Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers

Bin Chen; Wenying Xie; Fuyou Huang; Juan He

doi:10.3934/jimo.2020100

Article Contents

2021, Volume 17, Issue 5: 2903-2924. Doi: 10.3934/jimo.2020100

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$ {BMAP/BMSP/1} $

queue with Markov dependent arrival and Markov dependent service batches

Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers

1.
Institute of Transportation Development Strategy & Planning of Sichuan Province, Chengdu 610041, China
2.
School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610036, China

^* Corresponding author: Fuyou Huang
^* Corresponding author: Fuyou Huang

Received: October 31, 2019

Revised: February 29, 2020

Early access: May 2020

Published: September 2021

The paper is supported by the Science and Technology Project of Sichuan Province (Grant No.20CXTD0081) and the Science and Technology Project of Transportation Department of Sichuan Province (Grant No.2019-D-05)

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Abstract

Quality competition and risk aversion have become more and more common in today's many industries, making it a challenge to supply chain management and coordination. This paper considers a vendor-managed inventory (VMI) supply chain comprising two risk-averse manufacturers who sell their competing products through a common retailer. Market demand shared by each manufacturer is dependent on the quality level of its own product as well as on the competitor's product quality. The Conditional Value-at-Risk (CVaR) criterion is employed to formulate the risk aversion of manufacturers. This study first develops basic models without coordination mechanism and analyzes the effect of the quality sensitivity, competition intensity, risk aversion degree and cost coefficient of quality improvement on equilibrium decisions and supply chain efficiency. Further, a combined contract composed of option and cost-sharing is proposed to investigate the supply chain coordination issue. The results reveal that the combined contract can coordinate the supply chain and achieve a win-win outcome only when the manufacturers are low in risk aversion, and the system-wide profit of the supply chain can be allocated arbitrarily only by the option price. Also, this research examines the effect of the quality sensitivity, competition intensity, risk aversion degree and cost coefficient of quality improvement on the feasible region of option price.

Keywords:

Mathematics Subject Classification: Primary: 90B50; Secondary: 91B30.

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Figure 1. Structure of the supply chain

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Figure 2. Effect of the option price on profit allocation under channel coordination

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Table 1. Differences between this paper and other relevant papers

Literature	[1]	[16]	[24]	[26]	[37]	[43]	[46]	This paper
Product quality	Yes	Yes	No	Yes	Yes	Yes	No	Yes
Competition	Yes	No	No	No	No	Yes	No	Yes
Stochastic demand	No	No	Yes	Yes	No	No	Yes	Yes
Risk aversion	No	No	Yes	No	No	No	Yes	Yes
Coordination	No	Yes	Yes	Yes	Yes	No	Yes	Yes

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Table 2. Notations

Symbol	Definition
$ i $	Index for product, $ i = 1, 2 $
$ {d_i} $	Quality dependent deterministic demand for the $ i $th product
$ {D_i} $	Demand faced by the retailer for the $ i $th product
$ {c_i} $	Production cost per unit of the $ i $th product
$ {w_i} $	Wholesale price per unit of the $ i $th product
$ {p_i} $	Retail price per unit of the $ i $th product
$ {\upsilon _i} $	Salvage value per unit of the $ i $th product
$ {x_i} $	Random demand faced by the retailer for the $ i $th product
$ {L_i}, {U_i} $	Lower bound and upper bound on $ {x_i} $
$ {f_i}({x_i}) $	Probability density function of the random variable $ {x_i} $
$ {F_i}({x_i}) $	Cumulative distribution function of the random variable $ {x_i} $
$ {a_i} $	Initial market size of the $ i $th product
$ \alpha $	Demand sensitivity of product $ i $'s own quality improvement level
$ \beta $	Competition intensity
$ {s_i} $	Quality improvement level of the $ i $th product
$ {Q_i} $	Production quantity for the $ i $th product
$ {\eta _i} $	Risk aversion coefficient of the $ i $th manufacturer
$ {k_i} $	Cost coefficient of investment in quality improvement of product $ i $

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Table 3. Effect of the quality sensitivity on the expected profits and supply chain efficiency

$ \alpha $	$ E\pi _r^{wp*} $	$ E\pi _m^{wp*} $	$ E\pi _{sc}^{wp*} $	$ E\pi _{sc}^{I*} $	$ {E_f} $
1	24133	7722	39577	46960	84.28%
2	26053	7962	41977	49960	84.02%
3	28933	8362	45657	54960	83.07%
4	32773	8922	51576	61960	81.69%
5	37573	9642	56857	70960	80.13%

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Table 4. Effect of the competition intensity on the expected profits and supply chain efficiency

$ \beta $	$ E\pi _r^{wp*} $	$ E\pi _m^{wp*} $	$ E\pi _{sc}^{wp*} $	$ {E_f} $
1	37573	9642	56857	80.13%
2	39973	9402	58777	82.83%
3	42373	9002	60377	85.09%
4	44773	8442	61657	86.89%
5	47173	7722	62617	88.24%
6	49573	6842	63257	89.14%
7	51973	5802	63577	89.60%
8	54373	4602	63577	89.60%
9	56773	3242	63257	89.14%
10	59173	1722	62617	88.24%

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Table 5. Effect of the risk aversion degree on the expected profits and supply chain efficiency

$ \eta $	$ E\pi _r^{wp*} $	$ E\pi _m^{wp*} $	$ E\pi _{sc}^{wp*} $	$ {E_f} $
1	38148	9833	57814	81.47%
0.95	37861	9738	57337	80.80%
0.9	37573	9642	56857	80.13%
0.85	37286	9546	56378	79.45%
0.8	36998	9451	55900	78.78%

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Table 6. Effect of the cost coefficient of quality improvement on the expected profits and supply chain efficiency

$ k $	$ E\pi _r^{wp*} $	$ E\pi _m^{wp*} $	$ E\pi _{sc}^{wp*} $	$ E\pi _{sc}^{I*} $	$ {E_f} $
0.1	51973	11562	75097	95960	78.23%
0.2	37573	9642	56857	70960	80.13%
0.3	32773	9002	50777	62627	81.08%
0.4	30373	8682	47737	58460	81.66%
0.5	28933	8490	45913	55960	82.05%

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Table 7. Effect of the quality sensitivity on the feasible region of option price

$ \alpha $	1	2	3	4	5
feasible region of $ o $	$ [3.76, 4.16] $	[3.75, 4.17]	[3.75, 4.20]	[3.74, 4.23]	[3.73, 4.27]

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Table 8. Effect of the competition intensity on the feasible region of option price

$ \beta $	1	2	3	4	5
feasible region of $ o $	[3.73, 4.27]	[3.73, 4.23]	[3.72, 4.20]	[3.72, 4.17]	[3.71, 4.16]
$ \beta $	6	7	8	9	10
feasible region of $ o $	[3.69, 4.16]	[3.68, 4.19]	[3.66, 4.26]	[3.63, 4.38]	[3.59, 4.59]

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Table 9. Effect of the risk aversion degree on the feasible region of option price

$ \eta $	0.94	0.92	0.90	0.88	0.86
feasible region of $ o $	[3.24, 3.97]	[3.49, 4.12]	[3.73, 4.27]	[3.98, 4.42]	[4.24, 4.57]

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Table 10. Effect of the cost coefficient of quality improvement on the feasible region of option price

$ k $	0.1	0.2	0.3	0.4	0.5
feasible region of $ o $	[3.72, 4.33]	[3.73, 4.27]	[3.74, 4.24]	[3.75, 4.22]	[3.75, 4.21]

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