research article sourcing for quality: cooperating...

Research ArticleSourcing for Quality: Cooperating with a Single Supplier orDeveloping Two Competing Suppliers?

Jingxian Chen1,2

1School of Business, Nantong University, 9 Seyuan Road, Nantong 226019, China2School of Management, University of Science & Technology of China, 96 Jinzhai Road, Hefei 230026, China

Correspondence should be addressed to Jingxian Chen; [email protected]

Received 25 January 2016; Accepted 5 April 2016

Academic Editor: Alireza Amirteimoori

Copyright © 2016 Jingxian Chen.This is an open access article distributed under theCreative CommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Supplier efforts regarding product quality are an important issue in outsourcing and play a critical role in a manufacturer’schoice of sourcing strategy. Consider a manufacturer that wants to outsource the manufacturing of two substitute products toexternal suppliers. This paper studies the strategic interactions under two sourcing strategies: single and dual sourcing. A four-stage noncooperative game model is established to describe each member’s decisions. We further propose four decision scenarios:single sourcing with and without manufacturer quality investment sharing and dual sourcing when suppliers cooperate or do notcooperate on quality decisions. By the backward induction approach, we obtain analytical equilibrium solutions for each decisionscenario. By comparing each pair of equilibrium profiles, we find that an appropriate proportion of quality investment sharing bythe manufacturer can enable a cooperating strategy with a single supplier to be the dominant strategy. When the manufacturerdoes not want to share or does not want to share a relatively large portion of its supplier’s quality investment, it will always preferto develop two competing suppliers when the cost of dual sourcing is sufficiently low. However, dual sourcing can be extremelyrisky for the manufacturer because the suppliers could provide a relatively low product quality level by cooperating on the qualitydecision to extract the manufacturer’s profit.

1. Introduction

Due to many benefits, such as reduced costs, decreasedinvestments, increased productivity, and increased core com-petency, outsourcing has become a pervasive supply chainfeature and has contributed significantly to the growth ofthe global economy [1–3]. A recent report estimated that,globally, organisations will outsource US $507 billion worthof business and information technology (IT) services in 2014alone [4]. However, some argue that outsourcing has alsocreated a new set of risks and challenges for organisations,as it has become an increasingly common business practice.Reduced control of supplier quality, a well-known downsideof outsourcing, will drive poor product (service) quality,thus representing a risk to the buyer. For example, a 2012Global Outsourcing and Insourcing Survey found that 48%of companies had previously terminated an outsourcing con-tract, primarily due to service quality concerns [5].Therefore,how to encourage supplier quality improvement plays an

important role in strategic outsourcing. The objective of thispaper is to link the sourcing strategy with the supplier qualityeffort when the buyer wishes to outsource the manufacturingof multiple products to external suppliers.

With increasing overemphasis on cost reduction, leadtime compression, and capacity expansion by the buyer,outsourcing enables suppliers to have no incentives on qualityimprovement, particularly when the quality cannot be regu-lated by a contract [6, 7]. As a result, firms typically enforcesupply quality control by resorting to quality inspection poli-cies. A more rigorous quality standard would be beneficial tothe buyer for enhancing quality in the end market. However,such a standard could negatively affect the supplier anddisrupt the supply chain due to the pressure of a standardimplementation. For example, one factory of the giant con-tractmanufacturer,HonHai Limited (also known as FoxconnTechnology Group), in mainland China underwent a large-scale strike triggered by instructions to strengthen qualityinspections for the iPhone 5; these instructions were given

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016, Article ID 3040343, 13 pageshttp://dx.doi.org/10.1155/2016/3040343

2 Mathematical Problems in Engineering

by Hon Hai’s customer, Apple Inc. [8]. Hence, enablingthe supplier to participate in quality improvement could becritical to the buyer.

The majority of opinions regarding the handling ofsupplier quality incentives could be divided into two mainstreams. The first stream advocates that the buyer cooperatedirectly with its supplier, such as by providing technologyassistance through sending technical engineers to the sup-plier site and offering quality management education andtraining to the supplier’s employees [7]. For example, Boeingpersonnel are embedded into supplier factories at the globalscale to monitor quality, work with suppliers on processimprovements, and ensure adherence to Boeing standardsand schedules [9]. These policies could be categorised asinvestments in supplier quality improvement or payment forsupplier quality efforts, that is, cooperative quality investment[10].

There is another avenue for the buyer to pursue regardingsupplier quality improvement—developingmultiple compet-ing suppliers. Because competition could be used as a mech-anism for the buyer to elicit quality from suppliers, in prac-tice, many giant manufacturers take pleasure in introducingcompetition among suppliers to mitigate the supplier qualityrisk in outsourcing [11]. For example, Apple Inc. continuallyseeks alternative suppliers and prefers to choose whoeverhas the best quality and best production rate [12]. Toyotainvested in its auto seat supplier, Trim Masters, to introducecompetition for its other supplier, Johnson Controls ([13] andreference therein).

Although vertical quality cooperation and horizontalquality competition are commonly used as supplier qualityimprovement mechanisms, which strategy will be more suit-able for quality aspects and/or manufacturer profit remainsunclear. Specifically,most of the extant literature established aquality enhancement mechanism for single product sourcing[1, 7, 10, 11, 13–15]. In many industries, however, manufactur-ers outsource the provisioning of a series of substitute prod-ucts to external suppliers. For example, Apple provides iPadsand iPad minis with different prices and features to the panelcomputer market. Nearly all of these iPads and iPad minisare assembled by the contract manufacturers Foxconn andPegatron, respectively [16].

Product quality has a positive effect on market demand[10, 17, 18]. When a manufacturer outsources two substituteproducts and each product is manufactured by a specialsupplier, then the suppliers could have more incentives toimprove product quality for competing for a larger demandshare. Thus, each supplier’s product decision could be dif-ferent from the case of single sourcing. This paper aims toinvestigate the effects of the sourcing strategies on suppliers’quality decisions.

Consider a manufacturer that wants to outsource themanufacturing of two substitute products to external sup-pliers. This paper studies the strategic interactions for twosourcing strategies: single and dual sourcing. In addition, wepropose four decision scenarios: single sourcing with andwithout manufacturer quality investment sharing and dualsourcing when suppliers cooperate or do not cooperate on

quality decisions.This paper addresses the following researchquestions using a four-stage noncooperative model.

(i) Which strategy works better for improving supplierquality? If the manufacturer is willing to share a sufficientlylarge portion of quality investment for both products, coop-erating with a single supplier can be a dominant strategy forthe quality level; otherwise, the strategy of developing twocompeting suppliers can provide the highest product quality.

(ii) Which strategy works better for manufacturer profit?If the sourcing cost is sufficiently low, the manufacturerprefers to use the strategy of developing two competingsuppliers. Otherwise, if the portion of the quality investmentdefrayed by the manufacturer is sufficiently small, cooper-ating with a single supplier benefits the manufacturer byincreasing profit. Moreover, when the manufacturer’s share issufficiently large, using a single supplier without investing inits quality is better for the manufacturer.

(iii) Which strategy works better for product quality andmanufacturer profit? An appropriate proportion of qualityinvestment sharing by the manufacturer can enable domi-nance of the cooperatingwith a single supplier strategy; whenthe manufacturer does not want to share or does not want toshare a relatively large portion of its quality investment funds,it will prefer to develop two competing suppliers when thecost of dual sourcing is sufficiently low.

In addition, dual sourcing can be extremely risky forthe manufacturer because the suppliers could establish arelatively low product quality level by cooperating on thequality decision and extract the manufacturer profit.

The remainder of this paper is organised as follows:Section 2 briefly reviews the related literature, and Section 3details our model’s general framework. In Sections 4 and 5,we investigate four decision models of the quality choice:single sourcing with and without a manufacturer qualityinvestment sharing and dual sourcing when the supplierscooperate or do not cooperate on quality decisions. Section 6studies which strategy is more effective for product qualityand/or manufacturer profit. Concluding remarks and futuredirections are presented in Section 7. All proofs are deferredto the Appendix in Supplementary Material available onlineat http://dx.doi.org/10.1155/2016/3040343 for clarity of expo-sition.

2. Literature Review

There are three streams of literature related to our paper:strategic quality choice in a vertical channel, mechanisms ofproduct (service) quality improvement, and sourcing strate-gies considering product quality.

Quality, as an important competitive feature in themajor-ity of industries, has received considerable attention. Pioneer-ing studies focused on the strategic quality decision thatmax-imised social value or amonopoly firm’s profit [19, 20].There-after, Banker et al. [18] andChambers et al. [17], amongothers,began to analyse the equilibriumquality level in a competitiveenvironment. These studies provided fundamental insightsinto the issue of the effort tied to firm’s quality choice. How-ever, they did not investigate the strategic interaction among

Mathematical Problems in Engineering 3

the players in a supply chain channel environment. We referto Chen et al. [10] for a comprehensive survey on this topic.

As a seminal work of strategic quality choice in avertical channel, Reyniers and Tapiero [21] highlighted theimportance of strategic and contractual issues in supply chainquality management. Tsay and Agrawal [22] investigateda distribution system in which a manufacturer supplies acommon product to two independent retailers, who in turnuse both service and retail price to directly compete for endcustomers. The authors derived the closed-loop equilibriumsolution of retailers’ price and service and then characterisedthe structure of wholesale pricing mechanisms to coordinatethe system. Xiao and Yang [23] extended this model totwo competing supply chains and considered the effect ofuncertain demand and the risk attitude of the players. Xu [24]investigated a joint pricing and product quality decision ina manufacturer-retailer channel, in which the manufacturersells a product through the retailer. Other related literature onthis topic includes Balasubramanian and Bhardwaj [25], Lu etal. [26], Xie et al. [27], and Xie et al. [28]. In these studies, theinformation related to quality level is assumed to be symmet-ric among supply chain members. A number of researchersrecognised that asymmetric quality-related information, suchas quality level and quality cost, could be vital to qualitychoice for supply chain players and developed many con-tractual agreements for mitigating the impact of asymmetricquality information [6, 29]. However, these studies did notinvestigate the effects of vertical quality cooperation orhorizontal quality competition on product quality.

The second stream related to our paper is that of qualityimprovement mechanisms and associated contract issues.Benjaafar et al. [11] developed two approaches (supplierallocation and supplier selection) to allocate fixed demand toelicit service quality from the suppliers.They concluded that abuyer could indeed orchestrate competition among potentialsuppliers to promote service quality. Jin and Ryan [30]extended themodel into the framework of supplier’s price andservice competition; however, the authors only consideredsupplier allocation. Chen and Deng [31] introduced a certi-fication mechanism to improve supplier quality consideringasymmetric quality information. They showed that a deter-ministic certification may lead to underinvestment in qualityimprovement technology for efficient suppliers, whereas anoisy certification may alleviate this underinvestment prob-lem. Yan [32] studied contract efficiency for a decentralisedsupply chain in the presence of quality improvements. Usinga numerical experiment, the author also showed that a qualityeffort-sharing contract could be effective for improving prod-uct quality. Other examples includeChing et al. [33] andElahi[14]. Although these studies address the competition andcooperation mechanism for improving supplier quality, theydid not demonstrate which strategy would be more effective.Zhu et al. [34] considered cases in which both a buyer anda supplier invest in quality improvement. They showed thatthe buyer’s involvement in quality investments can have asignificant impact; in addition, they investigated the effect ofsupplier competition on quality improvement. However, theydid not provide an answer for the question of which strategyis better for quality improvement when focused on quality

investment decisions as well as its effects on the buyer’s orderquantity and the supplier’s production lot size.

The third stream related to our paper is that of suppliercompetition under the framework of outsourcing mode.Thisliterature focused either on price competition ([1, 35, 36], etc.)or on product competition [11]. None of them consider thecase of suppliers’ competitions both on price and on productquality. Jiang [37] considered a setting in which a manufac-turer sequentially sources two components and uses reverseauction to select a supplier with the lowest bidding price foreach component. However, the author did not investigate theeffects of sourcing strategies on suppliers’ decisions and theproduct quality decisions are not considered. Nagarajan andBassok [38] examine a decentralised supply chain in whicha single assembler buys complementary components from 𝑛

suppliers and assembles the final product in anticipation ofdemand. The authors employed the Nash bargain techniqueto investigate the effects of suppliers’ cooperative coalition onthe manufacturer’s performance. The paper also neglects theimpacts of different sourcing strategies.

Recently, many scholars investigated firm product qual-ity-related sourcing decisions. Hsieh and Kuo [15] modelleda service provision game between two vendors under sym-metric and asymmetric cost structures with the objective ofwinning the larger share of the buyer’s fixed reward. Lee andLi [7] studied three different strategies that a buyer coulduse to manage supplier quality: cooperation, incentivisation,and inspection. Xiao et al. [3] employed Hotelling’s model tocharacterise the strategic outsourcing decisions of two com-peting manufacturers whose key components have qualityimprovement opportunities. Jin et al. [39] integrated supplierqualification into the manufacturer’s sourcing decision anddeveloped a dual-sourcing process model. Yim [40] derived aclosed-form characterisation of the optimal quota allocationfor the latent defect-undependable product-external failurein single and multiple sourcing. These articles mainly inte-grated product quality into sourcing decisions; they also anal-yse the optimal (equilibrium) decisionwhen a buyerwishes tooutsource a single product but does not consider multiprod-uct sourcing.

Our paper differs from the above studies in that (1) weconsider amanufacturer that outsources two substitute prod-ucts and develop a game model to describe strategic inter-actions among supply chain players; (2) we integrate qualitychoice into sourcing decisions; and (3) we compare single anddual sourcing in terms of quality level and profits. Moreover,we also investigate the effects of vertical cooperation andhorizontal competition on product quality and profits.

3. Model Development

We consider a sourcing system in which a monopolisticmanufacturer seeks to outsource the provisioning of twosubstitute products to external suppliers. In purchasing ahigh-quality product, themanufacturer can choose a strategyamong three alternatives. We label these strategies separatelyas the traditional strategy (T-strategy), cooperation strategy(C-strategy), and competition strategy (D-strategy). Withthe T-strategy, the manufacturer sources two products from


a single supplier; however, with the cooperating strategy,the manufacturer partially shares the single supplier’s qualityinvestment expenses for improving quality. With the D-strategy, the manufacturer purchases substitute productsfrom two individual suppliers. The first two strategies aresingle-sourcing strategies, whereas the third strategy is adual-sourcing strategy. In addition, we consider that supplierscan cooperate or not cooperate on quality decisions when themanufacturer uses a dual-sourcing strategy, as discussed inSection 5. This paper will model the strategic interactions ofsupply chain players for each decision scenario. For a betterunderstanding of these models, we first summarise the basicnotations of this paper in the Notations section.

For the Notations section, 𝑃𝑖, 𝑊𝑖, and 𝑋

𝑖are decision

variables. Other related parameters are exogenous, whichmeans that they are known to all supply chain members.

3.1. Demand Structure. In this paper, we characterise eachproduct’s demand by employing the Bertrand-style model,which has precedent in previous studies, such as Ingene andParry [41], Liu et al. [42], and Zhang et al. [43]. We proposethe demand function of product 𝑖 in the following equation:

𝑄𝑖(𝑃𝑖, 𝑃𝑗, 𝑋𝑖, 𝑋𝑗)

=

𝐴𝑖+ 𝑘𝑋𝑖− 𝜃 (𝐴

𝑗+ 𝑘𝑋𝑗) − 𝑃𝑖+ 𝜃𝑃𝑗

1 − 𝜃2

.

(1)

The demand function shown in the above equationcaptures both product substitutability and the impact ofquality effort. Equation (1) indicates that the manufacturerhas an incentive to improve product quality because itcould obtain more customer demand through investing inquality enhancement. However, improving product quality isnot without cost. Hence, given the manufacturer’s sourcingstrategy, each supplier should trade off the cost and benefitsof quality improvement and then optimally select the qualityeffort level. To facilitate our analyses, we further assume thatproduct 𝑖’s quality investment cost function isΘ

𝑖𝑋

2𝑖withΘ

𝑖>

0, that is, improving the quality level has an increasing incre-mental cost at high levels, which yields a diminishing returnon the quality expenditure. This relationship is commonlyobserved in the extant literature [10, 18, 22, 26, 32].

3.2. Sequence of Events. We model the strategic interactionsof vertical members in the outsourced supply chain as a four-stage noncooperative game, as shown in Figure 1.

Given the sourcing strategy, Figure 1 illustrates a standardsupplier-Stackelberg game process, that is, the supplier firstsets the quality level and wholesale price for each product,and themanufacturer responds and establishes each product’ssales price after observing the supplier’s choice. If the dual-sourcing mode is selected at stage 1, there are two indepen-dent suppliers that simultaneously set the product quality andwholesale price. This decision structure is commonly usedin the literature of channel prices and quality decisions [28,42, 44, 45].

In an outsourcing mode, one can expect that the OEMalways has full power on the choice of the product quality,whereas we consider that the CM is in charge of settingthe quality for the manufactured products. We suggest thisassumption given the fact that contract manufacturers (CMs)have grown rapidly in many industries and often achievedsome degree of power over OEMs [46]. For example, Kayaand Ozer [6] noted that several CMs in the pharmaceuticalsindustry have been undertaking research and development,creating a $30 billion drug-development and manufacturingmarket. These facts provide some rational explanations forthe assumption that the CM optimally chooses the productquality, which has also been studied in the literature [6, 11, 30].

4. Single-Sourcing Strategy

Wefirst investigate the case inwhich themanufacturer selectsthe single-sourcing strategy at stage 1, that is, the C- andT-strategies will be analysed in this section. The C-strategyimplies that the manufacturer proportionally shares thesupplier quality investment under the single-sourcing config-uration. We assume that the manufacturer’s share of qualityinvestment of product 𝑖 is 𝜏

𝑖, where 0 ≤ 𝜏

𝑖< 1. The case of

𝜏𝑖= 0means that all quality investment expenses are defrayed

by the supplier, that is, the T-strategy. Hence, the equilibriumoutcomes of the T-strategy can be derived by setting 𝜏

𝑖= 0 in

the equilibrium of the C-strategy.According to (1) and the quality investment function,

we derive the supply chain member’s profit function of thesingle-sourcing case as

Π𝑚=

2

∑

𝑖=1,𝑗 ̸=𝑖

[(𝑃𝑖−𝑊𝑖)

⋅ (



1 − 𝜃2

) − 𝜏𝑖Θ𝑖𝑋2

𝑖]

− 𝑓𝑆,

(2)

Π𝑠=

2

∑

𝑖=1,𝑗 ̸=𝑖

[𝑊𝑖(



1 − 𝜃2

)

− (1 − 𝜏𝑖)Θ𝑖𝑋2

𝑖] .

(3)

From (3), this paper assumes that the unit production cost ofeach product is zero, which is commonly used in the relatedliterature [25, 47]. Relaxing this assumption will not changeour main results or the models’ managerial insights.

Based on the players’ payoff functions shown in (2) and(3), we solve this dynamic gamemodel by using the backwardinduction approach and derive the following proposition.

Proposition 1. For the C-strategy case, if 8(1 − 𝜏𝑖)Θ𝑖(1 − 𝜃) ≥

𝑘2, the equilibrium quality level of product 𝑖 is


Table 1: Equilibrium outcomes of the single-sourcing strategy.

Item Equilibrium outcome

Quality level 𝑋C∗𝑖

=

𝑘 {𝐴𝑖[8 (1 − 𝜏

𝑗)Θ𝑗− 𝑘2] − 8𝜃𝐴

𝑗(1 − 𝜏

𝑗)Θ𝑗}

𝑘4− 8𝑘2[(1 − 𝜏

𝑖)Θ𝑖+ (1 − 𝜏

𝑗)Θ𝑗] + 64 (1 − 𝜃

2) (1 − 𝜏

𝑖)Θ𝑖(1 − 𝜏

𝑗)Θ𝑗

Wholesale price 𝑊C∗𝑖

=

64 (1 − 𝜃2) 𝐴𝑖(1 − 𝜏


𝑗)Θ𝑗− 8𝑘2[𝐴𝑖(1 − 𝜏

𝑖)Θ𝑖+ 𝜃𝐴𝑗(1 − 𝜏

𝑗)Θ𝑗]

2 {𝑘4− 8𝑘2[(1 − 𝜏

𝑖)Θ𝑖+ (1 − 𝜏

𝑗)Θ𝑗] + 64 (1 − 𝜃

2) (1 − 𝜏


𝑗)Θ𝑗}

Sales price 𝑃C∗𝑖

=

6 {8 (1 − 𝜃2) 𝐴𝑖(1 − 𝜏


𝑗)Θ𝑗− 𝑘2[𝐴𝑖(1 − 𝜏

𝑖)Θ𝑖+ 𝜃𝐴𝑗(1 − 𝜏

𝑗)Θ𝑗]}

𝑘4− 8𝑘2[(1 − 𝜏

𝑖)Θ𝑖+ (1 − 𝜏

𝑗)Θ𝑗] + 64 (1 − 𝜃

2) (1 − 𝜏


𝑗)Θ𝑗

Demand quantity 𝑄C∗𝑖

=

2 (1 − 𝜏𝑖)Θ𝑖[8 (𝐴

𝑖− 𝜃𝐴𝑗) (1 − 𝜏

𝑗)Θ𝑗− 𝐴𝑖𝑘2]

𝑘4− 8𝑘2[(1 − 𝜏

𝑖)Θ𝑖+ (1 − 𝜏

𝑗)Θ𝑗] + 64 (1 − 𝜃

2) (1 − 𝜏


𝑗)Θ𝑗

Manufacturer’s profit ΠC∗𝑚

=

2

∑

𝑖=1

[(𝑃C∗𝑖

−𝑊C∗𝑖

)𝑄C∗𝑖

− 𝜏𝑖Θ𝑖(𝑋

C∗𝑖

)

2

] − 𝑓𝑠

Supplier’s profit ΠC∗s =

2

∑

𝑖=1

[𝑊C∗𝑖

𝑄

C∗𝑖

− (1 − 𝜏𝑖)Θ𝑖(𝑋

C∗𝑖

)

2

]

The manufacturer selects a proper sourcing strategy

Step 1

The supplier(s)optimally set(s)

quality levels

Step 2

The supplier(s)optimally set(s)wholesale prices

Step 3

The manufacturer optimally sets sales

prices

Step 4

Demands are satisfied

Figure 1: Sequence of decision events.

𝑋𝐶∗

𝑖=

𝑘 {𝐴𝑖[8 (1 − 𝜏

𝑗)Θ𝑗− 𝑘2] − 8𝜃𝐴

𝑗(1 − 𝜏

𝑗)Θ𝑗}

𝑘4− 8𝑘2[(1 − 𝜏

𝑖)Θ𝑖+ (1 − 𝜏

𝑗)Θ𝑗] + 64 (1 − 𝜃

2) (1 − 𝜏

𝑖) (1 − 𝜏

𝑗)Θ𝑖Θ𝑗

. (4)

In (4), the superscript C∗ denotes the optimal value forthe C-strategy case. We present all proofs in the Appendix.Substituting the equilibrium product quality level into theother decision variables and the payoffs, we derive allequilibrium outcomes of this strategy, as shown in Table 1.Moreover, the equilibrium outcomes of the T-strategy canbe derived by setting the proportion coefficient 𝜏

𝑖to zero

and substituting it into the second column of Table 1. Theconditions that guarantee the equilibrium can be derivedby the same approach, that is, substituting 𝜏

𝑖= 0 into the

condition 8(1 − 𝜏𝑖)Θ𝑖(1 − 𝜃

2) ≥ 𝑘2.

The outcomes shown in Table 1 are not sufficiently simpleto establish the effects of key parameters. Fortunately, wecan investigate the effect of each parameter by imposingsimplifying conditions on the remaining parameters, as isthe extant literature [22, 26]. Corollaries 2 and 3 summarisethe impacts of the market base, unit quality investment,and coefficient of the proportion of the quality investment

share on the equilibrium outcomes under the single-sourcingsetting.

Corollary 2. For the C-strategy case, the comparison resultsof the equilibrium outcomes with regard to the asymmetricparameters are shown in Table 2.

Corollary 3. For the C-strategy case, the effects ofmarket base,unit quality investment, and coefficient of the proportion ofthe quality investment share on the equilibrium outcomes areshown in Table 3.

5. Dual-Sourcing Strategy

Supplier competition could be used as a mechanism for elic-iting quality improvement in a decentralised supply chain [11,14, 48]. Amanufacturer may enable product quality improve-ments by choosing the dual-sourcing strategy to outsource


Table 2: Comparison results for the single-sourcing model when the parameters are asymmetric.

Case Quality level Wholesale price Sales price Demand quantityΘ𝑖= Θ𝑗, 𝜏𝑖= 𝜏𝑗, 𝐴𝑖> 𝐴𝑗

𝑋C∗𝑖

> 𝑋C∗𝑗

𝑊C∗𝑖

> 𝑊C∗𝑗

𝑃C∗𝑖

> 𝑃C∗𝑗

𝑄C∗𝑖

> 𝑄C∗𝑗

𝐴𝑖= 𝐴𝑗, 𝜏𝑖= 𝜏𝑗, Θ𝑖> Θ𝑗

𝑋C∗𝑖

< 𝑋C∗𝑗

𝑊C∗𝑖

< 𝑊C∗𝑗

𝑃C∗𝑖

< 𝑃C∗𝑗

𝑄C∗𝑖

< 𝑄C∗𝑗

𝐴𝑖= 𝐴𝑗, Θ𝑖= Θ𝑗, 𝜏𝑖> 𝜏𝑗

𝑋C∗𝑖

> 𝑋C∗𝑗

𝑊C∗𝑖

> 𝑊C∗𝑗

𝑃C∗𝑖

> 𝑃C∗𝑗

𝑄C∗𝑖

> 𝑄C∗𝑗

Table 3: Effect of key parameters on the equilibrium outcomes in the single-sourcing case.

𝑋C∗𝑖

𝑊C∗𝑖

𝑃C∗𝑖

𝑄C∗𝑖

ΠC∗𝑚

ΠC∗𝑠

Case 1 Θ𝑖= Θ𝑗= Θ, 𝜏

𝑖= 𝜏𝑗= 𝜏

𝐴𝑖

≥0 ≥0 ≥0 ≥0 ≥0 for𝑀1𝑖≥ 0

≥0≤0 for𝑀1

𝑖≤ 0

𝐴𝑗 ≤0 ≤0 ≤0 ≤0 ≥0 for𝑀1

𝑗≥ 0 ≥0 for 𝑆1

𝑗≥ 0

≤0 for𝑀1𝑗≤ 0 ≤0 for 𝑆1

𝑗≤ 0

Case 2 𝐴𝑖= 𝐴𝑗= 𝐴, 𝜏

𝑖= 𝜏𝑗= 𝜏

Θ𝑖

≤0 ≤0 ≤0 ≤0 ≥0 for𝑀2𝑖≥ 0

≤0≤0 for𝑀2

𝑖≤ 0

Θ𝑗 ≥0 ≥0 ≥0 ≥0 ≥0 for𝑀2

𝑗≥ 0

≤0≤0 for𝑀2

𝑗≤ 0

Case 3 𝐴𝑖= 𝐴𝑗= 𝐴, Θ

𝑖= Θ𝑗= Θ

𝜏𝑖

≥0 ≥0 ≥0 ≥0 ≥0 for𝑀3𝑖≥ 0

≥0≤0 for𝑀3

𝑖≤ 0

𝜏𝑗 ≤0 ≤0 ≤0 ≤0 ≥0 for𝑀3

𝑗≥ 0

≥0≤0 for𝑀3

𝑗≤ 0

Note: definitions of notations𝑀1𝑖,𝑀2𝑖,𝑀3𝑖, and 𝑆1

𝑗are presented in online supplements.

the provisioning of two substitute products to two externalsuppliers, that is, the D-strategy is selected at stage 1 of thefour-stage noncooperative game process (see Figure 1). Theendogenous demand function of (1) means that each prod-uct’s demand is not solely dependent on price but is also rel-ative to product quality; this creates challenges for verifyingthe dual-sourcing strategy’s quality improvement advantageand causes our studies to differ from the extant literature,such as Benjaafar et al. [11], Jin and Ryan [30], and Elahi [14].Those authors considered customer demand as fixed and notaffected by product price and quality.

In practice, different suppliers are often employed toman-ufacture substitute products in business practices. For exam-ple, in mainland China, most iPads are assembled at Fox-conn’s factory, whereas themore inexpensive iPadmini prod-uct orders are allocated to Pegatron, Inc. [16]. To investigatewhether the dual-sourcing strategy benefits quality improve-ment, we consider two types of decision structures for thequality decision stage: centralised and decentralised qualitydecisions. For centralised decisions, two suppliers jointlydecide their product’s quality level; however, for decentraliseddecisions, they simultaneously choose the quality level tomaximise their own profits. For expositional simplicity, welabel the former as the DC-strategy and the latter as the DD-strategy.

5.1. Centralised Quality Decision. This case considers thesituation in which two suppliers cooperatively select eachproduct’s quality level after they observe the upstream firm’s

dual-sourcing strategy. The decision structure implies that𝑋𝑖and 𝑋

𝑗are jointly set to maximise Π

𝑖+ Π𝑗. We first

characterise each supply chain entity’s payoff function asfollows:

Π𝑚=

2

∑

𝑖=1,𝑗 ̸=𝑖

[(𝑃𝑖−𝑊𝑖)

⋅ (



1 − 𝜃2

)] − 𝑓𝐷,

Π𝑖= 𝑊𝑖[



1 − 𝜃2

]

− Θ𝑖𝑋2

𝑖.

(5)

By using the backward induction approach, we derive thefollowing.

Proposition 4. For the DC-strategy case, if

𝑘2(4 − 3𝜃

2+ 𝜃4) ≤ 2 (1 − 𝜃

2) (4 − 𝜃

2)

2

Θ𝑖,

2𝑘2(4 − 3𝜃

2+ 𝜃4) (Θ𝑖+ Θ𝑗)

≤ 𝑘4(1 − 𝜃

2) + 4 (1 − 𝜃

2) (4 − 𝜃

2)

2

Θ𝑖Θ𝑗,

(6)


then the equilibrium quality level of product 𝑖 is

𝑋𝐷𝐶∗

𝑖=

2𝑘 (4 − 3𝜃2+ 𝜃4)𝐴𝑖Θ𝑗− 4𝑘𝜃 (2 − 𝜃

2)𝐴𝑗Θ𝑗− 𝑘3(1 − 𝜃

2)𝐴𝑖

𝑘4(1 − 𝜃

2) − 2𝑘

2(4 − 3𝜃

2+ 𝜃4) (Θ𝑖+ Θ𝑗) + 4 (1 − 𝜃

2) (4 − 𝜃

2)2Θ𝑖Θ𝑗

. (7)

In (7), the superscript DC∗ denotes the optimal value ofthe DC-strategy case.The other equilibrium outcomes of thisstrategy are provided in Table 4.

5.2. Decentralised Quality Decision. In this case, two sup-pliers noncooperatively set the product quality level at thesecond stage, that is, 𝑋

𝑖is set to maximise Π

𝑖. The fol-

lowing proposition is obtained from the payoff functionsin (5).

Proposition 5. For the DD-strategy case, if

𝑘2(2 − 𝜃

2)

2

≤ 2 (1 − 𝜃2) (4 − 𝜃

2)

2

Θ𝑖,

2𝑘2(2 − 𝜃

2)

2

(4 − 𝜃2) (Θ𝑖+ Θ𝑗)

≤ 𝑘4(2 − 𝜃

2)

2

+ 4 (1 − 𝜃2) (4 − 𝜃

2)

3

Θ𝑖Θ𝑗,

(8)

then the equilibrium quality level of product 𝑖 is

𝑋𝐷𝐷∗

𝑖=

𝑘 (2 − 𝜃2) [2 (2 − 𝜃

2) (4 − 𝜃

2)𝐴𝑖Θ𝑗− 𝑘2(2 − 𝜃

2)𝐴𝑖− 2𝜃 (4 − 𝜃

2)𝐴𝑗Θ𝑗]

𝑘4(2 − 𝜃

2)2− 2𝑘2(2 − 𝜃

2)2(4 − 𝜃

2) (Θ𝑖+ Θ𝑗) + 4 (1 − 𝜃

2) (4 − 𝜃

2)3Θ𝑖Θ𝑗

. (9)

In (9), the superscript DD∗ denotes the optimal value ofthe DD-strategy case.The other equilibrium outcomes of thisstrategy are provided in Table 4.

5.3. Effects of the Key Parameters. To examine the effects ofthe various parameters, such as market base and unit qualityinvestment, we first compare the equilibrium outcomes withthe asymmetric setting on the related parameters. We derivethe following corollary based on the analytical solutions inTable 4.

Corollary 6. For the DC- and DD-strategy cases, the com-parison results of the equilibrium outcomes with regard to theasymmetric parameters are as shown in Table 5.

Corollary 7. For the DC- and DD-strategy cases, the effects ofthemarket base and unit quality investment on the equilibriumoutcomes are shown in Table 6.

6. Which Sourcing Strategy Is MoreEffective for the Manufacturer?

We now begin the analysis of the choice of strategy in thefirst stage, that is, which sourcing strategy will be selectedby the manufacturer. There are two quality decision channelstructures for the dual sourcing.Therefore, we must compareeach pair of equilibriumoutcomes for the above four decisioncases. To facilitate our analysis, we assume that two substituteproducts are identical in the market base, unit quality invest-ment, andmanufacturer’s investment sharing and then define𝐴𝑖= 𝐴𝑗= 𝐴, Θ

𝑖= Θ𝑗= Θ, and 𝜏

𝑖= 𝜏𝑗= 𝜏. This assumption

could allow this paper to focus on the comparison results of

the sourcing strategy choice. In the interim, this assumptionwill facilitate our computation. Furthermore, we performthe comparison based on two performance aspects: productquality level and manufacturer’s profit.

6.1. A Manufacturer Who Pursues Quality Level. This caseprimarily investigates which strategy is more effective interms of quality improvement. To answer this question,we must compare each equilibrium quality level, whichwas established in the aforementioned discussion. Formally,Proposition 8 provides the preferable sourcing strategy withrespect to quality level.

Proposition 8. Assume that 𝐴𝑖= 𝐴𝑗= 𝐴, Θ

𝑖= Θ𝑗= Θ,

and 𝜏𝑖= 𝜏𝑗= 𝜏; there exists a unique threshold value 𝜏

0for the

manufacturer’s sharing of its supplier’s quality investment suchthat when 0 ≤ 𝜏 < 𝜏

0, 𝑋𝐷𝐷∗𝑖

> 𝑋𝐶∗

𝑖≥ 𝑋𝑇∗

𝑖> 𝑋𝐷𝐶∗

𝑖(the

equality is satisfied if and only if 𝜏 = 0) and when 𝜏0≤ 𝜏 < 1,

𝑋𝐶∗

𝑖≥ 𝑋𝐷𝐷∗

𝑖> 𝑋𝑇∗

𝑖> 𝑋𝐷𝐶∗

𝑖(the equality is satisfied if and

only if 𝜏 = 𝜏0). The threshold value is defined as

𝜏0=

𝜃 [4 − 𝜃 (2 + 𝜃)]

4 (2 − 𝜃2)

. (10)

The above proposition implies that if the manufactureris willing to share a sufficiently large quality investment, itwill prefer to cooperate with a single supplier. However, if themanufacturer’s quality investment share is smaller than thethreshold value 𝜏

0, it will prefer to develop two competing

suppliers. We illustrate this result in Figure 2. Based on theparameters in this illustration, if 0 ≤ 𝜏 < 𝜏

0= 0.1964,𝑋DD∗

𝑖>

𝑋C∗𝑖, whereas if 0.1964 = 𝜏

0≤ 𝜏 < 1, then 𝑋

C∗𝑖

≥ 𝑋DD∗𝑖


Table4:Eq

uilib

rium

outcom

esin

thed

ual-sou

rcingcase.

Centralise

dqu

ality

decisio

n(D

C-str

ategy)

Decentralise

dqu

ality

decisio

n(D

D-strategy)

Qualitylevel

𝑋DC∗𝑖=

2𝑘(4−3𝜃2

+𝜃4

)𝐴𝑖Θ𝑗−4𝑘𝜃(2−𝜃2

)𝐴𝑗Θ𝑗−𝑘3

(1−𝜃2

)𝐴𝑖

𝑘4(1−𝜃2)−2𝑘2(4−3𝜃2+𝜃4)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)2

Θ𝑖Θ𝑗

𝑋DD∗

𝑖=

𝑘(2−𝜃2

)[2(2−𝜃2

)(4−𝜃2

)𝐴𝑖Θ𝑗−𝑘2

(2−𝜃2

)𝐴𝑖−2𝜃(4−𝜃2

)𝐴𝑗Θ𝑗]

𝑘4(2−𝜃2)2

−2𝑘2(2−𝜃2)2

(4−𝜃2)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)3

Θ𝑖Θ𝑗

Who

lesaleprice

𝑊DC∗𝑖=

2(1−𝜃2

)[2(2−𝜃2

)(4−𝜃2

)𝐴𝑖Θ𝑖Θ𝑗−𝑘2

(2−𝜃2

)𝐴𝑖Θ𝑖−2𝜃(4−𝜃2

)𝐴𝑗Θ𝑖Θ𝑗−𝑘2

𝜃𝐴𝑗Θ𝑗]

𝑘4(1−𝜃2)−2𝑘2(4−3𝜃2+𝜃4)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)2

Θ𝑖Θ𝑗

𝑊DD∗

𝑖=

2(1−𝜃2

)(4−𝜃2

)Θ𝑖[2(2−𝜃2

)(4−𝜃2

)𝐴𝑖Θ𝑗−2𝜃(4−𝜃2

)𝐴𝑗Θ𝑗−𝑘2

(2−𝜃2

)𝐴𝑖]

𝑘4(2−𝜃2)2

−2𝑘2(2−𝜃2)2

(4−𝜃2)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)3

Θ𝑖Θ𝑗

Salesp

rice

𝑃DC∗𝑖=

2(4−5𝜃2

+𝜃4

)[2(3−𝜃2

)𝐴𝑖−𝜃𝐴𝑗]Θ𝑖Θ𝑗−2𝑘2

(3−3𝜃2

+𝜃4

)𝐴𝑖Θ𝑖−𝑘2

𝜃(5−3𝜃2

)𝐴𝑗Θ𝑗

𝑘4(1−𝜃2)−2𝑘2(4−3𝜃2+𝜃4)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)2

Θ𝑖Θ𝑗

𝑃DD∗

𝑖=

(4−𝜃2

){2(4−5𝜃2

+𝜃4

)[2(3−𝜃2

)𝐴𝑖−𝜃𝐴𝑗]Θ𝑖Θ𝑗−𝑘2

[(6−7𝜃2

+2𝜃4

)𝐴𝑖Θ𝑖+𝜃(2−𝜃2

)]𝐴𝑗Θ𝑗}

𝑘4(2−𝜃2)2

−2𝑘2(2−𝜃2)2

(4−𝜃2)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)3

Θ𝑖Θ𝑗

Dem

andqu

antity

𝑄DC∗𝑖=

2(2−𝜃2

)(4−𝜃2

)𝐴𝑖Θ𝑖Θ𝑗−𝑘2

[(2−𝜃2

)𝐴𝑖Θ𝑖+𝜃𝐴𝑗Θ𝑗]−2𝜃(4−𝜃2

)𝐴𝑗Θ𝑖Θ𝑗

𝑘4(1−𝜃2)−2𝑘2(4−3𝜃2+𝜃4)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)2

Θ𝑖Θ𝑗

𝑄DD∗

𝑖=

(4−𝜃2

)Θ𝑖[2(2−𝜃2

)(4−𝜃2

)𝐴𝑖Θ𝑗−𝑘2

(2−𝜃2

)𝐴𝑖−2𝜃(4−𝜃2

)𝐴𝑗Θ𝑗]

𝑘4(2−𝜃2)2

−2𝑘2(2−𝜃2)2

(4−𝜃2)(Θ𝑖+Θ𝑗)+4(1−𝜃2)(4−𝜃2)3

Θ𝑖Θ𝑗

Manufacturer’s

profi

tΠ

DC∗𝑚=

2

∑ 𝑖=1

[(𝑃DC∗𝑖−𝑊

DC∗𝑖)𝑄

DC∗𝑖]−𝑓𝐷

ΠDD∗

𝑚=

2

∑ 𝑖=1

[(𝑃DD∗

𝑖−𝑊

DD∗

𝑖)𝑄

DD∗

𝑖]−𝑓𝐷

Supp

lier’s

profi

tΠ

DC∗𝑖=𝑊

DC∗𝑖𝑄

DC∗𝑖−Θ𝑖(𝑋

DC∗𝑖)2

ΠDD∗

𝑖=𝑊

DD∗

𝑖𝑄

DD∗

𝑖−Θ𝑖(𝑋

DD∗

𝑖)2


Table 5: Comparison results for the dual-sourcing model when the parameters are asymmetric.

Strategy Case Quality level Wholesale price Sales price Demand quantity Supplier’s profit

DC-strategy Θ𝑖= Θ𝑗, 𝐴𝑖> 𝐴𝑗

𝑋DC∗𝑖

> 𝑋DC∗𝑗

𝑊DC∗𝑖

> 𝑊DC∗𝑗

𝑃DC∗𝑖

> 𝑃DC∗𝑗

𝑄DC∗𝑖

> 𝑄DC∗𝑗

ΠDC∗𝑖

> ΠDC∗𝑗

𝐴𝑖= 𝐴𝑗, Θ𝑖> Θ𝑗

𝑋DC∗𝑖

< 𝑋DC∗𝑗

𝑊DC∗𝑖

< 𝑊DC∗𝑗

𝑃DC∗𝑖

< 𝑃DC∗𝑗

𝑄DC∗𝑖

< 𝑄DC∗𝑗

ΠDC∗𝑖

< ΠDC∗𝑗

DD-strategy Θ𝑖= Θ𝑗, 𝐴𝑖> 𝐴𝑗

𝑋DD∗𝑖

> 𝑋DD∗𝑗

𝑊DD∗𝑖

> 𝑊DD∗𝑗

𝑃DD∗𝑖

> 𝑃DD∗𝑗

𝑄DD∗𝑖

> 𝑄DD∗𝑗

ΠDD∗𝑖

> ΠDD∗𝑗

𝐴𝑖= 𝐴𝑗, Θ𝑖> Θ𝑗

𝑋DD∗𝑖

< 𝑋DD∗𝑗

𝑊DD∗𝑖

< 𝑊DD∗𝑗

𝑃DD∗𝑖

< 𝑃DD∗𝑗

𝑄DD∗𝑖

< 𝑄DD∗𝑗

ΠDD∗𝑖

< ΠDD∗𝑗

Table 6: Effect of key parameters on the equilibrium outcomes of the dual-sourcing case.

Strategy 𝑋DC(D)∗𝑖

𝑊DC(D)∗𝑖

𝑃DC(D)∗𝑖

𝑄DC(D)∗𝑖

ΠDC(D)∗𝑚

ΠDC(D)∗𝑖

DC-strategy

Case 1 Θ𝑖= Θ𝑗= Θ

𝐴𝑖

≥0 ≥0 ≥0 ≥0 ≥0 for𝑀4𝑖≥ 0 ≥0 for 𝑆2

𝑖≥ 0

≤0 for𝑀4𝑖≤ 0 ≤0 for 𝑆2

𝑖≤ 0

𝐴𝑗 ≤0 ≤0 ≤0 ≤0 ≥0 for𝑀4

𝑗≥ 0 ≥0 for 𝑆3

𝑗≥ 0


𝑗≤ 0

Case 2 𝐴𝑖= 𝐴𝑗= 𝐴

Θ𝑖

≤0 ≤0 ≤0 ≤0 ≥0 for𝑀5𝑖≥ 0 ≥0 for 𝑆4

𝑖≥ 0


𝑖≤ 0

Θ𝑗 ≥0 ≥0 ≥0 ≥0 ≥0 for𝑀5

𝑗≥ 0 ≥0 for 𝑆5

𝑗≥ 0


𝑗≤ 0

DD-strategy

Case 1 Θ𝑖= Θ𝑗= Θ

𝐴𝑖

≥0 ≥0 ≥0 ≥0 ≥0 for𝑀6𝑖≥ 0 ≥0 for 𝑆6

𝑖≥ 0


𝑖≤ 0

𝐴𝑗 ≤0 ≤0 ≤0 ≤0 ≥0 for𝑀6

𝑗≥ 0 ≥0 for 𝑆7

𝑖≥ 0


𝑖≤ 0

Case 2 𝐴𝑖= 𝐴𝑗= 𝐴

Θ𝑖

≤0 ≤0 ≤0 ≤0 ≥0 for𝑀7𝑖≥ 0 ≥0 for 𝑆8

𝑖≥ 0


𝑖≤ 0

Θ𝑗 ≥0 ≥0 ≥0 ≥0 ≥0 for𝑀7

𝑗≥ 0

≥0≤0 for𝑀7

𝑗≤ 0

Note: definitions of notations𝑀4𝑖,𝑀5𝑖,𝑀6𝑖,𝑀7𝑖, 𝑆2𝑖, and 𝑆4

𝑖are presented in online supplements.

Qua

lity

leve

l

22

20

18

16

14

12

10

𝜏

0.0 0.2 0.4 0.6 0.8

𝜏 = 𝜏0 XC∗i

XDD∗i

XT∗i

XDC∗i

Figure 2: Comparison results of the equilibrium quality level. Note:𝐴 = 100, Θ = 2, 𝑘 = 2, and 𝜃 = 0.5.

is observed. Moreover, the difference 𝑋C∗𝑖

− 𝑋DD∗𝑖

increaseswith increases in the manufacturer’s investment share when𝜏 ≥ 𝜏0.

The second insight observed in Proposition 8 is that thetraditional strategy is dominated by the quality cooperationstrategy. An interesting observation found in the aboveproposition is that the DC-strategy is dominated by the otherthree cases. Thus, the manufacturer should consider supplierquality collusion when it decides to outsource substituteproducts to two external suppliers. The manufacturer mayobtain products with poorer quality levels if the two supplierscooperate on quality decisions.

6.2. A Manufacturer Who Pursues Profit. We now considerwhich strategy can best service the manufacturer’s profitpursuit. By analysing the difference between each pair of themanufacturer’s equilibrium payoffs, the following proposi-tion summarises the results of which strategy ismore effectivefor increasing profit. For a better understanding of the effectof strategy choice on the profit, we assume that the fixedcost of single sourcing is zero (i.e., 𝑓𝑆 = 0), but the dual-sourcing strategy’s cost is 𝐹 > 0 (i.e., 𝑓𝐷 = 𝐹 > 0). Relaxingthis assumption cannot change our primary results and


managerial insights but does increase the computationalcomplexity. Furthermore, the fixed cost 𝐹 cannot exceed themanufacturer’s reservation profit 𝐹max (i.e., 𝐹 < 𝐹

max), whichis defined in (11). Without this constraint, the manufacturercannot derive a positive profit in the dual-sourcing case.Consider

𝐹 ≤ 𝐹max

= min{

{

{

2𝐴2(1 + 𝜃) (4 − 𝜃

2)

2

Θ2

[2 (2 − 𝜃)2(1 + 𝜃) (2 + 𝜃)Θ − 𝑘

2(2 − 𝜃

2)]

2,

2𝐴2(1 + 𝜃) (2 − 𝜃)

2Θ2

[2 (2 − 𝜃)2(1 + 𝜃)Θ − 𝑘

2(1 − 𝜃)]

2

}

}

}

=

2𝐴2(1 + 𝜃) (2 − 𝜃)

2Θ2

[2 (2 − 𝜃)2(1 + 𝜃)Θ − 𝑘

2(1 − 𝜃)]

2.

(11)

Proposition 9. Assume that 𝐴𝑖= 𝐴𝑗= 𝐴,Θ

𝑖= Θ𝑗= Θ, and

𝜏𝑖= 𝜏𝑗= 𝜏; when 0 ≤ 𝜏 < 𝜏

1and 0 ≤ 𝐹 < 𝐹

1, the DD-strategy

is the dominant strategy; however, when 0 ≤ 𝜏 < 𝜏1and

𝐹1≤ 𝐹 < 𝐹

max, the C-strategy is the dominant strategy. When𝜏1≤ 𝜏 < 1 and 0 ≤ 𝐹 < 𝐹

2, the DD-strategy is the dominant

strategy; however, when 𝜏1≤ 𝜏 < 1 and 𝐹

2≤ 𝐹 < 𝐹

max, theT-strategy is the dominant strategy. The threshold values 𝜏

1, 𝐹1

and 𝐹2are defined as

𝜏1=

𝑘2[8 (1 + 𝜃)Θ − 𝑘

2]

4 (1 + 𝜃)Θ [16 (1 + 𝜃)Θ − 𝑘2]

,

𝐹1= max

{

{

{

0, −2𝐴2Θ

{

{

{

4 (1 + 𝜃) (1 − 𝜏)2Θ − 𝑘

2𝜏

[8 (1 + 𝜃) (1 − 𝜏)Θ − 𝑘2]2

−

(1 + 𝜃) (4 − 𝜃2)

2

Θ

[2 (1 + 𝜃) (2 + 𝜃) (2 − 𝜃)2Θ − 𝑘

2(2 − 𝜃

2)]

2

}

}

}

}

}

}

,

𝐹2= max

{

{

{

0, −2𝐴2(1 + 𝜃)Θ

2{

{

{

4

[8 (1 + 𝜃)Θ − 𝑘2]2

−

(4 − 𝜃2)

2

[2 (1 + 𝜃) (2 + 𝜃) (2 − 𝜃)2Θ − 𝑘

2(2 − 𝜃

2)]

2

}

}

}

}

}

}

.

(12)

The above proposition illustrates that when the fixed costof dual sourcing is sufficiently low, the manufacturer willprefer to develop two competing suppliers regardless of theinvestment share. However, when the dual-sourcing cost issufficiently high, the manufacturer will prefer to cooperatewith the single supplier when sharing a sufficiently small por-tion of the quality investment. In contrast, the manufacturerwill prefer to use the traditional strategy when the qualityinvestment share is sufficiently high. Figure 3 illustrates theseresults through a numerical example.

𝜏

0 0.05 0.1 0.15 0.2 0.25 0.3

F

1200

1190

1180

1170

1160

1150

1140

C-strategy T-strategy

DD-strategy

Figure 3: Dominant strategy of the manufacturer who pursuesprofit. Note: 𝐴 = 100, Θ = 2, 𝑘 = 2, and 𝜃 = 0.5.

In addition, the profit-pursuing manufacturer will neverchoose the dual-sourcing strategy when both suppliers coop-eratively set product quality. In conjunction with Propo-sition 8, the DC-strategy cannot be a dominant strategyin both aspects of quality level and profit. Therefore, themanufacturer should prevent supplier quality collusion whenit decides to use the dual-sourcing strategy. However, thesuppliers have incentives for quality cooperation because theycan extract more profits by producing a low-quality product(the relation Π

DC∗𝑖

> ΠDD∗𝑖

can be derived by computing thedifference of ΠDC∗

𝑖and Π

DD∗𝑖

). Therefore, in this situation,it is important to design an efficient contract to encourageimprovements in supplier quality. A quality contest amongsuppliers could be used to enable quality improvementamong suppliers; this is also established in the fixed demandmodel [11, 30]. However, with the quality-dependent demandmodel, contesting for demand may not be applicable becausethe equilibrium solution cannot be derived or, at a minimum,cannot prove the existence and uniqueness; thus, the effect ofthismechanism on quality level will be unclear.Themanufac-turer can design a quality contest among suppliers to strive fora fixed quality investment subsidy. However, this problem isnot the main focus of this study; thus, we would encourageresearchers to devote additional attention to this issue inthe future.

6.3. Summary. Propositions 8 and 9 summarise the results ofwhich strategy is more effective for product quality andman-ufacturer profit, respectively. We now consider whether thereis a sourcing strategy that benefits quality level in additionto manufacturer’s profit. First, the T- and DC-strategies areexcluded because the former is strictly dominated by the C-strategy in the aspect of quality and the latter is the worst caseof the four strategies in both aspects. Therefore, we considerthe C- and DD-strategy cases. The following observationprovides useful materials for answering this question.


Observation 1. Assume that 𝐴𝑖= 𝐴𝑗= 𝐴, Θ

𝑖= Θ𝑗= Θ, and

𝜏𝑖= 𝜏𝑗= 𝜏; then, we obtain the following conclusions: (i)

when the unit quality investment is neither sufficiently largenor sufficiently small, that is, Θmin

≤ Θ ≤ Θmax, the C-

strategy could be beneficial to both supplier quality improve-ment and manufacturer’s profit enhancement if and only if𝜏0≤ 𝜏 ≤ 𝜏

1and 𝐹 ≥ 𝐹

1; and (ii) when the fixed cost of dual

sourcing is sufficiently small, that is,𝐹 ≤ min(𝐹1, 𝐹2), theDD-

strategy could be beneficial to both supplier quality improve-ment and manufacturer profit enhancement if and onlyif 0 ≤ 𝜏 < 𝜏

0.

TheAppendix provides theoretical support for this obser-vation. Parameters Θmin and Θ

max can also be found in theAppendix. The following insights can be obtained from theabove observation:

(i) Quality cost information plays an important rolein implementing the strategy of cooperating with asingle supplier. Because the supplier has incentivesto hide the private quality cost information [6], themanufacturer should design a mechanism to revealthe type of supplier, with regard to quality cost, whenthe manufacturer wants to employ the C-strategy toimprove quality and profits. Moreover, ensuring thatthe quality investment share is in the appropriaterange is also important to successfully implement theC-strategy. In the interim, a relatively high sourcingcost for dual sourcing could ensure that the manufac-turer has an incentive to implement C-strategy.

(ii) When the manufacturer does not want to share ordoes not want to share a large portion of the sup-plier quality investment, developing two competingsuppliers could be the optimal strategy for improvingquality level and profit if the sourcing cost is suffi-ciently low. Moreover, if the supplier demands a largeshare of the quality investment, the manufacturer willswitch to developing two competing suppliers. In thisscenario, preventing collusion on the two suppliers’quality becomes a critical issue for the manufacturer.Otherwise, the manufacturer could migrate into theworst case if the two suppliers cooperatively set theproduct quality level.

7. Conclusions

In this paper, we examine the equilibrium quality levels oftwo substitute products in four decision scenarios belongingto two sourcing strategies: single sourcing and dual sourcing.There are two different decision scenarios for the single-sourcing strategy: the supplier optimally sets each product’squality level with and without the manufacturer’s investmentsharing. Two decision scenarios also exist for the dual-sourcing strategy: two suppliers cooperatively or noncooper-atively set product quality levels. This study employs a four-stage noncooperative game process to model the strategicinteractions among supply chain players. Given each decisionscenario, we derive the closed-loop equilibrium outcomes of

each game model and propose the conditions that guaranteethat the Nash equilibrium of each game uniquely exists.Moreover, this paper examines the effects of key parameters,such as the market base, quality cost margin, and investmentshare, on players’ decisions and the equilibrium payoffs.

Finally, we compare the equilibrium quality levels andmanufacturer’s profits of each decision scenario.The questionof which strategy is more effective for product quality ormanufacturer’s profit is resolved. By combining these results,we further demonstrate that cooperating with a single sup-plier and developing two competing suppliers could be thedominant strategy in terms of both quality level and profit.The conditions for guaranteeing the optimal strategy are alsoestablished. These results will help to effectively implementthe sourcing strategy in practice. This paper also providesvaluable insights into the quality management strategy thatleads to quality improvement and the selection of a supplychain channel structure for supply chain outsourcing.

There are several directions for future research. First, wederive the effects of the key parameters on the equilibriumoutcomes by assuming partially or completely symmetricalparameters settings. A similar assumption could be found inthe comparison results between each pair of decision scenar-ios. One possible extension is to compute these results withcomplete asymmetrical parameters. Second, we prove thatsuppliers’ quality cooperation in the dual-sourcing strategyis dominated by the other three strategies. Hence, integratingwell-known mechanisms, such as a quality contest into thevertical channel to break through suppliers’ quality collusion,could be worth investigating. Finally, we assume that thequality investment margin of each product is commonknowledge in this study. However, quality effort costs can beprivate information. Moreover, the manufacturer’s strategychoice could be dependent on quality investment unit. Thus,it is interesting but challenging to discuss sourcing strategywhen suppliers keep quality cost information private.

Notations

𝑖 = 1, 2; 𝑗 = 1, 2, and 𝑗 ̸= 𝑖: Index to denote each product𝑄𝑖: Gross demand of product 𝑖

𝐴𝑖: Market base of product 𝑖

𝜃 (0 ≤ 𝜃 < 1): Coefficient of capturing productsubstitutability

𝑘 (𝑘 > 0): Coefficient of capturing theimpact of quality level onmarket base

𝑃𝑖: Product 𝑖’s sales price

𝑋𝑖: Product 𝑖’s quality level

𝑊𝑖: Product 𝑖’s wholesale price

Θ𝑖: Unit quality investment for the

𝑖th product𝑓𝑆: Fixed configuration cost of

single-sourcing mode𝑓𝐷: Fixed configuration cost of

dual-sourcing modeΠ𝑚: Manufacturer’s profit


Π𝑠: Supplier’s profit in single-sourcing mode

Π𝑖: Supplier 𝑖’s profit in dual-sourcing mode.

Competing Interests

The author declares no competing interests.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (no. 71401082) and Research Fundfor Humanities and Social Sciences of Chinese Ministry ofEducation (no. 14YJC630009).

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