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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  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:

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##### 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 $i$, $R_i>0$.
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