# American Institute of Mathematical Sciences

July  2021, 17(4): 1577-1591. doi: 10.3934/jimo.2020035

## Design of differentiated warranty coverage that considers usage rate and service option of consumers under 2D warranty policy

 1 School of Management, China University of Mining and Technology, Jiangsu, China 2 School of Management, Wuhan Textile University, Hubei, China

* Corresponding authors: flyingmantong@163.com; xgma@wtu.edu.cn

Received  June 2019 Revised  September 2019 Published  February 2020

Fund Project: The first author is supported by NSF grant the National Natural Science Foundation of China (No. 71701200); the Postdoctoral Fund of China (No. 2016M590525); the Postdoctoral Fund of Jiangsu (No. 1601246C)

Warranty service providers usually provide homogeneous warranty service to improve consumer satisfaction and market share. Considering the difference of consumers, some scholars have carried out studies on maintenance strategies, service pricing, payment method, claim behaviour and warranty cost analysis in recent years. However, few scholars have focused on the differentiated coverage of warranty service that considers usage rate and service option of consumers. On the basis of previous classification criteria on usage rate, this paper divides consumers into heavy, medium and light usage rate groups with clear boundaries. To avoid discrimination in warranty service, this study divides 2D warranty coverage into disjoint sub-regions and adopts different maintenance modes in each sub-region. By formulating and calculating warranty cost model under warranty cost constraints, we can obtain the maximum warranty coverage under usage rate $r$. Therefore, differentiated warranty scope for consumers in the three groups can be proposed, whilst consumers can choose the most suitable warranty service according to their usage rate. Evidently, the proposed warranty strategy can provide flexible warranty service for consumers, meet the requirements of the warranty cost constraints of warranty service providers and enable enterprises to occupy a favourable position in the market competition.

Citation: Peng Tong, Xiaogang Ma. Design of differentiated warranty coverage that considers usage rate and service option of consumers under 2D warranty policy. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1577-1591. doi: 10.3934/jimo.2020035
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##### References:
Termination point of 2D warranty service
Schematic of the maintenance strategy under 2D warranty
Trend diagram of $W_r-U_r$
Diagram of the differentiated warranty service strategy
Curve of $W_r-U_r$ ($ε = 0.9$)
Curve of $W_r-U_r$ ($\varepsilon = 1.1$)
The interval of usage rate intensity
 Usage intensity Low limit of interval Upper limit of interval Light $r_{l1}$ $r_{l2}$ Medium $r_{l2}$ $r_{h1}$ Heavy $r_{h1}$ $r_{h2}$
 Usage intensity Low limit of interval Upper limit of interval Light $r_{l1}$ $r_{l2}$ Medium $r_{l2}$ $r_{h1}$ Heavy $r_{h1}$ $r_{h2}$
The interval of usage rate intensity
 Failure $C_{mi}(Yuan)$ $C_{ci} (Yuan)$ $f_i(w,r_d)$ $\lambda_{0}$ $k$ A31 1000 5000 $6.32E-04 w^{1.06}{e^{-({w}/{4.03})}}^{2.06}$ 4.03 2.06 A18 3200 6400 $2.20E-02 w^{0.59}{e^{-({w}/{3.22})}}^{1.59}$ 3.22 1.59 A88 800 4800 $2.53E-03 w^{0.45}{e^{-({w}/{2.48})}}^{1.45}$ 2.48 1.45 A20 2600 7800 $5.67E-02 w^{0.49}{e^{-({w}/{2.90})}}^{1.49}$ 2.90 1.49 A30 4500 9000 $4.78E-03 w^{0.62}{e^{-({w}/{3.40})}}^{1.62}$ 3.40 1.62 A10 3000 12000 $5.82E-02 w^{0.51}{e^{-({w}/{2.94})}}^{1.51}$ 2.94 1.51 A16 2900 8700 $9.24E-03 w^{0.42}{e^{-({w}/{2.76})}}^{1.42}$ 2.76 1.42 A50 3500 10500 $6.98E-02 w^{0.85}{e^{-({w}/{3.28})}}^{1.85}$ 3.28 1.85 A15 1700 3400 $1.36E-02 w^{0.51}{e^{-({w}/{3.14})}}^{1.51}$ 3.14 1.51 A40 2800 5600 $1.33E-01 w^{0.49}{e^{-({w}/{2.69})}}^{1.49}$ 2.69 1.49 A17 4600 9200 $1.89E-02 w^{0.55}{e^{-({w}/{3.22})}}^{1.55}$ 3.22 1.55
 Failure $C_{mi}(Yuan)$ $C_{ci} (Yuan)$ $f_i(w,r_d)$ $\lambda_{0}$ $k$ A31 1000 5000 $6.32E-04 w^{1.06}{e^{-({w}/{4.03})}}^{2.06}$ 4.03 2.06 A18 3200 6400 $2.20E-02 w^{0.59}{e^{-({w}/{3.22})}}^{1.59}$ 3.22 1.59 A88 800 4800 $2.53E-03 w^{0.45}{e^{-({w}/{2.48})}}^{1.45}$ 2.48 1.45 A20 2600 7800 $5.67E-02 w^{0.49}{e^{-({w}/{2.90})}}^{1.49}$ 2.90 1.49 A30 4500 9000 $4.78E-03 w^{0.62}{e^{-({w}/{3.40})}}^{1.62}$ 3.40 1.62 A10 3000 12000 $5.82E-02 w^{0.51}{e^{-({w}/{2.94})}}^{1.51}$ 2.94 1.51 A16 2900 8700 $9.24E-03 w^{0.42}{e^{-({w}/{2.76})}}^{1.42}$ 2.76 1.42 A50 3500 10500 $6.98E-02 w^{0.85}{e^{-({w}/{3.28})}}^{1.85}$ 3.28 1.85 A15 1700 3400 $1.36E-02 w^{0.51}{e^{-({w}/{3.14})}}^{1.51}$ 3.14 1.51 A40 2800 5600 $1.33E-01 w^{0.49}{e^{-({w}/{2.69})}}^{1.49}$ 2.69 1.49 A17 4600 9200 $1.89E-02 w^{0.55}{e^{-({w}/{3.22})}}^{1.55}$ 3.22 1.55
Age and usage parameters of the 2D warranty coverage ($\varepsilon = 0.9$)
 $w_n$ Value $u_n$ Value $W_l$ 3.35 $U_l$ 2.18 $W_m$ 2.44 $U_m$ 4.39 $W_h$ 1.83 $U_h$ 5.49
 $w_n$ Value $u_n$ Value $W_l$ 3.35 $U_l$ 2.18 $W_m$ 2.44 $U_m$ 4.39 $W_h$ 1.83 $U_h$ 5.49
Age and usage parameters of the 2D warranty coverage ($\varepsilon = 1.1$)
 $w_n$ Value $u_n$ Value $W_l$ 3.53 $U_l$ 2.29 $W_m$ 2.28 $U_m$ 4.10 $W_h$ 1.50 $U_h$ 4.50
 $w_n$ Value $u_n$ Value $W_l$ 3.53 $U_l$ 2.29 $W_m$ 2.28 $U_m$ 4.10 $W_h$ 1.50 $U_h$ 4.50
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