.1093/rof/rfr027. [15] D. Kiritsis, Closed-loop PLM for intelligent products in the era of the Internet of things, Computer-Aided Design, 43 (2011), 479-501.  doi: 10.1016/j.cad.2010.03.002. [16] G. Kong, S. Rajagopalan and H. Zhang, Revenue sharing and information leakage in a supply chain, Management Science, 59 (2013), 556-572. [17] H. Markowitz, Mean-variance approximations to expected utility, European Journal of Operational Research, 234 (2014), 346-355.  doi: 10.1016/j.ejor.2012.08.023. [18] D. Martín, F. García, B. Musleh, D. Olmeda, G. Peláez, P. Marín, A. Ponz, C. Rodríguez, A. Al-Kaff, A. de la Escalera and J. M. Armingol, IVVI 2.0: An intelligent vehicle based on computational perception, Expert Systems with Applications, 41 (2014), 7927-7944. [19] V. Milanés, D. F. Llorca, J. Villagrá, J. Pérez, C. Fernández, I. Parra, C. González and M. A. Sotelo, Intelligent automatic overtaking system using vision for vehicle detection, Expert Systems with Applications, 39 (2012), 3362-3373. [20] P. M. Pardalos and V. K. Tsitsiringos (Eds), Financial Engineering, E-commerce and Supply Chain Kluwer Academic Publishers, 2002. doi: 10.1007/978-1-4757-5226-7. [21] M. E. Porter and J. E. Heppelmann, How smart, connected products are transforming competition, Harvard Business Review, 92 (2014), 64-88. [22] J. Shi and T. Xiao, Service investment and consumer returns policy in a vendor-managed inventory supply chain, Journal of Industrial and Management Optimization, 11 (2015), 439-459. [23] A. Sinha, P. Malo, A. Frantsev and K. Deb, Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm, Computers & Operations Research, 41 (2014), 374-385.  doi: 10.1016/j.cor.2013.07.010. [24] C. W. Tan, I. Benbasat and R. T. Cenfetelli, IT-mediated customer service content and delivery in electronic governments: An empirical investigation of the antecedents of service quality, MIS quarterly, 37 (2013), 77-109. [25] F. Tao, L. Zhang, Y. Liu, Y. Cheng, L. Wang and X. Xu, Manufacturing service management in cloud manufacturing: Overview and future research directions Journal of Manufacturing Science and Engineering 137(2015), 040912, 11pp. doi: 10.1115/1.4030510. [26] H. Wang and J. Ma, Complexity analysis of a Cournot-Bertrand duopoly game with different expectations, Nonlinear Dynamics, 78 (2014), 2759-2768.  doi: 10.1007/s11071-014-1623-7. [27] D. D. Wu, Bargaining in supply chain with price and promotional effort dependent demand, Mathematical and Computer Modelling, 58 (2013), 1659-1669.  doi: 10.1016/j.mcm.2010.12.035. [28] T. Xiao and D. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty, International Journal of Production Economics, 114 (2008), 187-200.  doi: 10.1016/j.ijpe.2008.01.006. [29] Y. Zhang, G. Zhang, J. Wang, S. Sun and T. Yang, Real-time information capturing and integration framework of the internet of manufacturing things, International Journal of Computer Integrated Manufacturing, 28 (2015), 811-822. [30] J. Zhao, W. Liu and J. Wei, Competition under manufacturer service and price in fuzzy environments, Knowledge-Based Systems, 50 (2013), 121-133.  doi: 10.1016/j.knosys.2013.06.003.

show all references

##### References:
 [1] M. R. Amin-Naseri and M. A. Khojasteh, Price competition between two leader-follower supply chains with risk-averse retailers under demand uncertainty, The International Journal of Advanced Manufacturing Technology, (2015), 377-393.  doi: 10.1007/s00170-014-6728-0. [2] O. Besbes and D. Saure, Product assortment and price competition under multinomial logit demand, Production and Operations Management, 25 (2016), 114-127. [3] W. Chen, Z. G. Zhang and Z. Hua, Analysis of price competition in two-tier service systems Journal of the Operational Research Society (2016). doi: 10.1057/jors.2015.123. [4] Y. Dai, X. Chao, S. C. Fang and H. L. W. Nuttle, Pricing in revenue management for multiple firms competing for customers, International Journal of Production Economics, 98 (2005), 1-16.  doi: 10.1016/j.ijpe.2004.06.056. [5] B. Dan, G. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, International Journal of Production Economics, 139 (2012), 312-320. [6] H. Demirkan and D. Delen, Leveraging the capabilities of service-oriented decision support systems: Putting analytics and big data in cloud, Decision Support Systems, 55 (2013), 412-421.  doi: 10.1016/j.dss.2012.05.048. [7] L. Duan, J. Huang and B. Shou, Duopoly competition in dynamic spectrum leasing and pricing, IEEE Transactions on Mobile Computing, 11 (2012), 1706-1719.  doi: 10.1109/TMC.2011.213. [8] B. C. Giri and B. R. Sarker, Coordinating a two-echelon supply chain under production disruption when retailers compete with price and service level, Operational Research, 16 (2016), 71-88.  doi: 10.1007/s12351-015-0187-8. [9] D. Guinard, V. Trifa, S. Karnouskos, P. Spiess and D. Savio, Interacting with the SOA-based internet of things: discovery, query, selection, and on-demand provisioning of web services, IEEE Transactions on Services Computing, 3 (2010), 223-235.  doi: 10.1109/TSC.2010.3. [10] D. Honhon, V. Gaur and S. Seshadri, Assortment planning and inventory decisions under stockout-based substitution, Operations research, 58 (2010), 1364-1379.  doi: 10.1287/opre.1090.0805. [11] Z. Hua and S. Li, Impacts of demand uncertainty on retailer's dominance and manufacturer-retailer supply chain cooperation, Omega-International Journal of Management Science, 36 (2008), 697-714.  doi: 10.1016/j.omega.2006.02.005. [12] W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279.  doi: 10.1016/j.ejor.2007.11.041. [13] G. Jiang, B. Hu and Y. Wang, Agent-based simulation of competitive and collaborative mechanisms for mobile service chains, Information Sciences, 180 (2010), 225-240.  doi: 10.1016/j.ins.2009.09.014. [14] A. Khorana and H. Servaes, What drives market share in the mutual fund industry?, Review of Finance, 16 (2012), 81-113.  doi: 10.1093/rof/rfr027. [15] D. Kiritsis, Closed-loop PLM for intelligent products in the era of the Internet of things, Computer-Aided Design, 43 (2011), 479-501.  doi: 10.1016/j.cad.2010.03.002. [16] G. Kong, S. Rajagopalan and H. Zhang, Revenue sharing and information leakage in a supply chain, Management Science, 59 (2013), 556-572. [17] H. Markowitz, Mean-variance approximations to expected utility, European Journal of Operational Research, 234 (2014), 346-355.  doi: 10.1016/j.ejor.2012.08.023. [18] D. Martín, F. García, B. Musleh, D. Olmeda, G. Peláez, P. Marín, A. Ponz, C. Rodríguez, A. Al-Kaff, A. de la Escalera and J. M. Armingol, IVVI 2.0: An intelligent vehicle based on computational perception, Expert Systems with Applications, 41 (2014), 7927-7944. [19] V. Milanés, D. F. Llorca, J. Villagrá, J. Pérez, C. Fernández, I. Parra, C. González and M. A. Sotelo, Intelligent automatic overtaking system using vision for vehicle detection, Expert Systems with Applications, 39 (2012), 3362-3373. [20] P. M. Pardalos and V. K. Tsitsiringos (Eds), Financial Engineering, E-commerce and Supply Chain Kluwer Academic Publishers, 2002. doi: 10.1007/978-1-4757-5226-7. [21] M. E. Porter and J. E. Heppelmann, How smart, connected products are transforming competition, Harvard Business Review, 92 (2014), 64-88. [22] J. Shi and T. Xiao, Service investment and consumer returns policy in a vendor-managed inventory supply chain, Journal of Industrial and Management Optimization, 11 (2015), 439-459. [23] A. Sinha, P. Malo, A. Frantsev and K. Deb, Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm, Computers & Operations Research, 41 (2014), 374-385.  doi: 10.1016/j.cor.2013.07.010. [24] C. W. Tan, I. Benbasat and R. T. Cenfetelli, IT-mediated customer service content and delivery in electronic governments: An empirical investigation of the antecedents of service quality, MIS quarterly, 37 (2013), 77-109. [25] F. Tao, L. Zhang, Y. Liu, Y. Cheng, L. Wang and X. Xu, Manufacturing service management in cloud manufacturing: Overview and future research directions Journal of Manufacturing Science and Engineering 137(2015), 040912, 11pp. doi: 10.1115/1.4030510. [26] H. Wang and J. Ma, Complexity analysis of a Cournot-Bertrand duopoly game with different expectations, Nonlinear Dynamics, 78 (2014), 2759-2768.  doi: 10.1007/s11071-014-1623-7. [27] D. D. Wu, Bargaining in supply chain with price and promotional effort dependent demand, Mathematical and Computer Modelling, 58 (2013), 1659-1669.  doi: 10.1016/j.mcm.2010.12.035. [28] T. Xiao and D. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty, International Journal of Production Economics, 114 (2008), 187-200.  doi: 10.1016/j.ijpe.2008.01.006. [29] Y. Zhang, G. Zhang, J. Wang, S. Sun and T. Yang, Real-time information capturing and integration framework of the internet of manufacturing things, International Journal of Computer Integrated Manufacturing, 28 (2015), 811-822. [30] J. Zhao, W. Liu and J. Wei, Competition under manufacturer service and price in fuzzy environments, Knowledge-Based Systems, 50 (2013), 121-133.  doi: 10.1016/j.knosys.2013.06.003.
The structure of market competition between the IoT-based manufacturer and the traditional manufacturer
The optimal retail price $p_{i, 1}^*$ versus the price sensitive coefficient $\alpha$ and $\beta$
The optimal retail price $p_{i, 1}^*$ versus the price sensitive coefficient $\alpha$ and $\beta$
First derivative of retail price $\frac{\partial p_{i, 1}^*}{\partial w_1}$ versus the service level $d_0$
The optimal retail price $p_{i, 1}^*$ versus the risk-averse coefficient $\lambda_i$
The optimal wholesale price $w_n^*$ versus the service level $d_n$
The optimal wholesale price $w_n^*$ versus the price sensitive coefficients $\alpha$ and $\beta$
The optimal wholesale price $w_n^*$ versus the risk-averse coefficients $\lambda_i$
NOTATIONS
 Symbol Meaning $\widetilde{a}_{i, n}$ manufacturer i's random market base in $nth$ period with mean $q_{i, n-1}$ and variance $\sigma^2$, where $q_{i, n-1}$ denotes the expected market demand in the previous period and $q_{2, 0}>q_{1, 0}$; $s$ marginal production cost of the supplier; $w_n$ unit wholesale price of the supplier in period $n$; $p_{i, n}$ unit retail price of manufacturer $i$ in period $n$; $\alpha, \beta$ price sensitive coefficients of demands of IoT-based and traditional products respectively; $\lambda_i$ risk-averse coefficient of manufacturer $i$, $\lambda_i\geq 0$; $I_n$ service investment of manufacturer 1 in the $nth$ period; $C$ investment efficiency coefficient of service expenditure; $\eta_n$ service improvement of manufacturer 1 in the $nth$ period, $\eta_n>1$; $d_n$ service level of IoT-based product in period $n$, $d_n=d_{n-1} \eta_n$; $K$ influence coefficient of service level on the demand of IoT-based product, $K>0$; $R_i$ reservation utility of manufacturer $i$, $R_i>0$.
 Symbol Meaning $\widetilde{a}_{i, n}$ manufacturer i's random market base in $nth$ period with mean $q_{i, n-1}$ and variance $\sigma^2$, where $q_{i, n-1}$ denotes the expected market demand in the previous period and $q_{2, 0}>q_{1, 0}$; $s$ marginal production cost of the supplier; $w_n$ unit wholesale price of the supplier in period $n$; $p_{i, n}$ unit retail price of manufacturer $i$ in period $n$; $\alpha, \beta$ price sensitive coefficients of demands of IoT-based and traditional products respectively; $\lambda_i$ risk-averse coefficient of manufacturer $i$, $\lambda_i\geq 0$; $I_n$ service investment of manufacturer 1 in the $nth$ period; $C$ investment efficiency coefficient of service expenditure; $\eta_n$ service improvement of manufacturer 1 in the $nth$ period, $\eta_n>1$; $d_n$ service level of IoT-based product in period $n$, $d_n=d_{n-1} \eta_n$; $K$ influence coefficient of service level on the demand of IoT-based product, $K>0$; $R_i$ reservation utility of manufacturer $i$, $R_i>0$.
 [1] Tao Li, Suresh P. Sethi. A review of dynamic Stackelberg game models. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 125-159. doi: 10.3934/dcdsb.2017007 [2] Lianju Sun, Ziyou Gao, Yiju Wang. A Stackelberg game management model of the urban public transport. Journal of Industrial and Management Optimization, 2012, 8 (2) : 507-520. doi: 10.3934/jimo.2012.8.507 [3] Weijun Meng, Jingtao Shi. A linear quadratic stochastic Stackelberg differential game with time delay. Mathematical Control and Related Fields, 2021  doi: 10.3934/mcrf.2021035 [4] Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control and Related Fields, 2021, 11 (4) : 797-828. doi: 10.3934/mcrf.2020047 [5] 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 [6] Jingzhen Liu, Lihua Bai, Ka-Fai Cedric Yiu. Optimal investment with a value-at-risk constraint. Journal of Industrial and Management Optimization, 2012, 8 (3) : 531-547. doi: 10.3934/jimo.2012.8.531 [7] Yuwei Shen, Jinxing Xie, Tingting Li. The risk-averse newsvendor game with competition on demand. Journal of Industrial and Management Optimization, 2016, 12 (3) : 931-947. doi: 10.3934/jimo.2016.12.931 [8] Jianxiong Zhang, Zhenyu Bai, Wansheng Tang. Optimal pricing policy for deteriorating items with preservation technology investment. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1261-1277. doi: 10.3934/jimo.2014.10.1261 [9] Nan Li, Song Wang. Pricing options on investment project expansions under commodity price uncertainty. Journal of Industrial and Management Optimization, 2019, 15 (1) : 261-273. doi: 10.3934/jimo.2018042 [10] Xiujing Dang, Yang Xu, Gongbing Bi, Lei Qin. Pricing strategy and product quality design with platform-investment. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2021224 [11] Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2563-2579. doi: 10.3934/jimo.2019070 [12] Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1937-1953. doi: 10.3934/jimo.2018130 [13] Jing Zhang, Jianquan Lu, Jinde Cao, Wei Huang, Jianhua Guo, Yun Wei. Traffic congestion pricing via network congestion game approach. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1553-1567. doi: 10.3934/dcdss.2020378 [14] Mrinal K. Ghosh, Somnath Pradhan. A nonzero-sum risk-sensitive stochastic differential game in the orthant. Mathematical Control and Related Fields, 2022, 12 (2) : 343-370. doi: 10.3934/mcrf.2021025 [15] Engel John C Dela Vega, Robert J Elliott. Conditional coherent risk measures and regime-switching conic pricing. Probability, Uncertainty and Quantitative Risk, 2021, 6 (4) : 267-300. doi: 10.3934/puqr.2021014 [16] Jing Shi, Tiaojun Xiao. Service investment and consumer returns policy in a vendor-managed inventory supply chain. Journal of Industrial and Management Optimization, 2015, 11 (2) : 439-459. doi: 10.3934/jimo.2015.11.439 [17] Wei Chen, Jianchang Fan, Hongyan Du, Pingsi Zhong. Investment strategy for renewable energy and electricity service quality under different power structures. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022006 [18] Bing-Bing Cao, Zai-Jing Gong, Tian-Hui You. Stackelberg pricing policy in dyadic capital-constrained supply chain considering bank's deposit and loan based on delay payment scheme. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2855-2887. doi: 10.3934/jimo.2020098 [19] Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial and Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73 [20] 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

2020 Impact Factor: 1.801