1 Introduction

Collaborating to research and develop new products is becoming unavoidable in firms’ strategic decision-making, particularly in high-technology industries where digital tools used to facilitate distance collaboration. Managers generally prefer their business partners to competitors to cooperate in research and development (R&D), because a vertical relationship can exploit synergy and eliminate such conflicts arising in a horizontal relationship. However, effectively leveraging R&D efforts and innovative outputs requires careful consideration of uncertainty and opportunism in operations and productions. In practice, there remain some difficulties to overcome when trying to confirm such a long-run cooperative relationship by strategic commitments (either informal communications or formal contracts). Let us begin with two cases.

One case is a famous auto manufacturer (Denoted by F) in China and his partner (Denoted by C) in the United States. F began to cooperate with C in the 1980s. By 1986, F had developed a prototype of its new product based on a car model of C under the commitment that C would sell the complete production line to F. However, C held up the agreement when it saw a hot-selling in its domestic market. An extremely high price was proposed. But it never happened. The negotiations failed at the end of 1987 due to disagreements on the quotation price.

Another case is the cooperation between Dongfeng Motor (DFM) and Cummins Inc. that started in 1986. During their cooperation, they committed to keeping a long-term and steady partnership with each other. Importantly, they did so. More than 70% of Cummins engines (produced by their joint venture) were assembled into DFM’s trucks, and the others were assembled into the non-DFM market but not DFM’s direct competitors. In 2005, DFM and Cummins jointly established Cummins East Asia R&D Center, and they extended it in 2011. DFM accumulated not only fortune but also human resources and knowledge through the cooperation. Their R&D cooperation was not a one-man show of either Cummins or DFM; both of them participated deeply. According to BIS R&D scoreboard^[1], DFM invested 2.3% of sales into R&D in 2010 with a 101% growth over average of last 4 years, and its rank climbed to 36th within the industry worldwide, and to 1st among Chinese auto makers. In 2013, Dongfeng planned to invest $2.5 billion in R&D over the next couple of years.

The two cases above have different cooperation paths and managerial senses for NPD collaborations in supply chain management (SCM). In the first case, F encountered its partner’s holdup (a type of opportunistic behavior) due to a hot selling in the upstream (a type of uncertainty). The collaboration failed due to disagreements on the quotation price. In the second case, the upper stream (Cummins) made a commitment that the extra-chain sales of the components (i.e., engines) were limited at a certain level, uncertainty is considered in the commitment in advance. Moreover, their complementary R&D inputs significantly increased synergy, which has resisted corrosion of opportunistic behaviors.

There is seldom NPD collaboration free from challenges of opportunism^[2]. The typically uncertain nature of R&D activities makes it more difficult to disentangle non-compliance of partners from exogenous sources of failure of the R&D process and to write contracts contingent on R&D input to curb opportunism^[2]. In general, firms involved in NPD collaboration have to make some decisions carefully. For example, how can partners’ opportunism be evaluated in such a long-run uncertain circumstance? In practice, many firms strategically commit something to each other to avoid a loss brought by opportunism. Then, how do they make a credible commitment? Does a commitment really promote R&D investments and enhance supply chain performance?

In this paper, we want to answer the questions above by proposing a flexible commitment that depends on previous interactions in the framework of a supply chain consisting of a manufacturer and its supplier. The rest of the paper is organized as follows. We will review the related literature in the Section 2. The basic problem on our topic is described in Section 3, followed by a model and its analysis of the chain without any commitment in Section 3.2. We study the bounded commitment in Section 4. Finally, Section 5 concludes the paper.

2 Related Literature Review

This paper is related to three streams of existing literature.

The first stream examines vertical R&D cooperation for demand creation within a supply chain. According to ^[3], demand creation is one of the two main goals of R&D^[3]. With regard to demand creation, most research on vertical NPD collaborations addresses partnership, cooperation patterns, and complementary drivers through empirical methods, e.g., ^{[7, 8]}. ^[9] offered a systematic review of IT usage in logistics and supply chain management to achieve a competitive advantage, where in such terms as collaborative innovation, flexibility, and value creation are addressed by the researchers. However, product development is an uncertain and long lead time activity with advance investments and collaboration between firms^[10]. Regarding collaborations in product development/design, ^[11] studied firms’ investment in green product development, while ^[12] investigated product design such as final product design and quantity of new and remanufactured products, and their impact on closed-loop supply chain operations. Compared with no investment, ^[11] found that manufacturers investing in green product development is dominating in the long term. ^[13] found that both revenue sharing contract and linear quantity discount contract cannot fully coordinate the supply chain with demand disruptions. To eliminate potential risks, members in the alliance may under-invest in R&D in the absence of commitment. This phenomenon was noted by some researchers, e.g., ^{[14, 15]}.

The research on R&D collaboration within supply chains is an important but under-studied stream, although that on either cooperative R&D or SCM has made significant strides over the last two decades. Readers can see ^[16] and ^[17] for excellent reviews on SCM and R&D cooperation, respectively. Currently, the research on this stream is scattered across divergent topics and methods, e.g., ^{[5, 7, 18, 19]} etc. But the work most related to ours is ^[10], who examine two collaboration mechanisms observed in industrial practice: Sharing development costs and sharing development work. They show that the former is more attractive for new products with significant timing uncertainty, and this mechanism plays an important role in environments with uncertain product quality, similar capabilities across firms, and controllable cooperation costs.

On the basis of the above studies, this paper investigates how a certain commitment enlarges the investments in the context of R&D collaborations, focusing on firms’ strategic commitments and flexibility in R&D investments (efforts).

The second stream of the literature examines commitments and opportunism in either R&D cooperation or supply chains. It consists of two topics.

First, evidence widely indicates that opportunism often exists in inter-firm relations^{[20, 21]}. ^[22] presented the drivers of opportunism from a contracting perspective; in a subsequent study, ^[23] proposed a conceptual framework to review the determinants of opportunism. ^[24] explored opportunistic behavior of purchasing professionals in strategic supplier relationships at the individual level, focusing on triggers, manifestations and consequences. However, as ^[25] noted, opportunistic behaviour erodes all members’ long-term gains from cooperation. Moreover, ^[21] used an incomplete contracts approach to show that both anticipation and observability of opportunistic behaviour are typically not sufficient to prevent it when members can renegotiate contractual outcomes. Consequently, members of an alliance may under-invest in R&D to eliminate potential risks in the absence of commitment, a phenomenon highlighted by ^[14] and ^[15].

Second, as shown above, it is necessary for firms to make some commitments in such environment. Commitment refers to the willingness of partners to comply with the negotiated practices on behalf of the relationship^[26]. Research has also been conducted on bilateral commitment within supply chains. For example, ^[27] and ^[28] analyze order commitment as an operational strategy in supply chain management, and its mutual strategies from the partners, such as price discounts, demand forecast, etc. Along this direction, ^[29] investigated strategic commitment to a production schedule in a day-ahead electricity market, while ^[30] propose a commitment-based revenue-sharing and penalty model. ^[31] applied game theory to analyze suppliers’ participation decision, identifying Bayesian Nash equilibrium strategies and characterize advantages of firm’s commitment that may foster more innovativeness in the supply chain management. These studies investigate strategic commitments in production/operations, and show some basic and positive effects on supply chain performance.

Most of the literature above discusses supply or production contracts, with a few notable exceptions on vertical R&D collaboration. ^[14] considered a supplier’s strategic commitment on price to stimulate downstream cost-reducing innovation. ^[32] demonstrated collaboration amongst the owners of the complementary producers with sectorwide commitments can be helpful in encouraging process innovation to support lean supply chains and sustainability. However, the supplier sacrifices an important means of responding to demand uncertainty once it makes a commitment. ^[33] studied collaborative cost reduction between two partners in a supply chain and propose an expected margin commitment to encourage the supplier to participate in this obviously profitable collaboration. By comparing this arrangement with a screening contract, they find that commitment is preferred when cost reduction is large or demand variability is low. ^[34] investigated a strategic commitment under cost uncertainty, and find that it encourages both firms’ investments.

Based on the research above, we investigate commitments and efforts in demand-creating R&D when both members face uncertainty, including technological and demand uncertainty.

The third stream of the literature examines the flexibility of decision-making within supply chain. The flexibility of decision-making can often serve as an important buffer against market uncertainty or means of mitigating supply chain risks^{[35, 36]}. ^[37] investigated the role of allocation flexibility for achieving allocation flexibility against market demand uncertainty in supply chain, while ^[38] explored the value of the flexibility created by the transportation options in mitigating supply chain transportation risks. Some research focus on the effect of flexibility as an important role among the collaboration, commitment and production. ^[39] empirically examined the relationship between commitment and flexibility by analysing the benefits of commitment in terms of the integrated development of components and the flexibility provided by externally sourcing components. ^[40] extended the theory of supply chain flexibility by considering two types of flexibility, logistics flexibility and process flexibility, and examine how it is affected by such factors as demand, production, etc. It is followed by ^[41] who studied the design of process flexibility in a multiperiod production system. By investigating interactions between policy adjustments from governments and production decisions, ^[42] showed that a flexible subsidy policy is, on average, more expensive, unless there is a significant negative demand correlation across time periods. ^[43] explored the effect of supply chain flexibility and market agility and their role in SME performance, including responsiveness to customer needs and the speed of new product launches. However, the flexibility of commitments is seldom discussed in the field of vertical R&D collaborations.

In contrast to the research above, this paper will investigate how the flexibility benefit cooperation and output effectiveness within a supply chain.

3 The Basic Problem

We investigate a simple supply chain with one manufacturer (denoted by “m”) and one supplier (denoted by “s”)^[4]. They first commit some items to each other and then collaboratively invest in R&D. After this, the supplier produces and sells a new component to the manufacturer, and finally the manufacturer makes and sells a new product. More specifically, the supplier invests in R&D for a new component, and the manufacturer invests in R&D for the final product. The event sequence is described in the following and can be seen as a first look in Figure 1.

Figure 1

The event sequence of collaborative NPD with commitments

4 Bounded Commitment

The commitments are made in Stage D0. Both firms first commit their own R&D investments x˜ and y˜,simultaneously. Subsequently, the supplier commits an upper bound of wholesale price w¯,followed by the manufacturer’s commitment of the lower bound of production volume, d_.

In practice, the two firms have different half-open intervals for opportunistic behaviors, which has been verified by ^[55]. In details, the supplier commits an upper bound of the wholesale price while the manufacturer commits a lower one of the production volume. Compared with the commitment at a certain level, the bounded commitment allows the firm to justify its actions according to the circumstance. Clearly, the commitment on both the upper bound w¯and the lower bound d_not only encourages flexibility, but also restrains themselves for a return from partners. Furthermore, the supplier generally expects an elevation of d_as a return when she drops w¯.Thus, it is reasonable to assume d_reversely changes with w¯ . Consistent with Equation (3), we suppose that there is a linear relationship between w¯ and d_,in the following manner:

where b is a exogenous coefficient reflecting a comparison between bargaining powers of the manufacturer and of the supplier in negotiations. In other words, b indicates a relative bargaining power between the manufacturer and the supplier. An increase in the bargaining power of the manufacturer will bring an increase in b. Inversely, b will decrease when the bargaining power of the supplier increases. Thus, the manufacturer will make a lower commitment of his production volume when the relative bargaining power b becomes a lower value. Exploiting Nash bargaining games, the literature has studied how barging powers affect the allocation of profit, e. g., ^{[56, 57]}, and so on. Essentially, the relative bargaining power in this study directly affects the allocation of their profits in the alliance. From the perspective of supply chain management, ^[58] empirically investigate, and point out how the manufacturer margins are scaled by the factor (1 − λ)/λ where λ is the bargaining power of the downstream. The relative bargaining power b in our model is similar to the factor (1 − λ)/λ proposed by ^[58]. In particular, the equation above becomes (3) when b = 1.

Let us begin with Stage D3. Given (w¯,d_)and a realization of (ϵ, θ), the manufacturer will optimize his profit function, the same with Equation (2), under the constraint d≥d_.Thus, given x˜,y˜ and w,the optimal production is

Substituting it into Equation (4), the supplier’s expected profit is

where F(·) is the distribution function of θ. The supplier will maximize her expected profit πs(w∣x˜,y˜,w¯,ϵ),subject to w≤w¯.Note that πs(w∣x˜,y˜,w¯,ϵ)depends on F(·). Suppose that θ is uniformly distributed in [θ_,θ¯],so does ϵ in [ϵ_,ϵ¯].Furthermore, let φ¯=θ¯x˜y˜−c,φ_=θ_x˜y˜−c,δ=ϵ¯−ϵ_ and Δ=(θ¯−θ_)x˜y˜.We have the following proposition.

Theorem 1

For b ∈ [1, 3/2], there must be a ceiling of ϵ in(μ1,ϵ¯),denoted byϵ′such that it uniquely corresponds to the optimal pricew¯,which is interior and above average.

The theorem is one of our significant findings in the sense that it ensures the existence of an interior point to commit. Otherwise, the setting of the ceiling at ϵ′does not make sense for managers. We verify the existence of w˙in bounded commitment in Proposition 1. According to Proposition 1 and Theorem 1, after the supplier observes the realization of ϵ, it can determine the optimal wholesale price according to the Equations (16) and (17). In fact, due to the constraint of the lower bound of the manufacturer’s production volume, even if the supplier is facing high external market demand, it will not always increase the external chain orders, which restricts the opportunistic behavior that may occur in the supply chain.

Abbreviate πs(ϵ′∣x˜,y˜) as πs(x˜,y˜)for short, and denote the manufacturer’s expected profit by πm(x˜,y˜).Then,

πm(x~,y~)=1(θ¯−θ−)δ∫ϵ−ϵ′∫θ−θ′πm(d−∣x~,y~,w˙,θ)+∫θ′θ¯πm(d∣x~,y~,w˙,θ)dθdϵ+1(θ¯−θ−)δ∫ϵ′ϵ¯∫θ−θ′πm(d−∣x~,y~,w¯,θ)+∫θ′θπm(d˙∣x~,y~,w¯,θ)dθdϵ=x~y~Δδ∫ϵ−ϵ′∫θ−θ′θx~y~−μ2x~y~−w¯−cm2−w˙−cmμ2x~y~−w¯−cm2k dθdϵ+∫ϵ′ϵ¯∫θ−μ2θ−μ2x~y~μ2x~y~−w¯−cm2k+μ2x~y~−w¯−cm24kdθdϵ+∫ϵ′ϵ¯∫μ2θ¯θx~y~−w¯−cm24k dθdϵ+∫ϵ−ϵ′∫θ′θ¯θx~y~−w˙−cm24k dθdϵ−ρy4,

where θ′=max{θ_,μ2−(w¯−w˙)/(x˜y˜)}.

We investigate the equilibrium by numerical observations. Figure 2 shows a change in the response functions with b, in which c_s = c_m = 50, k = 1, λ = 0.1, δ = 40, ρ = 6800, b ∈ [1.2, 1.5] and θ ∼ U[240, 560]. From the figure, we find that the manufacturer’s response function changes along the arrows, whereas the supplier’s scarcely moves, meaning that coefficient b has a significant effect on the manufacturer’s response; i.e., the manufacturer exhibits a more sensitive response (with respect to b) than the supplier. However, we cannot simply state that the value of b has no effect on the supplier because it still influences the profit of the supplier through equilibrium. Through numerical analysis, we find that the existence of equilibrium just holds for a certain area of b. In other words, the equilibrium may not exist when b is extremely low or high, as shown in Figure 2 where b falls outside [1.2, 1.5] around. Moreover, the response function of the manufacturer moves upward with increase of b. From Figure 2, we can verify that the intersection of the two response functions moves towards the lower left quarter. In other words, both firms’ investments generally decrease with b. This trend can be explicitly described by Figure 3.

Figure 2

The response curves change with b when b ranges in [1.2, 1.5]

Figure 3

The shift of equilibrium with b when b ranges in [1.356, 1.446]

In the bounded commitment, the investments decrease with b. Along this direction, the firms can set b as low as possible for larger profits and investments, but this action may challenge the existence of equilibrium. All in all, coefficient b in the bounded commitment plays a significant role in affecting the investments and profits. However, there is no sufficient evidence on how to determine b and who does it. A plausible interpretation lies in the fact that b appears in the collaboration as a parameter that may be influenced by, e.g., each member’s power and techniques in negotiation. Furthermore, the bounded commitment needs a strong tie between members to achieve a suitable coefficient, b, which guarantees the existence of the equilibrium of investments. When b is larger, the greater the flexibility between the supplier’s wholesale price and the manufacturer’s production volume, it indicates that one party believes that the other party is more likely to deviate from the optimal situation without commitment (b = 1), so that they have reasons to reduce their investment level to avoid the other party take opportunistic behavior to bring more losses to themselves.

Figures 4 and 5 describe investment changes with λ:x* and y*without commitment, x˜ and y˜under the bounded commitment when b = 1.35. Furthermore, Figures 6 and 7 compare the profits in which the sub-figures amplify slight variations in πs* and πm*. Similarly x* and y*have the same trends with πs* and πm*,respectively. The numerical comparison shows the dominance of the bounded commitment. Under the bounded commitment, the R&D investment level and profits of both firms increase significantly. We can also find that the supplier benefits from an increase in λ, it means the supplier can obtain more orders outside the chain, and inversely does the manufacturer when there is no commitment. This phenomenon is intuitive because the additional order of modified components primarily benefits the supplier, but it hurts the manufacturer because of externality.

Figure 4

The supplier’s investment across different scenarios

Figure 5

The manufacturer’s investment across different scenarios

Figure 6

The supplier’s profit across different scenarios

Figure 7

The manufacturer’s profit across different scenarios

Clearly, the commitment restrains opportunistic behaviors and then ties up members for a compatible pursuit of profit. Therefore, both firms benefit from the bounded commitment, but with a stable trend in general. In Figure 6 and 7, the high volatility may be caused by our numerical method in computing equilibrium, where a discrete method is adopted to find the intersection of both firms’ response curves. However, we can still form a basic result from these figures above, that is, there is no strong sign that an increase in λ can make both firms (or either firm) better. A plausible explanation is that the bounded commitment brings a moderate flexibility and a weak constraint for members. Note that the bounded commitment coordinates the firms’ decisions only when some extreme cases appear; otherwise, it gives them freedom in decision-making.

5 Conclusions

Opportunistic behavior appears to be a result of uncertainty in R&D cooperations, impeding strategic decisions in firms. Based on the literature review, we study R&D cooperation for demand creation within a supply chain and commitments and flexibility in either supply chains or R&D cooperation, respectively. In this paper, a bounded commitment was proposed in the framework of a supply chain consisting of a manufacturer and its supplier. This was to understand if commitments promote R&D investments and enhance supply chain performance as well as how an appropriate commitment can be made without loss of flexibility. We give a half-open interval bound of commitment with more flexibility. In doing so, we first identified the firms’ decisions and incorporated a 3-stage game model (by backward induction) to examine them then later extended it to a bounded commitment where action dependent in NPD collaboration was proposed. We find that the bounded commitment can benefit both firms through bringing moderate flexibility for decision making and that commitment restrains opportunistic behaviors thus enhancing investments and increasing profits.

The main contribution of this paper is the investigation of the bounded commitment in vertical NPD collaboration with a focus on decision flexibility. R&D cooperation is a new topic appearing recently in supply chain management, though it has long been studied from the standpoint of R&D management. In the context of the interface between supply chain management and R&D cooperation, the research on flexible commitments is still in its infancy, particularly those under a demand-creative collaboration of NPD. In this paper, we verify the dominance of bounded commitments by quantitative analysis and numerical observation under a supply contract of wholesale price and a manufacturers commitment of production volume. Generally, the bounded commitment restrains opportunistic incentives, promote R&D investments, and then improve the whole supply chain performance.