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

Peng Tong; Xiaogang Ma

doi:10.3934/jimo.2020035

Article Contents

2021, Volume 17, Issue 4: 1577-1591. Doi: 10.3934/jimo.2020035

This issue Previous Article Solving the facility location and fixed charge solid transportation problem Next Article Independent sales or bundling? Decisions under different market-dominant powers

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

Peng Tong^1, , and
Xiaogang Ma^2, ,

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

Received: June 2019

Revised: September 2019

Early access: February 2020

Published: July 2021

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)

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B50; Secondary: 90B25.

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Figure 1. Termination point of 2D warranty service

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Figure 2. Schematic of the maintenance strategy under 2D warranty

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Figure 3. Trend diagram of $ W_r-U_r $

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Figure 4. Diagram of the differentiated warranty service strategy

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Figure 5. Curve of $ W_r-U_r $ ($ ε = 0.9 $)

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Figure 6. Curve of $ W_r-U_r $ ($ \varepsilon = 1.1 $)

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Table 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} $

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Table 2. 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

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Table 3. 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

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Table 4. 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

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