Product quality selection: Contractual agreements and supplier competition in an assemble-to-order environment

Int. J. Production Economics 141 (2013) 626–638

Contents lists available at SciVerse ScienceDirect

Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Product quality selection: Contractual agreements and supplier competition in an assemble-to-order environment Mehmet Sekip Altug a,n, Garrett van Ryzin b a b

School of Business, 2201 G. Street Funger Hall George Washington University, Washington, DC 20052, United States Graduate School of Business, Columbia University, New York, NY 10027, United States

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 August 2011 Accepted 14 September 2012 Available online 9 October 2012

We consider a multi-supplier, single-manufacturer supply chain where each supplier sells a different component at varying quality levels. The manufacturer has to decide on which quality level to choose for each component, trading-off the total cost and total quality. Each supplier decides on a price per unit quality level for its component. We characterize the strategic interaction among the suppliers and analyze the inefficiencies. We find that the inefficiencies due to such quality competition can be quite significant. We then propose and analyze several mechanisms, such as quality-price schedules and revenue sharing, that restore efficiency. & 2012 Elsevier B.V. All rights reserved.

Keywords: Channel coordination Vertical differentiation Supply Chain Contracting Product Design Assemble-To-Order

1. Introduction Selecting the quality of different components used to build a product is a key challenge for manufacturers. Car manufacturers need to make decisions on the performance of the engine, the quality of the interior seating materials, the suspension and brake systems, etc. Similar component selection problems arise in aerospace manufacturing, consumer electronics and even home remodeling; each is characterized by a situation where the product quality is a function of the quality of its many individually-supplied components. On the other hand, customers generally have price points in their mind before making a purchase decision. For example, a customer who wants to have the highest performance engine for the car he is about to buy with several convenient options, may have to consider a less-known brand if all these come at a higher price with the brand he initially had in mind. Similarly, a customer that is about to buy an IPad who also does not want to pass a certain price point may have to do the necessary trade-off between (16 GB, with 3G) and (32 GB, no 3G) configurations. We can think of several such examples in different industries. We have encountered this problem as well during a research project with a leading semi-conductor company which designs, manufactures and sells CPUs whose quality (in this case performance) varies. The firm was able to charge more for higher quality parts and earned higher margins on those parts because

n

Corresponding author. Tel.: þ1 202 9946039; fax: þ 1 202 994 2736. E-mail addresses: [email protected] (M.S. Altug), [email protected] (G. van Ryzin). 0925-5273/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpe.2012.09.023

costs were roughly the same for all quality levels. As a result, they wanted to encourage their customers (computer manufacturers) to build systems using higher quality parts. They were concerned, however, that their current pricing structure might not create the right ‘‘sell up’’ incentives. One of this firm’s main customer groups are resellers. A reseller builds no-brand computers which compete with larger OEMs on the market. They source different components such as hard-disk, CPU and memory from various suppliers and assemble them into a computer. While large OEMs can sell to several market segments profitably, because these resellers do not have the brand name advantage, it becomes even more critical for them to identify the ‘‘right segment’’ and build a product that has the highest value for a given budget. This way, they can sell the same configuration that a large OEM sells at a cheaper price and compete more comfortably in that segment. Throughout the rest of the paper, we will refer to a reseller as ‘‘manufacturer’’ and the upstream component providers as ‘‘supplier’’ (including the semiconductor company that provides the CPUs). As shown in Fig. 1, when deciding on the bill-of material for the computer, a manufacturer needs to choose quality levels for each component. For example, they could design a system with a 2.8 GHz CPU, 140 GB hard disk and 1 GB memory or one with a 2.1 GHz CPU, 100 GB hard disk and 2 GB memory. Each component is vertically differentiated, meaning that a higher quality part is preferred over a lower quality one all else being equal. The problem the manufacturer faces is to optimally balance the total cost and total quality of their final product so as to obtain the highest value product that will give them the necessary pricing flexibility while competing with more branded counterparts. It might be that

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

Fig. 1. Computer manufacturer example.

627

these suppliers and show that the quality levels that the manufacturer selects in equilibrium from each supplier are lower in a decentralized system than in a centralized system. This means the final product built in a decentralized system will be of less value. In other words, a consumer will be paying more for less. Furthermore, we show that the inefficiency loss could be as high as 60% depending on the business environment telling us that its mitigation can result in substantial savings for the entire supply chain, which in turn means more value for the final customer. We explain this using various industry examples. We then identify potential contracts and mechanisms such as revenue sharing and quality-price discounting that restore efficiency. As an extension to this problem, we consider another model where we assume a fixed exogenous price for the final product (a ‘‘target price point’’) and both quality dependent cost and demand in the profit function of the manufacturer. This helps to test the robustness of our earlier coordinating mechanisms. To simplify this more complex case, we assume that the quality levels for all but one component are fixed and that the manufacturer decides on the quality of only one of its components. We again first study the system inefficiencies and show that the same revenue sharing and quality-price discounting mechanisms that we studied earlier still enable the system to achieve full coordination.

2. Literature review

Fig. 2. Value creation.

a product with very high performance designed for the highest segment may not be perceived as ‘‘high value’’ by this kind of reseller as it may also cost too much leading to very minimal price flexibility when competing with OEMs. The CPU supplier wanted to encourage the manufacturer to build systems with higher quality (and more profitable) components. On the other hand, other suppliers providing different components also wanted to sell higher quality parts. The result was a competition among components for share of the manufacturer’s total design budget. To model this situation, we view the manufacturer’s decision as a strategic design problem in which it maximizes the difference between the product value and its cost; that is, we assume the manufacturer attempts to maximize the added value of its design. We assume that how this added value is translated into total profit is a later-stage decision. This is in parallel to the value appropriation theory discussed in Brandenburger and Stuart (1996). For example, the firm could price the product close to its value (minimize consumer surplus) and make high margins on a low volume of sales; or it could price close to cost (maximize consumer surplus) and make a low margin on a high sales volume; or most probably it would adopt some strategy in between. We do not analyze this pricing decision however, and assume that it is made after the design decision. Fig. 2 from Brandenburger and Stuart (1996) illustrates the main idea of such value maximization. Each component supplier, in turn, needs to decide on a wholesale price per unit quality level of its component. As a supplier increases its wholesale price, its margin increases, but the quality level of that component selected by the manufacturer will decrease. We characterize the strategic interaction among

Our work is relevant to four different research streams: vertical differentiation, supply chain contracting and coordination, bundling and product design. Vertical differentiation is an important area of research in economics and marketing. Quality in this literature generally refers to the level of some attribute, such that higher quality is always preferred by the consumer to lower values. For example, one would prefer a faster processor over a slower one ceteris paribus. The same is true with a higher resolution vs. lower resolution LCD TV. This is in contrast to horizontally differentiated products in which there is no dominant ordering on the attribute of the product; for instance, not everyone prefers red over blue cars. Mussa and Rossen (1978) is a seminal paper in this area. They consider a monopolist selecting quality positions when serving a market with consumers that have heterogeneous valuations for quality. Moorthy (1984) looks at the same problem with a different model in which consumers self-select the product they purchase. They conclude that firms may need to provide highvalue customers with their preferred quality and distort the quality of the lower product. These monopolistic models have been extended to take into account competition. Gabszewicz and Thisse (1979) is the earliest paper that considers the effect of competition in vertically differentiated environments. Shaked and Sutton (1982), Gal-Or (1983), and Moorthy (1984) assume an environment where firms compete on not only quality but other decisions such as price and quantity and the main finding is that firm should differentiate the quality of the product to avoid competition in other dimensions. Almost all papers in this literature assume that the firms sell their products directly to the market without any intermediary. Hence the incentive issues were never discussed. Villas-Boas (1998) is one paper that considers such an intermediary when selling vertically differentiated products, but their main focus is on choosing quality positions within a product line and not necessarily coordination or competition issues as we do. Furthermore, they consider a one supplier, one retailer setting which is different than the multi-supplier model we consider. To the best of our knowledge, this is the first work that contributes to this

628

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

literature by studying incentive issues in a vertically differentiated environment under multi-supplier one manufacturer setup. After Spengler (1950) identified the double marginalization phenomenon, there have been several papers in economics, marketing and operations on channel coordination. The papers by Jeuland and Shugun (1983) and McGuire and Staelin (1983) are some of the earlier work in marketing. The work in this area can be categorized into two groups: (i) one-supplier and one or multiple retailers and (ii) multiple suppliers and one manufacturer (assemble-to-order). Lariviere (1998), Corbett and Tang (1998), Tsay et al. (1998), Cachon (2003) and Arshinder et al. (2008) provide excellent reviews on this category of the literature in operations management. Our setup falls under the second category: assembly systems. Bernstein and DeCroix (2006) seek to understand whether insights from previous research on centralized systems apply to assembly environments. Because assembly systems involve issues of horizontal balance (component inventory levels) as well as vertical coordination (sufficient inventory to meet demand), the impact of decentralized management of such systems is not clear. They consider two versions of the problem and show that Nash equilibrium exists for both cases and a coordinating contract is provided. Gurnani and Gerchak (2007) consider an assembly system with random component yield. Each supplier decides on quantity and the manufacturer penalizes suppliers with poor delivery performance. They analyze the conditions under which system coordination is achieved while respecting participation constraints. Gerchak and Wang (2004) compare revenue sharing contracts with wholesale price contracts in an assembly system with random demand. Wang (2006) considers n different suppliers providing n products that are perfectly complimentary and are sold to a retailer with a price sensitive uncertain demand. In a game where manufacturers set both price and quantity, under a multiplicative demand model, they characterize equilibria and a consignment sales contract with revenue sharing is also analyzed. Carr and Karmarkar (2005) consider decentralized assembly systems with price sensitive but deterministic demand. The literature on supply chain coordination and contracting does not consider vertically differentiated products—and the existing work that does focuses on price and quantity decisions as in above papers, not on quality choice. Our work fills the gap by showing that some of the ideas that were studied earlier will carry over to a supply chain coordination problem when the decision firms make is quality (as opposed to quantity or price) and that actually the magnitude of the inefficiency can be even more substantial compared to those more classical problems; hence concludes that its mitigation becomes even more crucial for supply chain partners. Another relevant research stream is on bundling, which has been extensively studied in economics and marketing. Bundling helps a seller extract value from a given set of goods since it provides a form of price discrimination. Adams and Yellen (1976), Schmalensee (1976), McAfee et al. (1989), Hanson and Martin (1989), Bakos and Brynjolfsson (1999), and Bakos and Brynjolfsson (2000) are prominent papers in this area. In terms of extracting value by combining parts, our work is similar. However, in our case, each component is not used individually once it is sold. Therefore, the literature on product design and positioning is also related to what we study on which, an excellent review of the academic literature has been provided by Krishnan and Ulrich (2001). However, in both these areas, non of earlier work studied potential incentive issues that could arise while bundling or designing and building a product from different components. Our work can be viewed as another contribution in this field. In summary, the vertical differentiation literature has not to date focused on supply chain coordination and contracting issues. On the

Fig. 3. Model.

other hand, the extant literature on supply chain coordination and contracting does not normally consider vertically differentiated products—and the existing work that does focuses on price and quantity decisions, not on quality choice. Finally, although bundling and product design are relevant research streams in terms of the basic decision making problem, to the best of our knowledge none of the prior work in this area looks at the incentive conflicts and coordination issues associated with such decision making in multiple-supplier, single-manufacturer environments. Yet this is, in a way, a strategic problem where the consequences of misaligned incentives can be of more significance for the entire supply chain and that is what we argue in our results. Our paper nicely combines all different aspects of these different literature streams and studies a basic problem in a well-known framework and concludes that incentive issues indeed arise and can be mitigated with the appropriately designed contracts.

3. Model We consider an environment, as in Fig. 3, where a manufacturer that uses N components from N different suppliers to make a final product. The utility of the final product is a function of the quality levels of each component. We take the perspective of a manufacturer making a strategic product design decision and assume the manufacturer seeks to maximize the difference between the total product value and its total cost (the total added value).1 Once the added value is maximized, the product price determines how much of that value stays with the consumer and how much is retained by the manufacturer. This is fundamentally a pricing decision which will determine total demand. As mentioned in the Introduction, we assume pricing is a separate decision made after the product design is finished (and hence is not studied here), although we show how demand and quality decisions can be incorporated in a separate setting in Section 6. Let xi represent the quality level for component i, i¼1yN and X ¼ ½x1 ,x2 . . . ,xN  denote the vector of quality levels. We assume that suppliers offer a continuum of quality levels; wi is the wholesale price and ci is the production cost per unit of quality for component i.2 We assume that wi A ½ci wH i . We also assume that the quality level xi’s are normalized and scaled for each supplier with a very high upper bound. Given the quality levels of each component, the final product quality will be a function of X. Note that we are considering cases where the quality of the final product is low when the quality of even one of these components is low. For example, when the engine of an airplane has low quality, the plane is low quality plane regardless of the quality levels of its instruments, interior, 1

We assume throughout that utility is measured in dollar terms. For example, quality might be storage capacity in GB of hard drive or the speed in GHz of CPU. For components where the measure of quality is less objective, our assumption should be considered a stylized representation of quality level. 2

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

etc. Hence, the manufacturer will tend to balance the quality levels of components as opposed to making one component extremely high quality and the rest extremely low. On the other hand, its natural to assume that the incremental contribution of component quality levels to the final product quality diminishes as the component quality levels increase. For example, a computer would not function without its CPU and even the slowest one would be sufficient to make it work; at that minimal level, an increase in the speed of the CPU would contribute significantly to the overall performance of the computer. However, after a certain level, additional speed does not contribute as much since other limitations (memory for example) become the performance bottleneck. We use a Cobb–Douglas function as a stylized model for this relation between component quality and final product quality and assume that the final product quality (value) is given by R(X) where b

b

involving several other factors that include the established market share, market size, the regions the company operates in, production capacity etc., so is not studied here. And that is the same reason why manufacturers need to be careful in determining which ones to build and which ones to ignore and that is what our model supports. In other words, what we are interested in this paper is studying the incentive issues that may arise between suppliers and a manufacturer that needs to find out the appropriate configuration (among several) that will give the highest value, which in itself is an important and complicated problem considering all potential combinations. However, given the supplier wholesale prices and quality levels offered, our model can also be used to determine the top highest value configurations i.e. the manufacturer can determine not only the highest, but the second highest, third highest, etc. value product as demonstrated in the example studied in Appendix B.

b

RðXÞ ¼ Aðx11 x22 . . . xNN Þ We call this the product value function. R(X) is assumed to be the monetary utility; that is the value a consumer is willing to pay for the final product. For a given constant A and a vector of b ¼ ½b1 , b2 , . . . bN , the sum of bi s determines how individual component qualities are translated into the final product quality. We will refer to bi as the ‘‘component quality power’’. There are three cases: 1.

629

P

i bi ¼ 1: This represents the case of constant returns to quality. For example, increasing each component quality by 20% increases the final product quality by 20%. P 2. i bi o1: This represents the case of decreasing returns to quality. Increasing each component quality by 20% in this case, increases the final product quality by less than 20%. P 3. i bi 41: This represents the case of increasing returns to quality; increasing each component quality by 20% in this scenario, increases the final product quality by more than 20%.

While clearly stylized, this model of the product value function R(X) has the basic properties we seek and is rich enough to study quality choice, supplier competition and contracting. As discussed in the Introduction as well, while higher quality of all components will surely result in a higher quality final product, it will also cost the manufacturer accordingly as all the components are vertically differentiated. That means the highest performance product may not always be the highest ‘‘value’’ for the manufacturer due to higher supplier prices. However, the manufacturer in our model is trying to find the highest value product design that will allow it to compete easily with the branded products in the same market segment the manufacturer is targeting with that product. Since it is most natural to assume the contribution of component quality levels toward the final product diminishes as the component quality levels increase, we assume that bi s are such that they meet the decreasing returns to quality condition i.e. P i bi o1. Yet the assumption of continuous quality levels and the Cobb–Douglas form has its limitations. It is more representative of environments like computer manufacturing where there are many quality levels for each component, the metric of quality is clear and a products overall quality is dependent on the lowest quality of its key component. We consider an alternative additive utility function for a variant of this problem in Section 6. Note that companies will serve to several different market segments and offer more than one configuration, but even large OEMs have to limit the number of configurations it offers (as there are practically hundreds of combinations) and hence how many configurations to offer is a much more complex problem

3.1. The manufacturer’s quality selection problem The manufacturer’s problem is to maximize the added value of its product, which is the difference between the products value and the total cost of the components (

Pm ðXÞ ¼ max Aðxb11 xb22 . . . xbNN Þ X

X wi xi

) ð1Þ

i

where wi is the wholesale price per unit quality charged by supplier i. Solving this maximization problem, the manufacturer determines the quality levels xi for each component required to produce the final product.

3.2. Supplier’s wholesale pricing problem Each supplier i, in turn, needs to decide on its wholesale price wi. Note that the manufacturer, as mentioned in the Introduction section, is a no brand computer assembler and hence may not be able to fully dictate wholesale prices to suppliers unlike branded OEMS which have more negotiation powers.3 It is easy to show from the manufacturer’s problem that, all else being equal, as the supplier increases its wholesale price, the quality level selected by the manufacturer decreases. Let xin ðwi ,wi Þ denote the manufacturer’s response function which is the quality level selected from supplier i as a function of that supplier’s wholesale price (wi) and the wholesale price of other suppliers (wi ¼ ðw1 ,w2 , . . . wi1 ,wi þ 1 ,: :wN Þ). Note that we make that dependence explicit in our notation in this section. Then the supplier’s problem can be stated as

Pis ðwi ,wi Þ ¼ maxfðwi ci Þxin ðwi ,wi Þg, wi

ð2Þ

where ci is the per unit quality cost for supplier i. Recall that the quality level selected by the manufacturer depends not only on its own wholesale price but also the wholesale prices of all other suppliers. We characterize this wholesale pricing game among suppliers in the next section. 3 We have obtained this information during our meetings with the CPU supplier who is quite dominant in its industry and the no brand reseller—which we refer to as ‘‘manufacturer’’ in this paper. When the large OEMs ask them, the suppliers generally end up giving their best deal as they do not want to lose such large accounts, yet manufacturers like the one considered in this paper without any brand advantage and has much less business with the supplier are not as powerful as the OEMs.

630

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

30

We begin by studying the price competition among suppliers and then identify inefficiencies that arise in a decentralized system under wholesale pricing. We then analyze mechanisms and potential contracts that eliminate these inefficiencies. 4.1. Price competition among suppliers Let Pis ðwi ,wi Þ ¼ maxwi fðwi ci Þxin ðwi ,wi Þg denote the profit of supplier i. The following theorem characterizes the supplier equilibrium (all proofs are in Appendix A):

% Decentralized to Centralized Quality Level

4. Analysis

Consider the performance of a centralized system in which the manufacturer sources all the components internally, i.e. it owns all the suppliers. How would the component quality decisions compare to those of a decentralized system where each party independently maximizes its profit? Denote: xCi : quality level the manufacturer selects for component i ¼ 1 . . . N in a centralized system. xD i : quality level the manufacturer selects for component i ¼ 1 . . . N in a decentralized system. X C ¼ ½xC1 ,xC2 . . . xCN  D D X D ¼ ½xD 1 ,x2 . . . xN 

The solution XC to the centralized system is determined by ( ) X PC ðXÞ ¼ max Aðxb11 xb22 . . . xbNN Þ ci xi XC

i

and the solution XD to the decentralized system is determined by ( ) X b1 b2 bN PD ðXÞ ¼ max Aðx1 x2 . . . xN Þ wi xi XD

i

Our first main result is as follows: Theorem 2. (a) xCi 4xD i i¼ 1,2. That is, the quality of each component in the centralized system is higher than that in the decentralized system. (b) The total value (R(X)) of the product in the decentralized system is lower than that of the centralized system. We see that the classical double marginalization result of Spengler (1950) manifests itself as in Theorem 2. This is due to the margin the suppliers add to their wholesale prices in the decentralized system, which decreases the quality levels the

15 10 5

0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 0.8 Component 1 quality power

0.9

1

C Fig. 4. Efficiency percentage for supplier 1’s quality (xD 1 =x1 ) vs b1 .

% Decentralized to Centralized Total Profit

4.2. System inefficiencies

20

0

Theorem 1. (a) Pis ðwi ,wi Þ is quasi-concave in wi. (b) There exists dominant strategy equilibrium wn in the suppliers’ wholesale pricing game. Let us take supplier i to understand this interaction. As the wholesale price of other suppliers increases, the manufacturer will start to decrease the quality level of a product i, xi as well since its overall cost increases. However, due to the multiplicative form of the product value function, as shown in the Appendix A, supplier i’s profit, Pis ðwi ,wi Þ, is in fact a multiplicatively separable function of wi and a function of wi . Therefore, the optimal price for supplier i to charge is independent of other suppliers’ prices, so the equilibrium is the strongest possible i.e. the dominant strategy type. To make the exposition simpler, we present the analysis for the case of N ¼2 suppliers. Although, the results generalize easily to the case of N 4 2 suppliers.

25

70 60 50 40 30 20 10 0

0.01

0.11 0.21 0.31 0.41 0.51 0.61 0.71 0.81 Component 1 quality power Fig. 5. Channel total profit inefficiency vs. b1 .

manufacturer selects. This result shows what undermines the ‘‘sell-up’’ incentive of the suppliers discussed in the introduction section. To illustrate this inefficiency loss, we tested different scenarios by changing the ‘‘b’’ values keeping the sum of bs at a constant value. Fig. 4 shows that the loss in quality for a given supplier can be quite substantial. As we also observe in Fig. 5, the total channel inefficiency can be as high as 60% and if this inefficiency can be restored, it can be an improvement that is much more significant compared to what was observed earlier in the literature that studied more classical supply chain coordination problems. The second result in Theorem 2 directly follows from the first. As argued earlier, since the utility R(X) is directly related to the revenue the manufacturer can generate, this second result says there will be loss of value creation potential for the entire channel when the system is decentralized. Given that the nature of our problem is product design decision, we can interpret that inefficiency as either the consumer will have to pay more for a less ‘‘valuable’’ final product or if the inefficiency can be restored, they can buy a better ‘‘more valuable’’ final product for the same price. If we can design mechanisms that would replicate the performance of the centralized system, we can then find ways to allocate this additional value to make each party significantly better off. 4.3. Contracts In this section, we will study two mechanisms that result in perfect coordination.

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

4.3.1. Revenue sharing In a revenue sharing, the manufacturer shares a certain fraction of the total revenue with its suppliers. A well-known case is Blockbuster Inc., who agreed to pay its suppliers a portion of its rental income in exchange for a reduction in unit price of video tapes. This reduced the break-even point for a tape and allowed Blockbuster to purchase more tapes. While the main objective of the Blockbuster revenue sharing contract was increasing quantity, our focus is ensuring the manufacturer has the correct incentive to select quality levels. Here we assume that revenue is equal to the final monetary value R(X); that is, the product is priced to leave zero consumer surplus where the assumption is that consumers are homogenuous in their valuation. The result can easily be extended to the case where they are assumed to be heterogenuous.4 Theorem 3. (a) Consider a contract with an agreed on revenue fraction lo for the manufacturer and a vector of ðl1 , l2 Þ of revenue P fractions such that i li ¼ 1lo , with agreed wholesale prices: wi ¼ lo ci , i¼1,2. Then under this contract, the channel is coordinated and the profit is allocated according to lo for the manufacturer and ð1lo Þ for the suppliers. (b) Consider the revenue sharing parameters

lo ¼ 1

P1s þ P2s PC

and

l1 ¼

P1s þð1lo Þc1 xC1 RC

and

l2 ¼

P2s þð1lo Þc2 xC2 RC

where P1s , P2s are decentralized optimal supplier profits and RC is the value of R(X) in the centralized system when quality levels xC1 and xC2 are selected. A revenue sharing contract implemented with these parameters make suppliers indifferent and the manufacturer better off. In a decentralized system, suppliers add a margin to the production cost when selling to the manufacturer, increasing the marginal cost for quality for the manufacturer. If the suppliers all provided their components at unit production cost, this would incentivize the manufacturer to take the same action as in a centralized system, but this is equivalent to transferring the supplier firms to the manufacturer. Revenue sharing is an intermediate solution. Under revenue sharing, the manufacturer is lo percent owner of the entire channel, since it gets lo percent of the total revenue generated and pays for lo percent of the production cost. Therefore, it is in manufacturer’s best interest to increase the total channel profit. This ensures that the manufacturer has the same quality incentives as the centralized system. To understand the magnitude of the potential outcomes, for b1 ¼ 0:2, b2 ¼ 0:5 and c1 ¼ c2 ¼ 1, we ran several different scenarios using different lo and li values and determined the percentage profit improvement (with respect to wholesale pricing) for all parties under revenue sharing. Some of these scenarios are summarized in Table 1. 4 With customers that are heterogeneous in their valuations, incorporating that together with a pricing decision will make the revenue function quite complicated; yet the result on revenue sharing contract will not change as it will still make manufacturer’s profit an affine transformation of the centralized system profit.

631

Table 1 Profit improvement (with respect to wholesale pricing) scenarios under revenue sharing. Rev. share %

Supp 1 share %

Mfg (%)

Supplier 1 (%)

Supplier 2 (%)

0.7 0.6 0.3 0.5 0.3

0.21 0.24 0.35 0.2 0.21

67 43 7 78 21

43 43 191 24 135

67 245 191 274 201

As a practical matter, it would be natural for the manufacturer to take the lead in offering this kind of a contract. The percentages characterized in Theorem 3 make manufacturer get all the additional profit due to an increase in supply chain efficiency. However, they can be slightly modified to redistribute the profit allocation. One difficulty in implementing this contract is the administrative burden of tracking the revenue the manufacturer collects. Moreover, determining an appropriate wholesale price requires knowledge of suppliers’ cost, which may not be always be obtainable. In short, information asymmetry is a potential obstacle since suppliers have to know the revenue that the manufacturer generates and the manufacturer has to know each supplier’s cost. Note that unlike the case of Blockbuster, this is a contract that is initiated by the downstream member of the supply chain. As an example of a revenue sharing contract initiated by an downstream member, we can here discuss the case of Indian mobile phone innovator (Martinez-Jerez and Narayanan, 2007). Because its customer base was growing 100% a year in 2004 in its home telecom market, Bharti faced a huge challenge just keeping up with its network expansion. Managing information technology (IT) capital expenditures was another major challenge. Yet Bharti felt their equipment vendors were more interested in selling them new ‘‘boxes’’ and the latest software release than in supporting their critical need for low-cost, rapid, reliable deployment of cell phone capacity and customer servicing technology. To create better alignment with their suppliers, Bharti came up with a plan which consisted of two outsourcing proposals, one to their key telecom network equipment vendors, Ericsson, Nokia, and Siemens and the other to their main IT vendor, IBM. Bharti proposed completely handing over the build-up and management of their telecom and IT infrastructure to these vendors. While in the old relationship technology vendors made more money when they sold more hardware to Bharti, under the new arrangement Bharti paid network equipment vendors only for usage. Similarly, IBM was responsible for supplying, installing and managing Bharti’s computer hardware, database software and various applications required for provisioning, billing and customer service. In return, IBM received a share of Bharti’s total revenues. The new contracts helped the company continue its rapid growth worldwide. 4.3.2. Quality-price discounting The main idea with this mechanism is that suppliers tie their wholesale prices to the end product value, R(X), of the manufacturer. Additionally, the supplier announces a quality-price discounting schedule rather than a fixed wholesale price per unit quality. First some notation: Let a denote an agreed-upon fraction that allocates the total profit between the manufacturer and all the suppliers, and ki denote another fraction that allocates the suppliers’ share of the revenue among all suppliers. Suppose suppliers charge wholesale prices RðXÞ xi Note that supplier i’s wholesale price decreases as the manufacturer asks for higher quality from the supplier; and it increases wi ¼ ð1aÞci þ aki

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

Theorem 4. (a) Consider a contract with all suppliers having the quality-price discount parameters (a,KÞ. With the wholesale prices for each supplier i set as wi ¼ ð1aÞci þ aki

RðXÞ xi

P where the vector K ¼ ðk1 ,k2 Þ is such that i ki ¼ 1 Then under this contract the channel is coordinated and the total profit is split according to ð1aÞ for the manufacturer, and a for the two suppliers, with supplier i receiving a fraction ki of total supplier profits. (b) Consider these contract parameters with

k1 ¼

c1 xC1 þ

P1s

a

RC

and

k2 ¼

c2 xC2 þ

P2s

a

RC

where P1s , P2s are decentralized optimal supplier profits and RC is the value of R(X) in the centralized system when quality levels xC1 and xC2 are selected. A quality–price discounting contract implemented with these parameters make suppliers indifferent and the manufacturer better off. In terms of the contracts studied in the literature, the price discount sharing (PDS) contract, studied by Lal et al. (1996) and Bernstein and Federgruen (2005), most resembles our contract. In PDS type agreements, the supplier discounts at a certain percentage from a suggested wholesale price based on the retailer’s price discount. In this way, a supplier ties its wholesale price to the end product price the retailer sets, similar to our arrangement. The wholesale price is set to combination of percentage of production cost and percentage of revenue per unit quality. Note that the above contract requires suppliers to agree on K and a. These parameters of course need to be set according to the opportunity profits of each party to ensure participation. And the presence of information asymmetry would create similar implementation issues as in revenue sharing, since knowledge of production cost and the product value function by all parties is required. However, assuming a long-standing relation between the manufacturer and the suppliers, we can expect that the suppliers can estimate the product value function, which can mitigate some of the difficulties associated with the implementation of the contract.

5. Numerical study In this section, we present results of a numerical study to identify several other important managerial insights. We ran these experiments by changing the b values (the component quality power) in two ways representing different business environments. All cases are for two suppliers. Case I. Sum of bi ’s are constant: This scenario represents an environment where the overall utility of the product is fixed for given quality values, but the component that is providing the greatest value changes depending on the relative value of the b’s. We did this by increasing b1 (decreasing b2 ) and keeping the sum at a constant value (in the this case, we set (b1 þ b2 ¼ 0:91). In this way, the component that plays the ‘‘dominant’’ role in determining the overall product value changes, because as one b

increases, the other one decreases. We see each set of b’s as exogenous potential business scenarios (e.g., a result of technology, brand recognition, etc.) and not as variables that the firms can control in the short term. As we see from Fig. 5 in the earlier section, the efficiency loss in total supply chain profit is greatest when the suppliers are ‘‘symmetric’’, i.e. when there is no dominant component supplier. That is observed in Fig. 6 as well. This is counter intuitive, because when the b’s are close, one would expect that the competition among components is more intense and that this might lead to wholesale prices that are closer to marginal costs. However, our model shows that the main factor driving efficiency loss here is not competition among suppliers but how the supplier’s incentive to price changes with respect to b. As b1 increases (and b2 decreases), supplier 1’s component becomes the dominant factor determining quality. While this gives it greater bargaining power, as we see in Fig. 7, supplier 1 nonetheless charges lower prices. The reason is that the incremental increase in quality selected by the manufacturer from a marginal decrease in wholesale price is much higher for a dominant supplier; that is, a dominant supplier faces a higher price elasticity of demand from the manufacturer for its quality. This increase in elasticity more than offsets their increased pricing power and leads to lower wholesale prices, which in turn implies greater supply chain efficiency. What happens to the profit values? Does a manufacturer do better with one dominant component or a product where components are more symmetric in terms of contributing to the product value? If we denote the sum of supplier 1’s (P1s ), supplier 2’s (P2s ) and the 35 30 %Uitlity Loss

as the total value of the final product, R(X), increases. With that, we get our coordinating contract, as summarized in the next theorem:

25 20 15 10 5 0

0

10

20

30 40 50 60 70 80 Component 1 quality power

90

100

Fig. 6. Utility loss in decentralized systems vs. b1 —Case I.

12 Per quality wholesale price (w1)

632

10 8 6 4 2 0

0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 Component 1 quality power

0.8

Fig. 7. Per quality wholesale price (w1 ) vs. b1 .

0.9

1

50 45 40 35 30 25 20 15 10 5 0

Supplier 2's profit %

Supplier 1's profit %

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Component 1 quality power

1

50 45 40 35 30 25 20 15 10 5 0

0

633

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Component 1 quality power

1

60

Mfg's profit %

50 40 30 20 10 0

0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 0.8 Component 1 quality power

0.9

1

Fig. 8. Supplier 1, supplier 2 and manufacturer’s profit share with respect to total channel profit—Case I.

manufacturer’s (Pm ) profit as PTot , then we want to understand the distribution of each party’s profit within the total and how that changes as b1 increases (and b2 decreases). In other words, we are testing the three ratios:

P1s P2s , PTot PTot

and

Pm PTot

Our observation with supplier 1 and supplier 2 is consistent with expectations. As supplier 1 becomes the dominant component provider, both its profit and share of total profit increases. As we see from the third chart in Fig. 8, the manufacturer is also better off when there is one dominant component as its share of the total profit increases. This is again due to what we observed in Fig. 7. As one supplier becomes dominant, its incentive is to lower wholesale prices, so the overall channel becomes more efficient and channel profits rise. A plausible industry example of this phenomenon is found in the history of personal computers (PCs). In the early days of the PC, the CPU was a dominant factor in determining system performance and quality. In this era, customers eagerly awaited each new release of an Intel processor, which promised substantially increased system performance. And the primary component provider (Intel) and primary manufacturer (IBM) both flourished. Today, however, the CPU is much less important in the eyes of most consumers. Other components, like a computer’s display, its media and communication components, and even the form factor of the system are equally, if not more important, determinants of system quality. And relative to the early era of PCs, Intel’s margins today are lower (Tran, 1999; Intel, 2009) and IBM decided to exit the PC business entirely (Scott-Joynt, 2004). Case II. b2 is constant and b1 increases: The experiments under this scenario reflect the cases where the total value of the product increases as well. However, the contribution of component 1 in that overall value increases. As seen in Fig. 9, even though it is b1 that increases while b2 stays constant (b2 ¼ 0:2 in all the experiments run under this case), the profit share of supplier 2 increases as well. This positive

externality for supplier 2 is due to the overall increase in utility of the product that enables not only supplier 1 but also supplier 2 to obtain a larger share of the overall profit, especially for high values of b1 . This shows that even suppliers that provide ‘‘insignificant’’ components can benefit from the presence of a ‘‘very significant’’ component in the product that they are supplying. In effect, suppliers become more powerful and as a result gain a larger share of the overall profit pie. The manufacturer’s profit share shown in the third chart in the same figure, decreases as b1 increases. Continuing with the PC industry case, one can find an analog to this phenomenon in the change in relative dominance of Microsoft and IBM during the early evolution of the industry. Initially, the PC operating system (OS) was considered so insignificant to the PC that IBM was willing to outsource it to Microsoft, a small upstart firm. But as PC technology evolved, the operating system became an increasingly important determinant of product value, along with the CPU needed to run the latest OS.5 As these two components increased in importance, the so-called ‘‘Win-tel monopoly’’ came to dominate the industry and the importance of system assemblers like IBM declined. Assembly of complete systems became much more of a commodity business and the bulk of supply chain profits flowed to the key component suppliers—Microsoft and Intel (Scott-Joynt, 2004).

6. Quality-dependent demand Thus far, we have assumed that the manufacturer is making a strategic design decision about the quality levels of individual components and that the manufacturer wants to maximize the difference between the product value and its cost. Deciding what 5 For this discussion to exactly reflect our numerical example, we can argue that an increase in b1 reflects first the increase in importance of operating systems and then the CPU in a few years apart. Also, note that even though we have two components in our example, same argument can be extended to an example with three or more components as our discussion here suggests.

0

0.1

0.2 0.3 0.4 0.5 0.6 0.7 Component 1 quality power

Mfg's profit %

40 35 30 25 20 15 10 5 0

Supplier 2's profit %

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

Supplier 1's profit %

634

90 80 70 60 50 40 30 20 10 0

0

0.1

0.8

30 25 20 15 10 5 0

0

0.1

0.2 0.3 0.4 0.5 0.6 0.7 Component 1 quality power

0.2 0.3 0.4 0.5 0.6 Component 1 quality power

0.7

0.8

0.8

Fig. 9. Supplier 1, supplier 2 and manufacturer’s profit share with respect to total channel profit—Case II.

price to charge we assumed is a second-stage problem. However, an alternative model is to assume the manufacturer wants to design for a target price point and include the dependence of demand on quality in its decision problem. To do so, we define the additional decision variables and parameters: p: the market price for the end product (exogenous). N: the market size. bi : the coefficient of quality for component i. b ¼ ½b1 , b2 . . . bn . U(X): utility from consuming an end product with quality vector X. E: random term for consumer utility with density f and distribution F. d(X): the total demand for the end product with quality X. c(X): the total cost for the manufacturer for procuring n components with quality levels X.

Pm ðXÞ ¼ maxfðpcðXÞÞdðXÞg X

T

T

ð4Þ

Recall a distribution (with cdf F and pdf f), has increasing 0 failure rate (IFR), if its failure rate hðuÞ 4 f ðuÞ=fðuÞ. We assume the manufacturer’s cost function c(X) is jointly convex and F is IFR. We then have the following result: Theorem 5. Under above assumptions, the manufacturer’s problem (4) has a unique solution Xn.

Note that the earlier notation representing quality (xi, X) and wholesale prices (wi) remain the same. We assume that bi ’s are fixed for all consumers in the market and that the consumer T utility UðXÞ ¼ b X þ E. With this dðXÞ ¼ NPrðUðXÞ 4 pÞ ¼ NPrðb X þ E 4pÞ ¼ N F ðpb XÞ

the manufacturer faces is that as the quality level for components goes up, both the procurement cost and the total utility (and therefore in this case the total demand d(X)) increases. The selling price is assumed to be exogenous. Therefore, the manufacturer needs to balance its margin and volume of sales, both of which are a function of quality. Denoting the manufacturer’s profit by Pm , the manufacturer’s problem is

ð3Þ

Note that, while we assumed the utility function had a multiplicative form in the earlier section, here we assume an additive form with a random term which determines the total demand for the product. There are two main reasons for this change. First, we want to understand the affect of an additive vs. multiplicative utility model and how robust the results are to the form of this function. Second, the linear model simplifies the task of adding the demand component to the objective function. We first analyze the manufacturer’s problem and then turn to the supplier’s problem. 6.1. Manufacturer’s problem The problem for the manufacturer is the same as described earlier; to design the end product by choosing quality levels xi for each of the components in the final product. Again the trade-off

6.2. Supplier’s problem For each supplier i, the problem is the same as in the strategic problem. Each supplier has to decide on a wholesale price wi per unit quality. We assume that the supplier’s cost of quality increases linearly with ci. In this setting, each supplier decides on its own wholesale price wi anticipating that the manufacturer will ask for quality level xi ðwi ,wi Þ in the amount of d(X) to make d(X) units of final product. Hence, with Pis ðXÞ denoting the profit function, supplier i’s problem can be written as

Pis ðXÞ ¼ maxfðwi ci Þxi ðwi ,wi Þdðxi ,xi Þg wi

ð5Þ

The sequence of events is as follows:

(1) The suppliers decide on wholesale prices wi anticipating that the manufacturer will select quality level xðwi ,wi Þ in the amount of d(X) to make d(X) units of the final product. (2) The manufacturer takes these price offers from its n suppliers and decides on quality levels X, generates demand d(X), orders d(X) from each supplier i and pays them ðwi xi ÞdðXÞ.

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

(3) Suppliers make and deliver the required amounts, the manufacturer makes and sells the final product at p and collects the revenue.

635

first given the demand function. This says the final product the manufacturer builds ends up being a lower quality product and also the total demand that it satisfies is less than the channel optimal.

6.3. Analysis To simplify our analysis, we will again assume the special case of two suppliers, although the results are valid for the general case of multiple suppliers. We further make another assumption on the distribution of the random term in our utility function: namely, that the random term E has uniform distribution over (0,1). With this assumption, the manufacturer’s problem is

Pm ðXÞ ¼ maxfðpcðXÞÞNð1p þ bT XÞg X

ð6Þ

We then have the following result for the manufacturer’s problem: Theorem 6. (a) Pm ðXÞ is concave in xi; i ¼1,2 (b) 2 3 ðwj bi þwi bj Þðpbj wj ð1pÞ pbi  6 7 62wi bi 7 4wi wj bi bj 7, i,j ¼ 1,2 xni ¼ 6 6 7 2 ðwi b þ w b Þ 4 5 j i j 1 4wi wj bi bj

Based on this characterization of the manufacturer’s problem, we see that analyzing the suppliers’ interaction in this multiple supplier setting is complex. Therefore, in the rest of our analysis, we focus on a simpler case where the manufacturer is interested in deciding on the quality level ðx1 Þ of one component and that the quality level of the other component is fixed at x2 . While clearly restrictive, this corresponds to a case where the manufacturer does not have a choice when it comes to making a quality decision except for all but one key component. We can redefine price p to include the fixed quality level x 2 both of which are constants in this model: p ¼ pb2 x 2 p^ ¼ pw2 x 2 which makes the demand function under uniform distribution assumption, dðx1 Þ ¼ ð1p þ b1 x1 Þ and hence the manufacturer’s problem can be represented as ^ Pm ðx1 Þ ¼ maxfðpw 1 x1 Þð1p þ b1 x1 Þg x1

ð7Þ

The supplier’s problem is then

P1s ðXÞ ¼ maxfðw1 c1 Þx1 ðw1 Þð1p þ b1 x1 Þg w

ð8Þ

1

As before, we want to understand the quality distortions introduced in this supply chain and understand their magnitude under different scenarios. We then develop mechanisms to eliminate these distortions. Our first result toward this goal is the following proposition: Theorem 7. (a) xC1 4 xD 1. C D (b) d 4d . This result says that the quality level the manufacturer selects from the supplier is lower in a decentralized system than in a centralized system. This is due to the fact that the supplier tries to make margin by increasing its wholesale price in a decentralized system, which increases the marginal cost of quality for the manufacturer, reducing the quality level the manufacturer selects. The second result in the proposition is a direct consequence of the

6.4. Contracts We next study two coordinating contracts. The first one is the revenue sharing contract, which was proved to be coordinating in the earlier multiple supplier one manufacturer setting. Since we have only one supplier, dropping the supplier subscript from the same notation used earlier, we can summarize the result as follows: Theorem 8. (a) Consider a contract with an agreed on percentage l that represents the manufacturer’s share of the total revenue generated and a wholesale price charged by the supplier of w ¼ lc Under this mechanism, the channel is coordinated and the profit is arbitrarily allocated according to l for the manufacturer and ð1lÞ for the supplier. (b) There exists a l where all firms make better profit than they do with wholesale pricing contract. This result shows us that the channel would benefit from a properly designed revenue sharing arrangement which helps the supplier sell up, eliminating the distortion that would otherwise be present in the decentralized system. The structure of the agreement is similar to before, since the supplier offers the per unit quality of the product at a given percentage of its production cost. The administrative difficulties associated with revenue sharing are still present, i.e. the manufacturer needs to keep track of the revenue generated from the product. We next explore a contract similar to the quality–price schedule we introduced above for the multiple supplier setting. The main idea is to tie the wholesale price the supplier charges to the quality the manufacturer selects and its end price. On the supplier side, this corresponds to the supplier announcing a quality–price schedule as opposed to a fixed wholesale price per unit quality. Let a be the agreed-on percentage that splits the total profit ^ as the per between the manufacturer and the supplier. Define p=x unit quality price. Then the supplier’s wholesale price, defined as ^ w ¼ ð1aÞc þ ap=x, will change based on the quality the manufacturer demands. Again, this can be interpreted as charging a percent of the total cost and receiving a percent of the total revenue. In this scheme, as the quality increases the supplier will discount more from its wholesale price. This yields our coordinating contract: Theorem 9. (a) Consider the contract where the supplier sets the ^ wholesale price as: w ¼ ð1aÞc þ ap=x then the channel is coordinated and the total profit is split according to a and ð1aÞ. (b) There exists an a where both players are better off than they are under wholesale pricing. The a needs to be set according to the opportunity profits of both parties to ensure participation.

7. Conclusion and future research We considered a multi-supplier single manufacturer environment where each supplier sells a different component with a predefined quality (performance) range. The manufacturer’s decision is not how many units to buy, but what quality level to choose for each component it uses in its final product. The ultimate value of the final product, and hence the revenue the manufacturer can

636

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

generate, increases as the quality of the individual components increases. Hence, the manufacturer’s problem is to trade-off between the total quality of the product with its total cost. We show how double marginalization manifests itself as quality distortion in the decentralized system. We then present potential mechanisms such as a quality-price schedule and revenue sharing that restore efficiency. Our numerical study shows us that the magnitude of the inefficiency in these systems can be quite substantial, which suggests that all parties may significantly benefit from more sophisticated contracts that help restore efficiency. Several extensions to this work are worth pursuing. Broadly speaking, product design is one of several higher level supply chain decisions a firm has to make. We believe that the incentive issues leading to inefficiencies in such strategic decisions may be more significant and require different forms of contract agreements than the operational decisions studied in earlier supply chain contracting literature. Also, we focused on maximizing the value gap and considered pricing a separate problem. However, depending on customer heterogeneity and demand elasticity, the firm might benefit more from maximizing its joint product design and pricing decisions. A model that considers both of these decisions would be a worthwhile extension. Finally, in industry we see that companies charge different wholesale prices for different quality components. As the quality increases, the wholesale prices in general increase. However, what is not clear is how they increase. It would be worth understanding empirically how these wholesale prices change with respect to quality in different industries and what determines these price schedules.

Appendix A. For ‘‘Product quality selection: contractual agreements and supplier competition in an assemble-to-order environment’’ This appendix is intended to supplement the paper and contains references to parts of it. The appendix contains the proofs of the results in the paper, along with supporting results. Proof of Theorem 1. (a) Because bi o1,8i, one can easily show that Pm is concave in xi (Even though wis are bounded, the assumption is that the quality levels xis are scaled such that they each have high upper bounds). We then have: b

x1 ¼

Ab1 x22 w1 b1

x2 ¼

Ab2 x1 w2

!1=1b1

@P1s =@w1 4 0 with w1 ¼ c1 and is non-increasing in w1. Therefore, Pis is quasi-concave with wn1 ¼ c1 ðb=ðb1ÞÞ and b Z1 8 b1 , b2 , b ¼ 1=ð1b1 Þn. (b) Due to the multiplicative form of the product value function, the profit function for each supplier i is a multiple of a function of w2 and therefore, it becomes an affine transformation of the other supplier’s wholesale prices. As we also see from the form of wn1 , the equilibrium is a dominant strategy equilibrium where each supplier charges wni regardless of what others charge (Tirole, 1988). & Proof of Theorem 2. (a) Based on Theorem 1, we know that  1=1b1  b =ðð1b1 Þð1b2 ÞÞ !1=n Ab1 Ab2 2 ½xC1 ¼ c1 c2  1=1b1  b =ðð1b1 Þð1b2 ÞÞ !1=n Ab1 Ab2 2 4 ¼ xD 1 w1 w2

b

b

b

(b) Because RðXÞ ¼ Aðx11 x22 . . . xnn Þ, based on part (a), we know that this value is lower in decentralized systems. & Proof of Theorem 3. (a) In this case, recall that since R(X) is the value of the product, it is assumed equivalent (or proportional) to the total revenue generated. Therefore R(X) will be used in the profit functions here as the revenue term. When wi ¼ lo ci for 8i, P P Pm ðXÞ ¼ l0 RðXÞ i l0 ci xi ¼ l0 ðRðXÞ i ci xi Þ ¼ l0 PC ðXÞ. Therefore, the quality levels, the manufacturer will decide on, i.e. X n ¼ X C ; hence the channel is coordinated and Pis ¼ li RðXÞð1lo Þci xi P i P P P which means i Ps ¼ ð i li ÞRðXÞð1lo Þ i ci xi ¼ ð1lo ÞðRðXÞ i ci xi Þ ¼ ð1lo ÞPC ðXÞ. (b) When a revenue sharing contract with l0 is implemented, supplier 1’s profit will be ðw1 c1 ÞxC1 þ l1 RC ¼ ð1l0 Þc1 xC1 þ l1 RC and supplier 2’s profit will be ð1l0 Þc2 xC2 þ l2 RC . By setting these profits under revenue sharing contract equal to the optimal decentralized profit of each (P1s and P2s respectively), we get

l1 ¼ !1=1b2

P1s þ ð1l0 Þc1 xC1 RC

and

Substituting into the above values, we obtain  1=1b1  b =ðð1b1 Þð1b2 ÞÞ Ab1 Ab2 2 xn1 ¼ ðMÞ1=n where M ¼ and w1 w2 n ¼ 1

where aðw2 Þ is the part that is function of w2.   @P1s 1 c þ ¼ aðw2 Þðw1 Þ1=ð1b1 Þn 1 ð1b1 Þn ð1b1 Þnw1 @w1

b1 b2

l2 ¼

P2s þ ð1l0 Þc2 xC2 RC

which makes suppliers indifferent between wholesale pricing and revenue sharing contract. We need to ensure that

l1 þ l2 ¼

ð1b1 Þð1b2 Þ

P1s þ P2s þ ð1l0 Þðc1 xC1 þ c2 xC2 Þ RC

¼ ð1lo Þ

which needs xn2 ¼ ðRÞ1=n



1=1b2  b =ðð1b1 Þð1b2 ÞÞ Ab2 Ab1 1 where R ¼ w2 w1

lo ¼ 1

P1s þ P2s PC

Pis ðwi ,wi Þ ¼ ðwi ci Þxi ðwi ,wi Þ, i ¼ 1,2

We now need to show that this l0 makes manufacturer better off. With this revenue sharing parameter manufacturer’s profit is

We can write

lo PC ¼ PC ðP1s þ P2s Þ 4 PD ðP1s þ P2s Þ ¼ Pm , by definition since

x1 ¼

aðw2 Þ 1=ð1b1 Þn

w1

PD ¼ Pm þ ðP1s þ P2s Þ (i.e. the total decentralized system profit is sum of channel members’ profit).

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

We know that the overall profit generated in the channel is greater i.e. PC ðXÞ 4 PD ðXÞ. The manufacturer will be better off. Hence, it follows that ðl1 , l2 Þ and l0 can further be adjusted to make all the players better off in this scheme. & Proof of Theorem 4. (a) With the wholesale price RðXÞ wi ¼ ð1aÞci þ aki xi

 RðXÞ ¼ RðXÞ ð1aÞci þ aki xi xi i X X ¼ RðXÞa ki RðXÞð1aÞ ci xi

&

p^ 1p  2w1 2b1

Hence xC1 ¼

i

X ci xi Þ

Plugging in the values, we get 2 3 ðwj bi þ wi bj Þðpbj wj ð1pÞ p bi  6 7 62wi bi 7 4wi wj bi bj 7, i,j ¼ 1,2 xni ¼ 6 6 7 2 ðwi b þw b Þ 4 5 j i j 1 4wi wj bi bj

x1 ¼

i

X

¼ ð1aÞðRðXÞ

pb2 w2 ð1pÞx1 ðw2 b1 þw1 b2 Þ 2w2 b2

Proof of Theorem 7. (a) The structure of the objective function stays the same with the additional assumption and we get

we have the manufacturer’s profit as: X Pm ðXÞ ¼ RðXÞ wi xi

i

x2 ¼

637

i

p^ p^ 1p 1p  4  ¼ xD 1 2c1 2b1 2w1 2b1

(b) The result simply follows from the first part and the nature of the demand function. &

¼ ð1aÞPC ðXÞ (b) This can be argued as in the earlier theorem and omitted for brevity. & Proof of Theorem 5. PLm ðXÞ ¼ log Pm ðXÞ ¼ logðpcðXÞÞ þ log dðXÞ. 0 We will show that PLm ðXÞ is concave. Let c0 , d and PL0 m be the derivative of the cost, demand and profit functions respectively with respect to quality levels xi.

Proof of Theorem 8. In this problem, the centralized system ^ 1 x1 Þð1p þ b1 x1 Þ. With the proposed profit would be PC ðXÞ ¼ ðpc scheme: ^ Pm ðXÞ ¼ lðpð1p þ b1 x1 ÞÞlc1 x1 ¼ lPC ðXÞ and as a result, the coordination is achieved. By setting l ¼ 1Ps =PC where Ps is supplier’s profit, we can make supplier indifferent and manufacturer better off; and by increasing l by a small amount, we can make both the supplier and the manufacturer better off. &

0

PL0m ¼

c0 ðXÞ d ðXÞ þ pcðXÞ dðXÞ

^ Proof of Theorem 9. With the wholesale price w ¼ ð1aÞc þ ap=x, we can now write the manufacturer’s profit function: ^ ^ 1 Þx1 Þðð1p þ b1 x1 Þ Pm ðx1 Þ ¼ ðpðð1 aÞc1 þ ap=x ^ apð1 ^ ¼ ðp aÞc1 x1 Þðð1p þ b1 x1 Þ ^ 1 x1 Þð1p þ b1 x1 Þ ¼ ð1aÞðpc

and

PL00 m ¼

c00 ðXÞðpcðXÞÞðc0 ðXÞÞ2 ðpcðXÞÞ

2

d ðXÞdðXÞd ðXÞ2 00

þ

0

2

dðXÞ

o0

¼ ð1aÞPC ðXÞ

if

which proves the first part (b) This part can be argued as in earlier theorem.

(1) c00 ðXÞ Z0 and 00 0 (2) d ðXÞdðXÞ od ðXÞ2

Appendix B. Extra example

We assume (1) and (2) are ensured by the IFR assumption on F. Note T

0

2

00

T

0

that d ðXÞ ¼ bi Nfðpb XÞ and d ðXÞ ¼ bi Nf ðpb XÞ. Condition 2

T

T

2

2

T

(2) requires: bi N f ðpb XÞðNF ðpb XÞÞ r N2 bi f ðpb XÞ (Let T

&

0

0

2

0

U ¼ pb X) 3 f ðuÞF ðuÞ o f ðuÞ 3 f ðuÞ= fðuÞ o fðuÞ=F ðuÞ 0 3 hðuÞ 4 f ðuÞ=fðuÞ which is known to be true for IFR distributions. Hence, Pm is unimodal. & P Proof of Theorem 6. (a) With CðXÞ ¼ i wi xi , the profit function P P for the manufacturer is Pm ðXÞ ¼ ðp i wi xi Þð1p þ i bi xi Þ and @2 Pm =@x2i ¼ 2wi bi o0 8i ¼ 1,2 proving the first part.

Consider a manufacturer that needs to select quality levels for the two components, as shown in Fig. 10, of a laptop it needs to build: x1 represents the performance level of the CPU and the supplier offers four levels (1.2, 2, 2.8, 3.2 GHz). x2 represents the performance level of the RAM and the supplier offers three levels (1,1.8, 2.8). b

(b) Based on (a) and @Pm ¼ w1 ð1p þ b1 x1 þ b2 x2 Þ þðpw1 x1 w2 x2 Þb1 ¼ 0 x1 @Pm ¼ w2 ð1p þ b1 x1 þ b2 x2 Þ þðpw1 x1 w2 x2 Þb2 ¼ 0 x2 will give us pb1 w1 ð1pÞx2 ðw1 b2 þ w2 b1 Þ x1 ¼ 2w1 b1

b

The manufacturer maximizes this difference p ¼ fAðx11 x22 P b . . . xNN Þ i wi xi g. In the main body of the paper we have

X1 (GHz Quality level)

X1 (Normalized)

X2 (GB)

X2 (Normalized)

1.2

37.5

1

35.71

2

62.5

1.8

64.28

2.8

87.5

2.8

100

3.2

100 Fig. 10. Example.

638

M.S. Altug, G. van Ryzin / Int. J. Production Economics 141 (2013) 626–638

Scenarios

1

2

3

4

5

6

A

12

12

12

12

12

12

β1

0.7

0.7

0.7

0.7

0.7

0.5

β2

0.2

0.2

0.2

0.2

0.2

0.4

w1

5.5

6

6

7

5

5

w2

1.5

1.5

1

1

1

1

58.61

31.58

69.87

22.05

157.14

186

x1 (GHz)

2

1.2

2

1.2

3.2

2

x2 (GB)

1.8

1

2.8

1.8

2.8

2.8

x1 (GHz)

2.8

1.2

2.8

1.2

2.8

1.2

x2 (GB)

2.8

2.8

2.8

2.8

2.8

2.8

Best configuration’s value ((π):

Second best configuration

Fig. 11. Highest value configurations for different scenarios.

characterized the optimal solution, however, here to illustrate how the function actually works capturing the main problem and how it can further be used to answer some of the questions that could be of interest, we did enumeration and calculated the above value for all 12 possible configurations. We have listed the highest and the second highest value configurations for several different scenarios (created by changing other model parameters) in Fig. 11. The best value configuration in the first scenario is in the medium range with x1¼2 and x2¼1.8. That means if the reseller targets the segment that wants this kind of configuration; it will have more room to adjust the price and as a result compete more comfortably with OEMs that build the same configuration. Probably, the reseller will want to sell more than one configuration in which case it will build the second highest value configuration which is x1¼2.8 and x2¼2.8. As we see, the highest value configuration is not necessarily the highest performance one. In the second scenario, the highest value configuration is the one with the lowest performance. This can be interpreted as the reseller is recommended to play in the lowest performance segment as it will have more power to cut prices and compete against bigger players. References Adams, W., Yellen, J., 1976. Commodity bundling and the burden of monopoly. Quarterly Journal of Economics 90 (3), 475–498. Arshinder, S., Kanda, A., Deshmukh, S., 2008. Supply chain coordination: perspectives, empirical studies and research directions. International Journal of Production Economics 115 (2), 316–335. Bakos, Y., Brynjolfsson, E., 1999. Bundling information goods: pricing, profits and efficiency. Management Science 45 (12), 1613–1630. Bakos, Y., Brynjolfsson, E., 2000. Bundling and competition on the Internet. Marketing Science 19 (1), 63–82. Bernstein, F., DeCroix, G., 2006. Inventory policies in a decentralized assembly system. Operations Research 54 (2), 324–336. Bernstein, F., Federgruen, A., 2005. Decentralized supply chains with competing retailers under demand uncertainty. Management Science 51 (1), 18–29. Brandenburger, A., Stuart, H., 1996. Value-based business strategy. Journal of Economics and Strategy 5, 5–24. Cachon, G., 2003. Supply chain coordination with contracts. In: deKok, A.G., Graves, S.C. (Eds.), Supply Chain Management: Design, Coordination and Operation. Elsevier, The Netherlands. Carr, S., Karmarkar, U., 2005. Competition in multi-echelon assembly supply chains. Management Science 51, 45–59.

Corbett, C., Tang, C., 1998. Designing supply contracts: contract type and information asymmetry. In: Tayur, S., Magazine, M., Ganeshan, R. (Eds.), Quantitative Models for Supply Chain Management. Kluwer, Boston, MA. Gabszewicz, J., Thisse, J., 1979. Price competition, quality and income disparities. Journal of Economic Theory 20, 340–359. Gal-Or, E., 1983. Quality and quantity competition. Bell Journal of Economics 14, 590–600. Gerchak, Y., Wang, Y., 2004. Revenue sharing vs. wholesale-price contracts in assembly systems with random demand. Production and Operations Management 13, 23–33. Gurnani, H., Gerchak, Y., 2007. Coordination in decentralized assembly systems with uncertain component yields. European Journal of Operational Research 176, 1559–1576. Hanson, W., Martin, K., 1989. Optimal bundle pricing. Management Science 32 (2), 71–84. Intel 2009. Financial Statements /www.intel.comS. Jeuland, A., Shugun, S., 1983. Managing channel profits. Marketing Science 2, 239–272. Krishnan, V., Ulrich, K., 2001. Product development decisions: a review of the literature. Management Science 47 (1), 1–21. Lal, R., Little, J., Villas-Boas, J., 1996. A theory of forward-buying, merchandising, and trade deals. Marketing Science 15 (1), 21–37. Lariviere, M., 1998. Supply chain contracting and coordination with stochastic demand: a review. In: Tayur, S., Magazine, M., Ganeshan, R. (Eds.), Quantitative Models for Supply Chain Management. Kluwer, Boston, MA. Martinez-Jerez, F.A., Narayanan, V., 2007. Strategic Outsourcing at Bharti Airtel Limited. Harvard Business School Case 9-107-003. McAfee, R., McMillan, J., Whinston, M., 1989. Multiproduct monopoly, commodity bundling, and correlation of values. Quarterly Journal of Economics 114 (May), 71–84. McGuire, T., Staelin, R., 1983. An industry equilibrium analysis of downstream vertical integration. Marketing Science 2, 161–191. Moorthy, K.S., 1984. Market segmentation, self-selection, and product line design. Marketing Science 2, 288–308. Mussa, M., Rossen, S., 1978. Monopoly and product quality. Journal of Economic Theory 18, 310–317. Schmalensee, R.L., 1976. Gaussian demand and commodity bundling. Journal of Business 57 (1), S211–S230. Scott-Joynt, J., 2004. Pc pioneer leaves its history behind, BBC News, 8 December. Shaked, A., Sutton, S., 1982. Relaxing price competition through product differentiation. Review of Economic Studies 49, 3–13. Spengler, J., 1950. Vertical integration and anti-trust policy. Journal of Political Economy 58, 347–352. Tirole, J., 1988. The Theory of Industrial Organization. MIT Press, Cambridge, MA. Tran, M., 1999. Intel becomes a moving target. The Guardian, 8 March. Tsay, A., Nahmias, S., Agrawal, N., 1998. Modeling supply chain contracts: a review. In: Tayur, S., Magazine, M., Ganeshan, R. (Eds.), Quantitative Models for Supply Chain Management. Kluwer, Boston, MA. Villas-Boas, J.M., 1998. Product line design for a distribution channel. Marketing Science 2, 156–169. Wang, Y., 2006. Joint pricing-production decisions in supply chains of complimentary products with uncertain demand. Operations Research 54, 1110–1127.