Impact of supplier technology innovation on supply chain efficiency based on revenue-sharing contract

This study constructs a two-period supply chain model consisting of two suppliers and one retailer using a revenue-sharing contract. Considering random investment cost, the impact of supplier competition on innovation strategy is analyzed and the equilibrium strategy of suppliers’ technology innovation game as well as the optimal revenue-sharing contract is derived. It is found that technology innovation degree influences supplier competition, technology innovation strategy and the form of the optimal revenue-sharing contract. Supplier innovation can improve retailer’s profit, but it may reduce supplier’s profit as well as the supply chain efficiency due to the uncertainty of investment cost and supplier competition.


INTRODUCTION
As corporation competition intensifies and market environment becomes more changeable, the importance of supply chain management keeps growing. Many companies try to optimize supply chain contract to avoid double marginal effect in the price-only contract (Lariviere and Porteus, 2001), so as to achieve supply chain coordination and improve supply chain efficiency. Revenuesharing contract is one of the supply chain coordination contracts, which has a simple form and wide application in several industries, such as automobile manufacturing industry (Foros et al., 2009), E-commerce (Chen et al., 2010), film production (Palsule-Desai, 2012), video rental (Cachon and Lariviere, 2005) etc.. When using revenuesharing contract, the supplier sells the product to the retailer with a lower wholesale price, as the retailer compensates the supplier with a certain ratio of the sales revenue. However, most studies of revenue-sharing contract assume the supplier's production technology remains unchanged, ignoring the impact of supplier technology change on revenue-sharing contract efficiency. As the speed of products upgrade quickens and the lifecycle of production technology reduces, supplier technology innovation is very common in various industries (Bartel et al., 2005).
In recent years, more and more enterprises increase their R&D investment to strengthen the cost advantage and their role in global supply chain (Nassimbeni and Sartor, 2007;Su et al., 2008). Supplier technology innovation strategy influences production cost and investment cost, which affects supply chain members' profits and the whole supply chain efficiency as well as the form of revenue-sharing contract (Bonaccorsi and Lipparini, 1994;Narayanan and Raman, 2004). What is the optimal form of a revenue-sharing contract considering supplier technology innovation? What is the impact of technology innovation on supply chain efficiency? These are the questions that have not been addressed in previous literature and are the focus of our paper.
In competing environment, the supplier needs to take into account the competitor's behavior in the process of decision making (Altug and Ryzin, 2013). In addition, new technology always has uncertain investment cost and uncertain lifecycle. However, competition and technology cost uncertainty, which has great impact on the revenuesharing contract efficiency, is not considered in existing studies. In our study, we try to analyze competing suppliers' technology innovation behavior, and further explore the impact of supplier competition and technology change degree on revenue-sharing contract efficiency considering technology cost and technology lifecycle uncertainty. Specifically, in this study we will focus on the following issues: Under a two supplier-one retailer supply chain structure, what is the optimal technology innovation strategy of two competing suppliers using revenue-sharing contract? What is the impact of technology change degree on the competition and profits of the suppliers? What is the optimal revenue-sharing contract？How does supplier technology innovation affect supply chain efficiency?

Literature Review
Under the price-only contract, supply chain is a decentralized system, where retailer makes the order decision with the target of optimizing his own profit rather than the whole supply chain. Thus, the order quantity under a decentralized supply chain is smaller than that under a centralized one, making the supply chain uncoordinated (Lariviere and Porteus, 2001). Perakis and Roels (2007) provide a quantitative analysis of the supply chain efficiency gap between price-only contract and coordinated contract under different supply chain structures. Revenue-sharing is a coordinated supply chain contract with simple form and is equivalent to many other coordinated supply chain contract. A detailed analysis can be found in Cachon and Lariviere (2005)'s study. For a multi-supplier-one-retailer supply chain structure, revenue-sharing can also achieve supply chain coordination, and increase supply chain each member's profit to obtain a Pareto optimal (Gerchak and Wang, Zuo et al. 383 2004). In a one-supplier-two-retailer supply chain, Kong et al. (2013) explore the potential of revenue-sharing contracts to facilitate information sharing in a supply chain and mitigate the negative effects of information leakage. They find out that the incentives of the supplier and retailers are better aligned under a revenue-sharing contract, as opposed to under a wholesale-price contract.
The above research assumes that supplier has a steady technology level, and gets a result that the revenuesharing parameter (the ratio of retailer's revenue to the whole product sales revenue) has no impact on the supply chain efficiency. However, how to choose an appropriate revenue-sharing parameter is of great importance for enterprises in real life (Yao et al., 2008). Palsule-Desai (2012) has found that the revenue-sharing parameter influences supply chain efficiency, and the optimal revenue-sharing parameter is a function of retailer's whole sales revenue. Technology innovation can be classified into discrete type and continuous one according to the characteristics of technology innovation process (Xu and Li, 2007). As technology change is always uncertain, thus continuous technology innovation is often characterized by a Markov process (Gjerde et al., 2002;Liu and Özer, 2009), while a discrete technology innovation is depicted by a binomial distribution (Li et al., 2003). When new technology appears in the industry, the supplier makes a decision about whether to adopt the new technology or how many products to produce using the new technology. As specialization division develops, the trend of adopting new technology from an external party becomes more significant, especially in high-tech industries such as telecommunication (Ransbotham and Mitra, 2010;Schmidt and Porteus, 2000). The adoption of new technology is often reflected by the decrease of supplier production cost. With an assumption that new production technology cuts down production cost, Schmidt and Porteus (2000) discuss how to achieve the target of becoming a technology leader in a competitive environment with the lowest cost. Kim (2000) studies the problem of optimizing an incentive mechanism of technology adoption, where the results show that supplier technology innovation can reduce manufacturer's raw material purchasing cost in a supply chain coordinated technology innovation mechanism. Wagner and Bode (2014) focus on the factors that contribute to suppliers' technology innovation through empirical study, and find that contract length and the relationship between the supplier and the retailer may affect supplier's technology innovation strategy.
In real life, suppliers often compete with each other to obtain orders from the retailer, thus to choose an appropriate supplier is an important decision for the retailer (Xia et al., 2008). Ho et al. (2010) provide a review about the research on supplier selection, which has found that supplier production cost and wholesale price are critical factors in the process of supplier selection. Suppliers are often characterized by operation performance terms of cost, delivery time, service level, or quality (Qian, 2014). In competitive circumstances, innovation is the key to the survival of enterprises and in recent ten years, to recognize a supplier with high innovation ability is an important task for the retailers (Schiele, 2006). In addition, supplier's investment on technology innovation and his innovation capability are also key factors in the retailer's supplier selection process (Petroni and Panciroli, 2002).
Although supplier technology innovation has a big impact on supply chain coordination and supply chain efficiency; so far scholars have used the assumption that supplier has unchanged production technology in their study on revenue-sharing contract. The studies on supplier technology innovation are mainly focusing on the coordination and optimization of supplier technology innovation mechanism, with few researches discussing the impact of competing suppliers' technology innovation on revenue-sharing contract. Different from the above studies, we would like to investigate the issue about how will the two factors, which are supplier competition and supplier technology innovation degree, affect the suppliers' equilibrium technology innovation strategies and the supply chain revenue-sharing contract efficiency.

Model description
Considering a two-stage supply chain model with two suppliers (supplier N and supplier S ), who have different initial production technology levels and one retailer. In each stage, the retailer places an order on one of the two suppliers. Assume in the first stage supplier N is the technology leader, who has lower unit production cost, that is N S c c  , where N c and S c are unit production cost of supplier N and supplier S in the first stage, respectively. The inverse market demand function is p a q   , where p is the product sales price of the retailer, 0 a  is the potential market demand and q is retailer's product order quantity. The sequence of event in the model is shown in Figure 1, where stands for supplier's new production technology, with a certain probability.
At the beginning of the first stage, the retailer selects his supplier and makes the order quantity decision 1 q for stage one. Retailer's supplier selection decision is shown by equation (1).  (2).

1, if supplier i adopts new technology;
If supplier adopts new production technology, the unit production cost reduces by  , where 0 N c    , and expends the corresponding investment cost K . According to supplier's technology innovation strategy, at the beginning of the second stage, the retailer chooses the supplier for the second stage and makes the order decision 2 q . Retailer's supplier selection decision for the second stage is shown by equation (3).

Supplier's technology innovation strategy
Cachon and Lariviere (2005)'s study shows that when using revenue-sharing contract, the condition of supply chain coordination is supplier i 's wholesale price i w and its unit production cost i c satisfy equation (4) as follows,   is revenue-sharing parameter (the ratio of retailer's revenue to the product's whole sales revenue). The supply chain profit allocation to the retailer and the supplier is also decided by  ; which means that the ratio of retailer's profit to the supply chain profit is also decided by  .
In the first stage, as supplier N has lower unit production cost, thus according to equation (4), supplier N 's wholesale price is lower than that of supplier S , that Thus, in the first stage, the retailer chooses supplier N , that is 1 0 y  . The first stage profit of the retailer and supplier N is shown by equations (7) and (6) as follows, is the whole sales revenue of the products. The first order derivative of   1 r q  to 1 q is shown by equation (7).
is a concave function, using the first order condition we get the retailer's optimal order quantity of the first stage . Correspondingly, we get the first stage profits of the retailer, supplier N and the whole supply chain, which are shown by equations (8) and (10).
If new production technology does not appear at the end of the first stage, that is =0  , the retailer will surely continue to choose supplier N in the second stage, that is 2 0 y  ; on the contrary, if new technology appears in the first stage, that is 0   , two suppliers will then make their technology innovation strategies, which are denoted by , and the retailer will make his second stage supplier selection decision 2 y .The following proposition shows two suppliers' equilibrium technology innovation strategies and retailer's optimal supplier selection decision of the second stage. ( , )= mixed strategy, if ; where the mixed strategy is shown by equation (12), (1,1) with probability ; (1,0) with probability 1 ; ( , )= (0,1) with probability 1 ; (0, 0) with probability 1 1 .
Retailer's corresponding second stage supplier selection decision is shown by equation Error! Reference source not found., strategies of the two suppliers are shown by equation (14), Retailer's corresponding second stage supplier selection decision is shown by Proof. Retailer's supplier selection decision and the profits of supply chain members of the second stage under different supplier technology innovation strategy combination are shown in Table 1. Two suppliers' which are discussed as follows. ( Solving equation (15)  According to suppliers' equilibrium technology innovation strategies, with the consideration of random  (17) and (19), and the supply chain two-stage efficiency is shown by equation (20).
When 0 S N c c     , the two-stage profits of the retailer, supplier N and supplier S are shown as equation (21) to equation (23), and the supply chain two-stage efficiency is shown by equation (24) (28) and (30).
When 0 S N c c     , the two-stage profits of the retailer and two suppliers also depend on investment cost, which are shown in equations (31) and (33).  (34) and (36).
From proposition 2 we find that, as supplier N 's potential competitor, under a certain condition, supplier S will replace supplier N , become the technology leader and obtain the second stage order opportunity. Therefore, a competitive environment will affect the technology leader's technology innovation strategy, and influence supply chain efficiency. For supplier N , in order to guarantee the sales opportunity of the second stage, when investment cost is bigger than revenue, he still will adopt new technology with a rather big probability. For example, when 1 2 M K M   , new technology cost is bigger than revenue, considering the competition of supplier S , supplier N still adopts new technology with probability N p . As for the retailer, supplier competition increases supplier N 's technology innovation probability, which can improve retailer's expected profit. Therefore, the aim of retailer's supplier evaluation and selection process is to intensify supplier competition so as to improve his own profit. From the above analysis, we can also find that the competition between suppliers plays a positive part in the improvement of supply chain product technology.
As competing suppliers' technology innovation behavior has impact on revenue-sharing contract efficiency, we would like to find out the optimal contract form (the optimal revenue-sharing parameter) in this circumstance so as to improve the supply chain efficiency. Proof. According to proposition 2, when technology change degree is small, revenue-sharing contract efficiency is shown as equation (37).
Take the first order derivative of sc  to  , we get the result shown as equation (38).
Thus, when technology change is small, revenue-sharing contract efficiency is a decreasing function of  and thus the optimal revenue-sharing parameter is 0 When technology change degree is big, revenue-sharing contract efficiency is shown as equation (39).
Therefore, the revenue-sharing contract efficiency sc  is a function of revenue-sharing parameter , and thus exists the optimal revenue-sharing parameter   , which can be found from the first order condition of equation (39). From corollary 3 we find that when technology change degree is small, supplier N makes a cautious and rational technology innovation decision without considering the competition of supplier S . Theoretically, to achieve the highest contract efficiency, the best revenuesharing parameter is 0    , with the aim of encouraging supplier N to adopt new technology. That explains the improvement of supplier production technology plays a critical role to the increase of supply chain efficiency. When technology change degree is big, however, revenue-sharing parameter has impact on supplier's technology innovation strategy, thus influences supply chain efficiency. In the following section, we will provide a detailed numerical analysis about the optimal revenuesharing parameter and its impact on supply chain efficiency when the technology change degree is big.

Numerical analysis
From the analysis of section 3, we find that supplier's technology innovation behavior influences revenuesharing contract efficiency. In this section, we would like to investigate the impact of new technology appearance probability, revenue-sharing parameter and potential market demand on supplier's technology innovation behavior and supply chain efficiency. As technology investment cost is uncertain, we will do the numerical analysis when  follows a uniform distribution, that is  

Impact of supplier technology innovation on supply chain members and revenue-sharing contract efficiency
The parameters in the numerical analysis are as follows, Tables 2 and 3 show the profits of supplier and retailer as well as the supply chain efficiency, using revenuesharing contract when revenue-sharing parameter is big( 0.8

 
)and small( 0.2   , respectively. We can find that supplier technology innovation is always beneficiary to the retailer, while it may decrease supplier's profit and the whole supply chain efficiency  (We obtain the same conclusion by altering the parameters several times). This is because if supplier adopts new technology, the production cost decreases. When using revenue-sharing contract, the wholesale price then also reduces and the retailer can increase market demand by cutting down the sales price of the product, thus increasing the expected profit the retailer. However, due to the supplier's irrational technology investment strategy caused by supplier competition, in some circumstances, the investment cost exceeds revenue, resulting in a lower supply chain efficiency and less supplier's expected profit.

Impact of new technology appearance probability
Impact of new technology appearance probability on revenue-sharing contract efficiency is shown in Figure 2.
As it can be seen, when technology innovation is small, competition does not exist between suppliers; therefore, technology innovation will improve supply chain efficiency, which is a function of new technology appearance probability. When technology innovation is big, impact of new technology appearance probability on revenuesharing contract efficiency is influenced by investment cost probability distribution. When investment cost follows an exponential distribution, supply chain efficiency is an increasing function of new technology appearance probability; while when investment cost follows a uniform distribution, supplier technology innovation decreases supply chain efficiency and supply chain efficiency is a decrease function of new technology appearance probability. Therefore, a small degree of technology innovation is not influenced by investment cost and can improve supply chain efficiency; on the contrary, when technology innovation degree is big, supplier competition exists and impact of supplier N 's irrational technology innovation decision on supply chain efficiency is affected by investment cost. When investment cost follows exponential distribution, new technology brings revenue that exceeds the investment cost, thus technology innovation can improve supply chain efficiency; while when investment cost follows uniform distribution, investment cost exceeds the revenue brought by the new technology, resulting in a lower supply chain efficiency.

Impact of revenue-sharing parameter
Impact of revenue-sharing parameter on revenue-sharing contract efficiency is shown in Figure 3. It can be found in the figure that revenue-sharing parameter has similar impact on supply chain efficiency under different investment cost distribution function. When technology innovation degree is relatively big, supply chain efficiency is a concave function of revenue-sharing parameter; while when technology innovation degree is small, supply chain efficiency decreases in revenue-sharing parameter. A small technology change eliminates the competition between suppliers, and from corollary 1, we find that supply chain efficiency is a decreasing function of revenue-sharing parameter. This is because when supplier competition does not exist, supplier makes a careful technology innovation strategy; thus when supplier has higher revenue, he will be more active to adopt new technology, resulting in higher supply chain efficiency.
When technology innovation degree is relatively big, competition exists between suppliers. By numerical analysis, we find that the optimal revenue-sharing parameter is in the range of   0,1    . In competing environment, in order to avoid supplier N 's irrational investment and the corresponding cost, the revenue-sharing parameter should not be set too high; meanwhile, the revenue-sharing parameter should not be too low, so as to inspire the supplier to adopt new technology. Therefore, the optimal revenue-sharing parameter   is decided by trading-off between the investment cost caused by irrational investment and the opportunity cost caused by giving up adopting new technology.

Impact of potential market demand
Impact of potential market demand on revenue-sharing contract efficiency is shown in Figure 4. As it is shown by the figure, when investment cost follows different distribution functions, the revenue-sharing contract efficiency always improves as the potential market demand increases. In addition, supplier technology innovation can improve supply chain efficiency, which also increases as technology innovation degree increases. Besides, impact of supplier technology innovation on supply chain efficiency becomes more significant as the potential market becomes larger. This shows that for different sizes of market demand, supplier technology innovation can always improve supply chain efficiency, which also increases in technology innovation degree.

Conclusion
This study analyzes the impact of competing supplier technology innovation on the revenue-sharing contract efficiency. A two supplier-one retailer two-stage supply chain model is constructed with different initial technology levels of the two suppliers. The equilibrium technology innovation strategies of two suppliers and the optimal revenue-sharing contract are analyzed. In addition, we discuss impact of new technology appearance probability, revenue-sharing parameter and potential market demand on supply chain efficiency. The results show that when technology innovation degree is big, suppliers need to trade-off between investment cost and revenue and make decision with the consideration of competition between the suppliers, which may decrease supply chain efficiency. However, when technology innovation degree is relatively small, there is no need to consider supplier competition, and technology innovation is always beneficial to supply chain efficiency. Different with the existing research, this study shows that the revenuesharing parameter affects the supply chain efficiency of revenue-sharing contract when considering supplier technology innovation and the optimal revenue-sharing parameter is influenced by the degree of technology change. Therefore, it is necessary to make an appropriate revenue allocation scheme considering different degree of technology innovation, so as to improve supply chain efficiency. It should be pointed out that we do not consider the downstream supply chain competition; thus the future studies should be on a supply chain consisting of multiple retailers and the impact of supplier technology innovation on revenue-sharing contract efficiency. In addition, the impact of technology innovation on other forms of supply chain contract, such as sales-rebate contract, buy-back contract, etc. is also a research direction worth studying.

Conflict of Interests
The author(s) have not declared any conflict of interests.

ACKNOWLEDGMENT
The work described in this paper was fully supported by the National Natural Science Foundation of China (Grant No. 71202114, 71390335 and 71372134), and the President Fund of UCAS (Y35101KY00).