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 & Management Optimization, 2018, 14 (3) : 1203-1218. doi: 10.3934/jimo.2018006
References:

show all references

References:
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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Management Optimization, 2019, 15 (1) : 261-273. doi: 10.3934/jimo.2018042 [10] Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2563-2579. doi: 10.3934/jimo.2019070 [11] Yong Ma, Shiping Shan, Weidong Xu. Optimal investment and consumption in the market with jump risk and capital gains tax. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1937-1953. doi: 10.3934/jimo.2018130 [12] Jing Zhang, Jianquan Lu, Jinde Cao, Wei Huang, Jianhua Guo, Yun Wei. Traffic congestion pricing via network congestion game approach. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1553-1567. doi: 10.3934/dcdss.2020378 [13] Mrinal K. Ghosh, Somnath Pradhan. A nonzero-sum risk-sensitive stochastic differential game in the orthant. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021025 [14] Jing Shi, Tiaojun Xiao. Service investment and consumer returns policy in a vendor-managed inventory supply chain. Journal of Industrial & Management Optimization, 2015, 11 (2) : 439-459. doi: 10.3934/jimo.2015.11.439 [15] 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 & Management Optimization, 2021, 17 (5) : 2855-2887. doi: 10.3934/jimo.2020098 [16] Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial & Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73 [17] Xuemei Zhang, Malin Song, Guangdong Liu. Service product pricing strategies based on time-sensitive customer choice behavior. Journal of Industrial & Management Optimization, 2017, 13 (1) : 297-312. doi: 10.3934/jimo.2016018 [18] Jinsen Guo, Yongwu Zhou, Baixun Li. The optimal pricing and service strategies of a dual-channel retailer under free riding. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021056 [19] Qingfeng Meng, Wenjing Li, Zhen Li, Changzhi Wu. B2C online ride-hailing pricing and service optimization under competitions. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021147 [20] Zhongbao Zhou, Yanfei Bai, Helu Xiao, Xu Chen. A non-zero-sum reinsurance-investment game with delay and asymmetric information. Journal of Industrial & Management Optimization, 2021, 17 (2) : 909-936. doi: 10.3934/jimo.2020004

2020 Impact Factor: 1.801