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Managing Raw Material in Supply Chains
Anupam Agrawal∗
University of Illinois at Urbana Champaign
Cite as: Managing raw material in supply chains, European Journal of Operational Research,
Volume 239, Issue 3, 2014, Pages 685-698. https://doi.org/10.1016/j.ejor.2014.06.012.
Abstract
In this paper, we explore how firms can manage their raw material sourcing better by
developing appropriate sourcing relationships with their raw material suppliers. We detail
three empirical case studies of firms explaining their different raw material sourcing strategies:
(a) firms can adopt a hands-off approach to raw material management, (b) firms can supply
raw material directly to their suppliers, and this may be beneficial for some agents in the
supply chain, and (c) firms can bring their component suppliers together, and the resulting
cooperation between suppliers can be beneficial for supply chain. We then analytically model
the three raw material scenarios encountered in our empirical work, examine the resulting
profits along the supply chain, and extend the results to a competitive buyer scenario. Overall,
our results show that active management of raw material sourcing can add value to supply
chains.
1 Introduction
As businesses focus more and more on cost reduction and fast response, policies on supplier
relationships and sourcing are fast becoming an effective tool for creating value for customers.
Such policies include decisions on purchasing, quality, and process improvement that buyers may
execute in the form of contracts between themselves and the suppliers. Our focus is on a crit-
ical component of sourcing - the raw material (RM). We believe that with increased focus on
core business activities, and the outsourcing of non-core activities, firms have slowly distanced
themselves from some of the sources of value in their sourcing–like managing upstream RM. For
example, in some contexts, like that of an automotive firm, a large number of direct suppliers of
the firm may be buying their RM from the same RM suppliers. In this scenario, building close
relationships with these RM suppliers may be valuable for the automotive firm.
In this paper, we explore how managers can create more value from better managing their
upstream sourcing via (i) empirical studies, and (ii) analytical models. Our results show that a
firm’s active management of RM sourcing can result in a more efficient supply chain.
∗anupam@illinois.edu, phone 1-217-265-0654
The paper is organized as follows: First, we review the extant literature and establish our
motivation for this study. Second, we describe our empirical work comprising case studies of
three firms in three countries. Third, we model three RM sourcing scenarios analytically, anchor
them to empirical findings, and then analyze the interactions between a buyer, its suppliers, and
its RM supplier. We then extend the models to the scenario of a competitive buyer. We conclude
with a discussion of how firms can develop better RM sourcing, the generalizability of our results,
and future research opportunities.
2 Literature and Motivation
Our work is related primarily to the literature in the area of sourcing and buyer-supplier rela-
tionships. Many empirical and modeling studies span this literature, and among these, we can
discern two interesting thoughts of creating value. The first assertion is that firms must operate in
a lean fashion, and move away from the complexity that surrounds them: such focus is beneficial
since it helps in improving efficiency (Masten, 1984). The second assertion is that managing the
complexity in itself could be valuable (Fiol and Lyles, 1985; Helper and Sako, 1995; Nishiguchi,
1994). Our paper is anchored in the latter stream of research – we focus on the complex RM
sourcing of a buyer and how managing this sourcing can be valuable.
Suppliers of a firm can provide valuable information to a firm (Gulati, 1999) and intangible
relationship-specific investments in a firm’s supply network can result in productivity gains in the
supply chain (Dyer, 1996). From a buyer perspective, investments in supply chain relationships
drive long term costs down (Nishiguchi, 1994), and affect new product development routines
(Clark and Fujimoto, 1991; Kim, 2000). Such investments are usually focused at reducing the
future uncertainty of costs, technology and information (Bensaou and Venkatraman, 1995) and
component complexity (Bensaou and Anderson, 1999).
Managing upstream sourcing can help create value in three ways. First, better RM sourcing
can help decrease the manufacturing complexity related to sourced components (Walker and
Weber, 1984; Masten, 1984; Novak and Eppinger, 2001; Parmigiani, 2007). Second, focus on RM
sourcing can help with new product development. When OEM designers have more information
about the RM, they are able to better predict the problems in new product development cycle,
and thereby develop more robust products (Takeishi, 2002; Clark and Fujimoto, 1991; Wynstra
et al., 2010). Finally, better RM sourcing can help reduce costs of sourcing by cost control at the
design stage of components (Monteverde, 1995, Ahmadjian and Lincoln, 2001).
In the modeling studies on buyer-supplier relationships, game theoretic modeling is common,
with a focus on buyer-supplier contracts. Most papers focus on the immediate suppliers of the
firm, usually at the downstream end of the supply chain (Lim, 2001; Baiman et al., 2000; Corbett
et al., 2005; Balachandran and Radhakrishnan, 2005) and for single or multiple periods (Tunca
and Zenios, 2006). Xia and Gilbert (2007) focus on interaction between a manufacturer and a
2
dealer for demand enhancing services, such as sales support. In this paper, in contrast, we model
the upstream end of the supply chain and focus on the raw material sourcing. In this vein, our
paper is closest in motivation to the work of Majumder and Srinivasan (2008), who focus on
supply chain networks.
Bernstein and K¨ok (2009) explore cost reduction via process improvement in an assembly
setting similar to that in this paper. Whipple and Russell (2007) discuss how collaborative trans-
actions, event management, and process management can create value between distributors and
retailers. Wynstra et al. (1999) discuss how value can be created in new product development
process between OEMs, their first tier suppliers and second tier suppliers. Ellram and Billing-
ton (2001) document how an automaker facilitates the raw material supply to its machine shop
contractor. This paper extends this research and explores how developing relationships with raw
material suppliers can create value.
This work is motivated by our empirical investigation into the RM supply chain practices
in the automotive industry. We worked with three OEMs in three different countries: DMV in
Germany, TMV in India, and TDV in South Korea1. We spent many months onsite at each of
these firms. In this paper, we first analyze these three case studies by exploring their RM sourcing
strategies, and then analytically model the three RM sourcing scenarios to generate managerial
insights.
A simple quote from a manager at DMV Germany exemplifies our motivation further. We
asked ”How much aluminum does DMV buy?”. The response was “We do not know. We don’t
need this information since this is not our core competence”. Our studies of the sourcing of DMV
(over many months) showed that the firm is the biggest buyer of aluminum in Germany, but it
does not have a direct relationship with its RM suppliers for its aluminum sourcing (Figure 1).
We found that the raw material information was not part of the decision making at OEM firms
such as DMV. TMV and TDV had different approaches to raw material management: TMV had
initiated direct RM buying for some of its suppliers, whereas TDV had gotten its component
suppliers together and was taking a cooperative approach to managing its raw material supply
chain. Can differential management of raw material supply chain be beneficial for firms? Our
focus in this paper is to study this very real and interesting problem, via three case studies, and
also by using parsimonious analytical models, to explore conditions under which raw material
supply chain management can be beneficial.
1Firm names are altered since we had to enter into confidentiality agreements with these firms, as we were
researching areas in the raw material supply chain, and the variables of study, such as component level prices, are
considered extremely confidential by firms.
3
Supplier 1
Suppl ier 4
Suppl ier 3
Supplier 2
Suppl ier 5
Supplier 8
Suppl ier 8
Supplier 16
Primary Aluminum
Supplier
Recycled Aluminum
Supplies
Adhoc supplies
Supplier 1
Supplier 4
Supplier 3
Supplier 2
Supplier 8
Supplier 8
Supplier 8
Supplier 30
Primary Aluminum
Supplier 1
Recycled Aluminum
Supplies
Inhouse Foundry
Primary Aluminum
Supplier 2
Occasional, adhoc
supplies
Supplier 5
Supplier 1
Supplier 4
Supplier 3
Supplier 2
Supplier 6
Supplier 8
Supplier 8
Supplier 23
Steel Supplier
Supplier 5
A B
C
Figure 1: Ashows the aluminum chain of TMV India. One primary aluminum supplier supplies
raw material for over 500 components supplied by 3 component suppliers and TMV’s inhouse
foundry. Bshows aluminum chain of DMV, Germany. Two primary aluminum suppliers supply
virgin aluminum to 5 vendors and inhouse foundry. Cshows steel chain of TDV Korea, with one
steel supplier supplying 23 component suppliers.
4
3 Three Case Studies on RM Sourcing Management
3.1 DMV’s Strategy - Hands-off RM Management
DMV is a European auto giant and is one of the world’s ten biggest car manufacturers. It has
14 plants worldwide, with six main plants in Germany. We studied DMV’s aluminum sourcing.
DMV’s annual consumption of aluminum is close to 150,000 tons. The firm has thirty aluminum
component suppliers (including its inhouse foundry) who are supplied by Germany’s three main
aluminum suppliers. The sourcing network for aluminum for DMV is shown in Figure 1B.
DMV’s aluminum suppliers, including the inhouse foundry, buy from all three of Germany’s
major aluminum suppliers. DMV’s sourcing network of aluminum is dependent on the technology
used by the suppliers for RM. In Germany, the aluminum component suppliers use molten alu-
minum as input, and a high volume of production is needed to ensure that the molten aluminum
process is viable. More importantly, molten aluminum cannot be transported further than 200 km
without undesirable temperature drop; therefore, it is imperative for component suppliers to be
physically located close to the RM suppliers. For DMV, most component suppliers, including the
inhouse foundry, are within a 200 km radius of the molten aluminum supplier plants. Production
and all the associated processes of DMV aluminum supply are structured around this delivery
model.
The suppliers of DMV make a 15% profit on the raw material and value addition of components
supplied to it. DMV is a significant purchaser of aluminum within Germany, yet it does not have
any direct relationships with its raw material suppliers for its total raw material consumption.
3.2 TMV’s Strategy - Buying RM for suppliers
TMV is an Indian automotive firm. In the earlier years of its raw material supply chain man-
agement, TMV engaged in a hands-off RM management. However, it has now embarked on a
policy of buying RM for many of its suppliers of steel and aluminum components. It now also
purchases RM as a single buyer from the RM suppliers, and manages the logistics, physical sup-
ply, inventories of raw material and disposal or salvage of scrap/offcuts of steel generated in the
manufacturing process at the component suppliers.
The transition from a hands-off to direct RM purchasing was complex (the firm still does not
buy RM for all its suppliers). The firm aligned the RM suppliers, drew up longer-term contracts
and developed processes for physical supply and tracking of raw material at the component suppli-
ers. The input RM, and all the scrap and offcuts generated during the production process, needed
to be tracked. Many of these activities were one-time investments to start the direct purchasing
processes; however, additional work was needed every time a new component was developed.
There were implementation issues related to direct RM purchasing. In India, taxes are levied
on direct transactions between any two parties. This creates some inefficiency in direct purchasing
5
transactions. If TMV wants to directly buy RM, then the material transfer from the RM supplier
to the component supplier needs to be executed in a way that is logistically inefficient – material
has to be transferred to TMV’s ownership and then sent out for processing to the supplier. This
logistical issue is local, and somewhat lowers the benefits that TMV can hope to accrue from
direct RM supplies.
In this direct RM supply strategy, the savings accrue from three modes. First, savings come
from the reduction of margins for the component supplier. The supplier does not have to buy
RM, and therefore, the double marginalization effect on RM purchasing is reduced. Second, direct
purchasing may lead to volume based reductions from the RM suppliers. The third avenue of cost
reduction comes from the differential cost of capital between TMV and its suppliers. TMV sources
its debt internationally and its weighted average cost of capital (WACC) is lower than that of
its suppliers (there is a difference of >3% between WACC of TMV and most of its suppliers).
Therefore, if purchasing is made with TMV capital, it may result in a lower cost to TMV than
purchasing made with the supplier’s capital. This effect is over and above the margin effect of
direct purchasing. TMV estimated that they achieve reductions of >2% over the prevailing
costs for their supplies where they institute direct RM supplies. For TMV, approximately 70% of
the cost of goods sold are related to RM. Additionally, their margins on their finished products
(automotives) are wafer-thin. Therefore such savings on RM are an important part of their cost
management.
In this scenario, the total landed cost of any component can be affected in three ways. First,
when TMV buys RM, then the RM cost for TMV is lower than (or equal to) the RM cost for any
component supplier. Second, for components where RM is supplied by TMV to the component
supplier, double marginalization on the RM is avoided, and this lowers the cost. Finally, TMV
has to invest in managing the RM transactions, and also use its own funds to buy RM, which
increases the cost to TMV. Note that different RM suppliers have different contract setting with
TMV. For example, the supplier of virgin aluminum has long-term (‘evergreen’) contracts while
the contract with recycled aluminum suppliers is open for yearly bidding.
3.3 TDV’s Strategy - Cooperation between suppliers
The raw material supply process at TDV is different from that of DMV, Germany or TMV, India.
The process is collaborative, and involves its RM supplier, as well as all its component suppliers.
The collaborative relationships between suppliers help increase understanding of raw material
sourcing.
On an annual basis, TDV and its suppliers come together and develop the annual production
plan, broken into half-yearly buckets. One of the outputs of this joint working with suppliers is
a detailed raw material plan. The plan is discussed and agreed upon between TDV and the raw
material suppliers. Quarterly and monthly plans are drawn and on a rolling basis, contracts are
6
settled for the following month.
On a monthly basis, the component suppliers work with each other to finesse the production
of components, including components for new products and those needing a joint development.
On a day-to-day operating level, a lot of information is shared between the firm, the component
suppliers and the raw material supplier. TDV manages this information centrally at its purchasing
or sourcing ”hub”. The purchasing hub has sourcing individuals working full-time on sourcing
transactions, including logistics and negotiations. The day-to-day transactions of sourcing run
on a web based system. The specific information available on the system includes details of
production plans for the coming months, new models, changes in drawings, production schedules,
quantity of components required and the quantity and grades of raw material required from the
raw material supplier. This web based information is used by component suppliers as well as raw
material suppliers, and is continually updated.
We have observed that there are two types of fixed costs in setting up RM sourcing for firms
such as TMV and DMV–startup and ongoing. The startup cost relates to the detailing of raw
material at component level and establishing a material database so that raw material supply is
streamlined. The raw material level details at the component bill of material level are not a part
of the day-to-day operations at other OEMs that we studied (such as DMV). In order to develop
such a database, the OEM has to collate accurate raw material information—grades, weights and
sources of material—for each component. This is not easy, but once in place, the database is an
invaluable source for raw material-related knowledge.
The ongoing cost consists of managing RM sourcing–developing periodic (frequently monthly)
schedules, linking supply with the payment cycle to the raw material and component suppliers, and
auditing the inventory. Our study of the TMV and TDV’s RM sourcing shows that the ongoing
costs of managing RM sourcing are insignificant compared to its cost savings— for example, TMV
manages its RM sourcing (for a single raw material, for a single country) with just three full-time
employees, and part-time support from one person in the finance department.
4 Analytical models
In this section, we analyze the strategies for RM sourcing deployed by the three firms we have
studied. We have two assumptions in our models. Our first assumption comes from the obser-
vation that there are very few, and many times only a single raw material supplier to an OEM.
Figure 1 shows three OEM supply chain networks: the current steel supply network of TDV, and
the aluminum supply networks of TMV and DMV. At TMV, over 10,000 tons of aluminum is
transacted in over 500 different components supplied by 4 component suppliers (including inhouse
foundry); and almost all of the virgin aluminum requirement of these four suppliers is supplied
by a single raw material supplier. TDV has a single steel supplier who supplies the raw material
needs of all its component suppliers. DMV has only three primary aluminum suppliers supplying
7
its aluminum needs. We abstract this empirical result in our models and consider only a single
raw material supplier.
The second assumption comes from the observation that at the supplier level, material flows
are fungible by an OEM, and therefore study of raw material flows for a single OEM can provide
insights which are similar to that of a network in which multiple OEMs are participating. Consider
an OEM such as TDV, and its brakes supplier. For their new truck, TDV’s development engineers
sit with the supplier’s manufacturing engineers to develop detailed specifications for the brake,
which will go into the truck that TDV wants to produce (call it Z). As plans develop, the brake
system for Z is broken into component level details that are used for detailed drawings. Usually,
the supplier takes over at this point, and starts the process of developing the Z brake system.
The component drawings, arising out of specifications for Z, are unique to Z. Next, the supplier
generates new part numbers and a detailed bill of material for the Z brake system. The bill of
material will have some small components that are common to other brake systems (for TDV
or another OEM): however, the sizes and specifications of material, the forgings, castings, and
machining tolerances, will be specific to Z. This pattern is repeated when TDV develops a variant
(“New Z”). Different brakes will be needed for TDV’s different trucks, requiring fresh development
by the supplier, and culminating in specific bills of materials for TDV’s specific truck models.
Thus, at the level of component supplier, bills of material for customer-specific, model-specific
products are available. Even when firms such as TDV and TMV have platform developments,
blurring the model-level details at component level, there is little commonality in components
used by different OEMs. The OEM level raw material supply chain is fungible. Therefore, we
can study the raw material chain for a single OEM, and should be able to generate insights which
are similar to that of a network in which multiple OEMs are participating. We therefore model
the raw material supply network as a single raw material supplier, ncomponent supplier, single
OEM setup, exactly similar to TDV’s steel supply chain setup. We relax this second assumption
in section 6, where we explore the case of competitive buyers.
We explore three facets of the raw material supply chain. We first study the hands-off strategy
of DMV. This setup is similar to a three stage chain - the RM supplier supplies to a number of
component suppliers, who then supply to the OEM. DMV’s strategy provides an interesting base-
case scenario with which we can compare and contrast other strategies.
We then study how OEMs and their suppliers can benefit from managing the RM supply
chain. We explore TMV’s strategy – an OEM buys raw material for its suppliers – and analyze
how relationships with raw material suppliers can bring in opportunities for value creation.
Finally, we explore TDV’s strategy - how can an OEM benefit by initiating cooperation between
suppliers? While cooperative game theory models in sourcing arena are well known (e.g. Kohli
and Park,1989; Reyniers and Tapiero, 1995), we explore a hitherto unexplored variation, where the
component suppliers of a buyer cooperate between themselves to streamline the RM operations,
8
while the OEM merely provides a platform for collaboration. Our analysis shows that such active
management of RM sourcing by the OEM can be beneficial for the OEM, the component suppliers
and the raw material supplier. Our model differs from those in the literature in that we explore
how cooperation between suppliers, managed by an OEM, can create value for the supply chain.
Moreover, we model the interaction with the raw material supplier, which is our key motivation
in this paper.
In what follows, we model the three RM sourcing scenarios - hands-off RM sourcing, direct
RM supply, and cooperation between suppliers. Our focus is on exploring how profits of agents
in the supply chain change depending on the situations of RM sourcing and cooperation between
agents. We assume that the OEM operates in a market with linear demand, and gets components
from nsuppliers. These nsuppliers get their raw material from a single raw material supplier and
supply unique (yet complementary) components that go into the buyer’s final product. Although
our context is the automotive industry, the model is general enough to apply to any industry that
has an assembly process for the final product, (e.g., digital equipment or apparel).
4.1 Modeling DMV’s Hands-off RM Sourcing
To model DMV’s hands-off sourcing strategy, we assume that the buyer OEM faces the demand
curve q= (a−Pm
b) in the market, where Pmis the market price. The linear demand assumption is
consistent with the literature (Bulow 1982, Weng 1995) and enables us to develop a parsimonious
model of raw material supply chain decisions, but the generalizability of the results to nonlinear
demand functions is a question of future research.
The OEM’s own manufacturing and assembly costs are vm.The ncomponent suppliers supply
unique components, i= 1,2, ..., n, which go into the final product made by the buyer. We use the
subscript ito denote the component suppliers as well as their components. Supplier isupplies
λicomponents per unit of final product produced. Thus for quantity qof final product sold in
the market, Pn
i=1 λiqamount of input components are consumed. Each unit of component i
consumes θiamount of raw material. Component supplier isupplies its components at price Pito
the buyer. The component suppliers get the raw material from a single raw material supplier at
rates ci, have variable costs viand fixed costs Fi.While ciis the price of raw material sourced by
component supplier i,videnotes the value that component supplier icreates by working on the
raw material. In doing so, component supplier iuses machines and processing equipment, and Fi
denotes all these costs that are fixed in nature. The raw material supplier has a cost crper unit of
raw material produced. Under this scenario, the profit functions can be defined for the OEM as
Πm=q(Pm−Pn
i=1 λiPi−vm),for the component supplier ias Πi=λiq(Pi−θici−vi)−Fi,and
for the raw material supplier as Πraw =q(Pn
i=1 λiθi(ci−cr)) .The buyer’s choice is consumer
price Pmunder contracts with component suppliers. Figure 3 shows this scenario.
We assume the following sequence of events: First, the raw material supplier announces a price
9
Component
Supplier 1
Component
Supplier 2
Market
Pm=a- (qb)
Price Pm
Quantity q
Price P1
Quantity 1q
Price P2
Quantity 2q
Raw
Material
Supplier OEM
Price Pn
Quantity nq
Component
Supplier n
per unit RM cost c1
per unit RM 1
per unit RM cost cn
per unit RM n
per unit RM cost c2
per unit RM 2
Figure 2: The Model: one RM supplier, ncomponent suppliers and one buyer (OEM )
schedule ci.Then component supplier ichooses price Pi.Finally the manufacturer chooses the
consumer price (or quantity). The game is solved by backward induction. This setup is similar to
that of DMV, and is aligned with our two assumptions - a single RM supplier supplies to many
component suppliers, and these component suppliers supply to a single OEM. Since the OEM
sees the demand q= (a−Pm
b), his problem is
max
Pm
(a−Pm
b)(Pm−Xn
i=1 λiPi−vm)].(1)
Then, the answer to the OEM’s problem is
P∗
m=a+Pn
i=1 λiPi+vm
2, q =a−Pn
i=1 λiPi−vm
2b.(2)
Hence, the component supplier i’s problem becomes
max
Pi
λi(a−Pn
i=1 λiPi−vm
2b)(Pi−θici−vi)−Fi.(3)
Now for component supplier i, the first order condition is
∂Πi
∂Pi
=λi(Pi−θici−vi)∂q
∂Pi
+qλ
i
=λiq−λi
2b(Pi−θici−vi)= 0
10
so a−vm−Pn
i=1λiPi
2b=λi(Pi−θici−vi)
2b.
This algebraic manipulation gives us the best response of component supplier i, assuming that
each supplier responds simultaneously given the action of the other suppliers, as
P∗
i=a−vm+ (n+ 1)λi(θici+vi)−Pn
i=1λi(θici+vi)
(n+ 1)λi
.
Substituting P∗
iinto (2), we get the optimal quantity,
q∗=1
2(n+ 1)b(a−vm−Xn
i=1(λi(θici+vi))).
The raw material supplier’s problem is
max
ci,i=1..n α
2(n+ 1)b(a−vm−Xn
i=1(λi(θici+vi)))Xn
i=1 (λiθi(ci−cr))
However, since the first order condition’s matrix of this system is not full rank, there exists a
family of solutions to this problem, namely
ci=1
λiθia−vm+Pn
i=1λi(θicr−vi)
2−Pn
j=1,j̸=iλjθjcj
c∗
j,j̸=i=cj.
(4)
and therefore ciwill satisfy the following relationship, in addition to the incentive compatibility
constraint of component supplier i
n
X
i=1
λiθici=a−vm+Pn
i=1 λi(θicr−vi)
2.(5)
Thereby, we get
q∗=a−vm−Pn
i=1 λi(θicr+vi)
4(n+ 1)b,(6)
So that Πraw = 2(n+ 1)bq∗2,Πm=bq∗2and Πi= 2bq∗2−Fi, i = 1,2, ..., n. For the total supply
chain, the profits are (4n+ 3)bq∗2−Pn
i=1 Fi.
4.2 Modeling TMV’s Direct RM Supply
In this section we focus on the case where the buyer engages in raw material supply (Figure ??).
The buyer buys the raw material directly from the RM supplier and gives it to the component
suppliers. We assume that cis a constant material cost from the RM supplier.
In line with the observations in the case study, we model three additional conditions. First, the
component suppliers’ fixed costs are reduced because the component suppliers are not purchasing
RM any more, and fixed costs associated with RM procurement reduce. In adition, associated
transaction costs of ordering and procurement decrease. We denote the changed fixed costs of the
component suppliers as Frm
i< Fi, i = 1,2, ..., n.
11
Component
supplier 1
Component
supplier 2
Market Demand
=a- (b )
Price
Quantity
Price
Quantity 1
Price
Quantity 2
Raw
Material
Supplier
OEM
buying
arm OEM
costc
per unit for Raw material
Price
Quantity n
Component
supplier n
per unit RM 1
per unit RM n
per unit RM 2
Figure 3: Modeling TMV’s Raw Material Supply
Second, the buyer incurs costs to set up and operate the RM supply, to develop relationships
with the RM supplier, and to manage the associated transactions associated with buying the RM
(such as delivery of RM to component suppliers, accounting, and scrap recovery transactions).
Let this new fixed cost of the buyer be denoted as Frm. The Frm
iand Frm terms mirror the
concepts of information costs ?or transaction costs ?in economics literature.
The game is akin to having (n+ 1) suppliers, with the last supplier being the raw material
supplier, and the other nsuppliers only having a value added component in their profit functions.
We model the game as a two step game. In the first step, the ncomponent suppliers as well as
the raw material supplier move simultaneously to determine their price levels (of components and
raw material respectively). In the second step, the buyer OEM determines the market price or
quantity. We use the superscript rm for the variables related to this game.
Proposition 1: The RM Supply Game
(a) The equilibrium quantity qrm∗=a−vm−Pn
i=1 λi(cr+vi)
2(n+2)band the component suppliers
prices
Prm∗
i=a−vm+ (n+ 2)λivi−Pn
i=1 λi(θicr+vi)
(n+ 2)λi
, i = 1..n.
(b) The supply chain profits are given as: Πrm∗
raw = 8( n+1
n+2 )2bq∗2,Πrm∗
m= 4(n+1
n+2 )2bq∗2−
Frm,Πr m∗
i= 8(n+1
n+2 )2bq∗2−Frm
i.2(n+ 1)bq∗2
12
Since Frm
i< Fi,the component suppliers have higher profits compared to the hands-off
scenario. The buyer will have higher profits provided that bq∗2((2n+2
n+2 )2−1) > F rm⊡
The value creation in this scenario results from a change in component level pricing. When the
component supplier does not buy the raw material, the working capital used by the component
supplier in its business with the buyer declines. Consequently, the buyer revises the purchase prices
Pito take into account the changed working capital requirement of the component suppliers. We
can understand this by writing the pricing contract of the buyer with its suppliers as follows:
Pi=kici+kiivi, i= 1..n ;ki, kii >1,(7)
where kiand kii are the mark-ups that the buyer provides on the raw material and value-adding
costs viof supplier i. Therefore when raw material supply is initiated, Pidoes not change merely
by cibut by kici−the component prices reduce by an amount greater than the input cost of the
raw material.
The counter intuitive result is that the component suppliers benefit from the policy of RM
supply by the OEM. The reduction in input costs of the component suppliers reduces the marginal-
ization problem of DMV’s hands-off chain to an extent, by moving towards optimal quantity, and
thereby increases profits of some agents. This effect is similar to that discussed in Majumder and
Srinivasan (2008) who show that if the leader is separated from the retailer and manufacturers
by more than one degree, then more marginalization can occur. The fixed costs of setting up the
raw material supply of the OEM (Frm) also affect the buyer’s profits. If these costs are less than
the increased revenue coming from the reduction in mismatch of supply and demand, then RM
supply is a viable option for the buyer.
4.3 Modeling TDV’s Collaborative Scenario
In this section we formulate the RM sourcing problem in a three step hybrid cooperative/non-
cooperative game setting. First, the raw material supplier announces the price for the raw ma-
terial. Then, the ncomponent suppliers bargain cooperatively and determine their component
price levels. Finally the manufacturer determines the market price or quantity.
We model the non-cooperative nodes of the game at the raw material supplier and at the
market frontier. At the component suppliers end, using the Nash bargaining solution, we model a
cooperative game between nsuppliers, who bargain over achievable joint profits. In this bargaining
game between suppliers, we assume that the outside options of the component suppliers are equal
to their non-cooperative profits (hands-off scenario), that is to say that the component suppliers
revert to playing the base-case non-cooperative game if they fail to make the cooperation work.
Why and how does cooperation happen? Cooperation between suppliers leads to a more
efficient, lower cost supply chain, creating higher value. However, as we saw in the TDV case
study, such cooperation does not ”happen” between the component suppliers, but is actively
13
managed by the OEM. Cooperation is not free - TDV incurs costs for managing the cooperation:
to develop relationships between the component suppliers. In our model, we denote this new cost
of the buyer as Fcoop.
Proposition 2 Cooperation between suppliers
(a) The expected cooperative quantity is
qcoop∗=a−vm−Pn
i=1 λi(θicr+vi)
8b=(n+ 1)
2q∗> q∗,(8)
and the intermediate prices for the component suppliers are given by
Pcoop∗
i=1
2nλi a−vm−
n
X
i=1
λivi−
n
X
i=1
λiθici+ 2nλi(θici+vi)!.
(b) The expected buyer profit is
Πcoop∗
m=b(qcoop∗)2−Fcoop,(9)
and the component suppliers’ expected profits are
Πcoop∗
i=b(qcoop∗)2−Fi.(10)
(c) The expected profit of the raw material supplier is
Πcoop∗
raw = 4b(qcoop∗)2.(11)
(d) When n > 2, qcoop∗> qrm∗> q∗, and the game results in the following relations
Πcoop∗
raw >Πrm∗
raw >Π∗
raw ,Πcoop∗
i>Πrm∗
i>Π∗
i,Πcoop∗
m>Π∗
m, i = 1..n. (12)
Therefore,
•The component suppliers as well as the raw material supplier in the cooperative scenario
have a higher profit compared to the hands-off RM supply or the direct RM supply scenario
•The buyer OEM has a higher profit in the cooperative scenario compared to the hands-off
RM supply scenario, and can have a higher profit compared to the direct RM supply scenario
if Fcoop < F rm ⊡
In our analysis above, we have ignored the possibility of cooperation among a subset of
suppliers—what happens when some suppliers would like to break away? In other words, is
the cooperation within suppliers a stable solution concept?
Let us now suppose that a subset of suppliers with n−mmembers wants to break away from
the central coalition, which is managed by the buyer. Let the original coalition be denoted by
Aand the breakaway coalition by B. Then, there are mmembers left in the coalition managed
14
by the buyer. We note that irrespective of this breakup, the members of Bneed to produce the
quantity being produced by A, since it is the quantity for the assembly process at the OEM. In
this scenario, we get the following results
Proposition 3 Breakaway groups
(a) The quantity bargained by both the coalitions (A and B) is
qnew∗=a−vm−Pn
i=1(λiθici+λivi)
6b< qcoop∗
and the intermediate prices for the component suppliers are given by
Pnew
i=(1
3mλi(a−vm−Pm
i=1 λiθici−Pm
i=1 λivi+ 3mλi(θici+vi)) , i ∈A
1
3(n−m)λia−vm−Pn−m
i=1 λiθici−Pn−m
i=1 λivi+ 3(n−m)λi(θici+vi), i ∈B.
(b) The profits made by the members of the two supplier groups are
Πnew∗
i=qnew∗λi(Pnew
i−θici−vi)−Fi, i ∈A, B .
(c) If the total profits made by the two groups of size mand n−mis denoted by
ΠA+B, then
ΠA+B< nΠcoop∗
i∀m
(d) For the two groups
Πnew
i<Πcoop∗
i, i ∈A, Πnew
j<Πcoop∗
j, j ∈B
Therefore,
•The total profit for all the component suppliers goes down whenever a group of suppliers
breaks away,
•The breakaway group as well as the remaining group of suppliers have lower profits compared
to their profits in a single cooperative group ⊡
5 Analysis of RM sourcing strategies
We now analyze the results of the three RM sourcing setups. Table 1 summarizes the profit values
from the various scenarios that we have discussed. Note that q∗(= a−vm−Pn
i=1 λivi−Pn
i=1 λiθicr
4(n+1)b) is
a decreasing function of the number of suppliers, n.
Game RM Supplier Supplier iBuyer OEM
Hands-off 2(n+ 1)bq∗22bq∗2−Fibq∗2
RM Supply 8(n+1
n+2 )2bq∗28( n+1
n+2 )2bq∗2−Frm
i4(n+1
n+2 )2bq∗2−Frm
Supplier Cooperation (n+ 1)2bq∗2(n+1
2)2bq∗2−Fi(n+1
2)2bq∗2−Fcoop
Table 1: Summary of firm level profits in different game scenarios
15
Table 1 depicts the supply chain agents’ profits on a common scale of the quantity sold by the
OEM in the hands-off chain (q∗).First, we note that the differences between various scenarios
depend on the number of suppliers, n. Second, q∗is a decreasing function of the number of
suppliers n, and can be extended to a convex domain.
Proposition 4 Number of suppliers and components per supplier
q∗has strictly increasing differences in (n, λi).For λL
i, λH
isuch that λH
i> λL
iand for
nL∈q∗(λL
i) and nH∈q∗(λH
i),we have nH> nL⊡
Proposition 4 says that when suppliers supply more number of items per unit of final product
(λiis higher), then an increase in the number of suppliers has a greater effect on increasing the
optimal quantity compared to a case when the component suppliers supply less items. Alterna-
tively, as component suppliers supply more components per supplier, the value addition provided
by RM supply setup or supplier cooperation setup increases with increasing number of suppliers
Proposition 5 Number of suppliers and RM content in components
q∗has strictly increasing differences in (n, θi).Therefore for θL
i, θH
isuch that θH
i> θL
i
and for nL∈q∗(θL
i) and nH∈q∗(θH
i),we have nH> nL⊡
Proposition 5 says that when the RM per unit of a component is more (θiis higher), then
an increase in the number of suppliers has a greater effect on increasing the optimal quantity
compared to a case when the components use less RM. Alternatively, as RM content in components
increases, the value addition provided by RM supply setup or supplier cooperation setup increases
with increasing number of suppliers
Proposition 6 Number of suppliers and RM costs
The difference in profits for the OEM between the RM supply and the Hands-off
scenario as well as the component supplier cooperation and the Hands-off scenario
has increasing differences in (n, c).Therefore,for cL
i, cH
isuch that cH
i> cL
iand for
nL∈q∗(cL
i) and nH∈q∗(cH
i),we have nH> nL⊡
Proposition 6 says that when the RM cost cis higher, then an increase in the number
of suppliers has a greater effect on increasing the differential profits from implementing a RM
supply scenario compared to a case when the RM costs are low. Alternatively, as the cost of RM
increases, the value addition provided by RM supply setup or cooperation setup increases with
increasing number of suppliers.
Managing RM supply may not be relevant when there is competition at the RM end, or RM
suppliers are changing across dynamic industries for the OEM. This is because on the one hand,
the fixed costs (of developing the infrastructure and relationships required to make the hubs work)
for the OEM’s will escalate, and on the other hand, the prices of RM will fall due to competition
16
of RM supply, thus making cooperation an unattractive proposition for the RM supplier. As a
firm’s sourcing base increases to more suppliers, the cooperation scenario or RM supply scenario
provide additional value with increasing RM content in sourced components.
6 Extension: Two buyers
In this section, we examine what happens when there are two buyers competing for the same
inputs and who engage in Cournot competition at the market end. In a Cournot competition
scenario, players make their quantity decisions independently of each other and at the same time.
Cvsa and Gilbert (2002) model a similar Cournot duopoly game, while Majumder and Srinivasan
(2008) model a Cournot game between supply chains. Such a formulation will help us examine
how RM sourcing can be beneficial in a competitive scenario.
6.1 Hands-off RM Management with two buyers - setup
We assume that there are two buyer OEMs j, j = 1,2, and e
j= 3 −j. The buyers face the demand
curve X= (a−Pm
b) in the market, where Pmis the market price, and X=x1+x2,where xjis
the quantity sold by OEM j. The manufacturing and assembly costs of the OEMs are vmj . The
ncomponent suppliers supply unique components, i= 1,2, ..., n, which go into the final product
made by both the buyers. Each unit of component iconsumes θiamount of RM. Component
supplier isupplies its components at price Pij to buyer j. The component suppliers get the RM
from a single RM supplier at rates ci, have variable costs vij and fixed costs Fij .The RM supplier
has a cost crper unit of RM produced. The variable λiis defined as earlier, so that for quantity
xjof final product sold in the market by OEM j,Pn
i=1 λixjamount of input components are
consumed. We use the symbol Ψ to denote the profits of the supply chain agents in the two buyer
scenario. Under this scenario, the profit functions for buyer jis
Ψjm =max
xjxja−bxj+xe
j−Xn
i=1 λiPi1−vmj , j = 1,2,e
j= 3 −j,
for component supplier iis
Ψi= max
Pi1,Pi2λiX2
j=1 xj(Pij −θici−vij )−X2
j=1 Fij ,for i= 1..n, j = 1,2,
and for the RM supplier is
Ψraw = max
ci
(x1+x2)Xn
i=1 λiθi(ci−cr).
The sequence of events is now different. First, the RM supplier announces a price schedule ci.
Then component supplier ichooses price Pi.Finally the two buyers choose the consumer quantity
by engaging in a Cournot competition at the market frontier.
17
6.2 RM Supply with two buyers - setup
For the RM supply scenario with two buyers, the only change from the hands–off chain is that the
two buyer OEMs get the RM from a single RM supplier at rates cjand give it to the component
suppliers. We use the superscript RM for this setup for the variables. Under this scenario, the
firm level profit function for buyer jis
Ψrm
jm =max
xrm
j xrm
j (a−b(xrm
1+xrm
2)) −cj
n
X
i=1
λiθi−
n
X
i=1
λiPij −vmj !!,(13)
for component supplier iis
Ψrm
i= max
Pi1,Pi2λiX2
j=1 xrm
j(Pij −vij )−X2
j=1 Fij ,for i= 1..n, j = 1,2 (14)
and for the RM supplier is
Ψrm
raw = max
c1,c2X2
j=1 xrm
j(cj−cr)Xn
i=1 λiθi(15)
Similar to the RM supply scenario with a single buyer, we model this game as a two step game.
In the first step, the ncomponent suppliers as well as the RM supplier move simultaneously to
determine their price levels (of components and RM respectively). In the second step, the buyer
OEMs determine the market quantity in a Cournot competition.
6.3 Cooperation between suppliers with two buyers - setup
The cooperative scenario is also complex. We assume that both buyers are operating cooperative
sourcing ”hubs” with the same suppliers, and the same raw material supplier. The profit function
for buyer jthen is
Ψcoop
jm =max
xjxja−bxcoop
j+xcoop
e
j−Xn
i=1 λiPi1−vmj −Fcoop, j = 1,2,e
j= 3 −j,
(16)
for supplier iis
Ψcoop
i= max
Pi1,Pi2λiX2
j=1 xcoop
j(Pij −θici−vij )−X2
j=1 Fcoop
ij ,for i= 1..n, j = 1,2,(17)
and for raw material supplier is
Ψcoop
raw = max
ci
(xcoop
1+xcoop
2)Xn
i=1 λiθi(ci−cr).(18)
The sequence of events is again different from the deterministic case. First, the RM supplier
announces the price for the RM. Then, the ncomponent suppliers bargain cooperatively and
determine their component price levels. Finally the two buyers compete on quantity.
18
6.4 The Two Buyer Scenario - Results
The proofs of the above two games are involved, and are presented in the Appendix. For notational
convenience, define
Υ =
n
X
i=1
λivie
j−
n
X
i=1
λivij +vme
j−vmj
If the two buyers have the same variable cost, and get inputs at the same total cost, then Υ = 0.
Proposition 7 Two buyer Scenario
(a) The optimal quantities in the three setups are:
x∗
j=2a−2vmj −2Pn
i=1 λi(θicr+vij ) + 5Υ
12b(n+ 1) , xrm∗
j=a−vmj −Pn
i=1 λi(θicr+vij )+Υ
3b(n+ 2) ,
xcoop∗
j=2a−2vmj −2Pn
i=1 λi(θicr+vij ) + 5Υ
24b.
(b) The firm level profits for the supply chain agents in different game scenarios are
as follows
Game RM Supplier Supplier iBuyer j
Hands-Off 3b(n+ 1)( P2
j=1 x∗
1)22b(P2
j=1 x∗2
j+x∗
1x∗
2)−P2
j=1 Fij bx∗2
j
RM Supply 2b(P2
j=1 xrm∗2
j+xrm∗
1xrm∗
2) 2b(P2
j=1 xrm∗2
j+xrm∗
1xrm∗
2)−P2
j=1 Frm
ij bxrm∗2
1−Frm
Cooperation 4b(P2
j=1 xcoop∗
j)22b
n(P2
j=1 xcoop∗2
j+xcoop∗
1xcoop∗
2)−P2
j=1 Fcoop
ij bxcoop∗2
1−Fcoop
Table 2: Summary of firm level profits in different game scenarios for two buyers
(c) If buyers j, j = 1,2,have the same variable cost, and get inputs at the same total
cost (Υ = 0), then x∗
j=2
3q∗, xrm∗
j=2
3qrm∗, xcoop∗
j=2
3qcoop∗.The introduction of
the second buyer improves the total quantity sold in the market, but each buyer sells
less than that in a monopoly situation. However, under these conditions (Υ = 0), for
n > 2, profit for buyer jin the cooperative scenario under competition is better than
its profit under the hands-off chain (Ψcoop
jm (Υ = 0) >Πm=bq∗2). So buyers can earn
more profits under competition with a cooperative scenario, than if they were operating
as a hands-off monopoly.
(d) For buyer j, the difference in buyer profits between the cooperative sourcing setup
and the hands-off chain setup Ψcoop
jm −Ψj mhas strictly decreasing differences in
(vie
j, θi). Therefore, for vL
ie
j, vH
ie
jsuch that vH
ie
j> vL
ie
jand for θiL∈Ψcoop
jm (vL
ie
j) and
θiH∈Ψcoop
jm (vH
ie
j),we have θiH< θiL.In words, when the competitor buyer can source
components from suppliers at a lower cost per unit of final product, then an increase
in the amount of RM used per component has an increasing effect on the difference
in profits between the two setups. So, as sourcing becomes more RM dominant, the
effect of competitive intensity reduces under cooperative sourcing operations.
19
7 Discussion
In this paper, we detail how buyers can capture value from their RM supply chain. We first detail
case studies of three OEM firms and explore how these firms manage their current RM supplies.
DMV prefers a hands-off strategy in managing its RM. TMV buys the RM and supplies the same
to its component suppliers: this helps the firm in overcoming the double marginalization on the
RM used in its components, in addition to a lower purchase price of the RM. The third firm,
TDV, brings its suppliers together to facilitate interaction between them. Such interaction helps
disseminate information about market demand, production schedules, new product introduction,
and cost reduction.
We then use the empirical observations of DMV, TMV, and TDV to model our single buyer,
ncomponent suppliers, single RM supplier setup assuming a linear demand function. In our
models, we divide the product cost into the RM and value added components. Our results com-
plement existing results in the outsourcing literature by focusing on the lesser explored RM part
of the outsourced components, by showing that firms can benefit from superior RM contracting
arrangements.
Our analysis shows that the OEM and its suppliers may have motivation for initiating supply
of RM directly from the RM supplier. However, the possible benefits accruing to the OEM and
the component suppliers may result from a reduction of the profits of the RM supplier. Therefore
the raw material supply scenario may be beneficial for only some members of the chain. Note that
we have not assumed any ‘buyer power’ effect in our models, and all results are valid irrespective
of the volume purchasing discounts that can be negotiated by a powerful upstream buyer.
The OEM can initiate cooperation between suppliers, and our analysis shows that such active
management of upstream sourcing by the OEM can be beneficial for RM supply management.
Cooperation can also lead to exchange of ideas on design as well as process improvements between
the component suppliers and the OEM.
A related aspect of these operating scenarios of RM sourcing is the change in the fixed costs of
the component suppliers and the OEM. For initiating RM supply management, the OEM needs to
invest in creating a material database at component level. This is not easy, since it means revisiting
the bill of material for all components; however, once completed, such a material database acts
as an important competitive lever. It helps promote relationships with RM suppliers, since the
OEM can identify its current RM requirements and project its future purchases in a much easier
and more efficient way. Thus strategic partnerships with RM suppliers can be built up, based
on deep knowledge of the RM. The relationship between TDV and TMV’s RM suppliers and the
firm is built up on the basis of detailed, bill of material level data.
At TMV, our continuing studies show how RM supply practice drives complexity reduction. As
the RM supply was initiated, TMV’s sourcing engineers went back to their designer counterparts
and had discussions about a reduction in the number of grades of aluminum being put on the
20
engineering drawings. This process helped in eliminating a number of grades of aluminum for
TMV. This, in turn, helped the aluminum supplier, since he had to produce less number of grades.
For another RM (steel), the supplier executives discussed how long-term relationships are more
important than short term prices. They told us, ”Volumes are not the main thing. Relationship
with a component supplier is usually short term in nature. Our pricing is related to relationships
with the customers, and we differentiate between OEMs and other second tier customers. Volumes
are important, but relationships override everything else.” When we queried them further as to
why volumes would not affect their input costs, they replied, ”You see, costs are not dependent on
individual customer volumes after a base level. As long as firms procure standard products from
us, our costs are really the same for TMV as for another buyer. Costs reduce by having a detailed
plan and leveled production. That only comes from our OEM customers, because their plans do
not vary too much for the next two months.” Essentially, the RM supplier argument seemed to be
that the RM demand from the OEM has a lower variation since the demand is pooled over all its
component suppliers, and also employs a longer time frame. Due to both these effects, demand
is less volatile, and the RM supplier benefits from reduced costs arising out of a better matching
of supply and demand.
What is the extent of savings that can accrue to different agents? The exact answer depends
on the relationship between the raw material and the fixed costs of the OEM and the component
suppliers. Our empirical research shows that direct RM purchasing and cooperative sourcing can
lead to savings of 3% −6% on the costs of raw material for the OEM. This is a huge benefit,
considering that RM costs amount to over 50% of the cost of goods sold for automotive OEMs
and the margins on the auto products are very low.
RM sourcing is a new concept that can help firms create value from upstream sourcing and
recapture some of the value that has been lost in the race to become a lean manufacturer. As we
have detailed, firms have started using it. Indeed, TMV is now changing its supply chain structure
to initiate RM sourcing for all its supplies, and build closer relationships with its suppliers and
its RM suppliers. Such sourcing is also robust under competitive scenarios.
There is a knowledge related effect of RM sourcing that we have not detailed in this paper. As
firms outsource more and more, in-house competence may diminish in areas that are outsourced.
A reconfiguration of the supply network may provide opportunities for the OEM to revisit these
sources of knowledge. As closer relationships are built in at RM level there may be opportunities
for developing and harnessing knowledge at primary process levels like forging and casting. For
example, one of the component suppliers to the OEM firms that we studied had an inhouse
aluminum foundry when it started interacting with the OEM. The designers had access to foundry
operations and had knowledge about the raw material and the related interactions with the final
product. As time progressed, this supplier firm focused on its design and assembly competencies at
the product level, and outsourced the foundry and machining operations, along with a lot of related
21
design work. The problem came when the foundry operations of some major castings were to be
shifted to China, to reduce cost. The supplier discovered that they no longer had the capability to
understand the intricacies of the foundry operations. This capability had been eroded over time,
as purchasers sourced machined sub components, and the machined sub component suppliers
sourced raw castings from established foundries. This experience helped the firm appreciate the
benefits of developing and maintaining knowledge about component design and raw material at
a process level. RM management can help in developing and deploying such knowledge practices
(See also Ferdows, 1997).
In this paper, we have not detailed processes related to knowledge creation due to RM sourcing,
as detailed in the above example. Furthermore, as the knowledge base about suppliers and
sourcing increases, the same can develop into a powerful center for streamlining new product
development by sharing process information —however this exciting area is not covered in this
paper. We have also not looked at modeling cooperative interaction under other scenarios such
as different demands, or non-assembly supplier networks. These areas provide interesting avenues
of research for us in the area of buyer-supplier relationships.
Acknowledgements
I am indebted to the managers at TDV, TMV and DMV for helping me explore raw material
sourcing concepts. This research would not have been possible without the constant guidance
of Prof. Luk Van Wassenhove (INSEAD) and Prof Arnoud De Meyer (Singapore Management
University). Both of them have continuously guided me, they have travelled with me to the firms
mentioned in this paper to discuss RM sourcing, and they have been instrumental in developing
the concept of raw material supply chain management. This work was generously supported by
the INSEAD Alumni Fund. Tianqin Shi helped with developing a part of the solution to the
two-buyers problem.
22
Appendix
Proof of Proposition 1
Proceeding just like in the Hands-off case,
qrm∗=a−vm−cPn
i=1 λiθi−Pn
i=1 λiPrm
i
2b(19)
Component supplier ihas profit function Πrm
i, where
Πrm
i=λiqrm(Pr m
i−vi)−Frm
i(20)
For the raw material supplier
Πrm
raw =qrm (c−cr)
n
X
i=1
λiθi(21)
Our focus variables are now Prm
iand c. In this game, the raw material supplier and compo-
nent suppliers move simultaneously to determine their price levels (price for the raw material
supplier is c). The first order conditions for maximization of the two profit functions, (20) and
(21) gives us a symmetric system and we get the following results,
c∗=1
(n+ 2) Pn
i=1 λiθi a−vm−
n
X
i=1
λivi+ (n+ 1)
n
X
i=1
λiθicr!
Prm
i=1
(n+ 2)λi a−vm+ (n+ 2)λivi−
n
X
i=1
λivi−
n
X
i=1
λiθicr!
whence from equation (19), we get the equilibrium quantity as
qrm∗=a−vm−Pn
i=1 λi(θicr+vi)
2(n+ 2)b= 2q∗n+ 1
n+ 2> q∗∀n≥1.(22)
Other results follow.
Proof of Proposition 2
In the noncooperative stage, the buyer maximizes profit, or
Πm= max
Pm q(Pm−
n
X
i=1
λiPi−vm)−Fcoop!
For the concave problem, first order condition gives
Pm=a+vm+Pn
i=1 λiPi
2, q =a−vm−Pn
i=1 λiPi
2b
We will first detail the non-cooperative profits of such a scenario. Component supplier imax-
imizes his profit Πi. Using backward induction, and following the same sequence of analysis
as used to derive (6), we get the resultant expected quantity
q∗=a−vm−crPn
i=1 λiθi−Pn
i=1 λivi
4(n+ 1)b.(23)
23
Now, the component suppliers bargain cooperatively. Assuming that the outside options of
all suppliers are equal to their non-cooperative profits (Π∗
i)and in the cooperative bargaining
phase, the component suppliers try to maximize the joint utility, we get the Nash bargaining
solution
N= max
Pi,i=1..n
n
Y
i=1
(Πcoop
i−Π∗
i) (24)
The Nash product is then equal to
N= max
Pi,i=1..n
n
Y
i=1
(λiq(Pi−θici−vi)−2bq∗2)
From the Pareto optimality property of the Nash Bargaining solution, the maximum of the
Nash product will occur at a qcoop∗such that
qcoop∗∈arg max
q∈QX
i∈L
((λiq(Pi−θici−vi)−2bq∗2)
where Qis the set of all feasible quantities. Since the threat options are given, this condition
reduces to
qcoop∗∈arg max
q∈Q
n
X
i=1
λiq(Pi−θici−vi).(25)
For symmetry of the Nash bargaining solution we must have
Πi(qcoop∗)−Π∗
i= Πj(qcoop∗)−Π∗
j, j ̸=i
which gives us the condition that
λi(Pi−θici−vi) = λj(Pj−θjcj−vj), j ̸=i(26)
Utilizing the conditions of equation (26), the result from the first stage in equation (23) and
the conditions of equation (25) we get, after some algebra,
Pi=1
2nλi a−vm−
n
X
i=1
λiθici−
n
X
i=1
λivi+ 2nλi(θici+vi)!
therefore, the optimal quantity is
qcoop∗=a−vm−Pn
i=1 λiPi
2b=a−vm−Pn
i=1 λiθici−Pn
i=1 λivi
4b
Now, for the raw material supplier,
Πraw =qcoop∗(
n
X
i=1
λiθici−
n
X
i=1
λiθicr)
where cris the production cost of the raw material supplier. We get from first order condition
n
X
i=1
λici=a−vm+Pn
i=1 λi(θicr−vi)
2(27)
24
so
qcoop∗=a−vm−Pn
i=1 λi(θicr+vi)
8b
and therefore
Πraw = 4bqcoop∗2(28)
Other results follow.
Proof of Proposition 3
(a) For any supplier i, of either coalition,
Πi=λiq(Pi−ci−vi)−Fi(29)
For the buyer, at the market front,
Πm= max
Pm
q(Pm−X
i∈A
λiPi−X
i∈B
λiPi−vm)
First order condition gives as in the base case
Pm=a+vm+Pi∈AλiPi+Pi∈BλiPi
2
The noncooperative expected profits are given as
EΠ∗
i= 2bq∗2−Fi(30)
In the cooperative bargaining phase, the component suppliers try to maximize the joint utility,
and we get the Nash bargaining solution for the two coalitions
NA= max
Pi,i=1..m Y
i∈A
(Πi−Π∗
i), NB= max
Pi,i=1..n−mY
i∈B
(Πi−Πcoop∗
i) (31)
Note that the outside option for the coalition A is just the decentralized chain profit, while
for coalition B, we take the outside option as the profit that the members can achieve if they
were in the original coalition. The Nash products are then equal to
NA= max
Pi,i=1..m
m
Y
i=1
(λiq(Pi−θici−vi)−2bq∗2), NB= max
Pi,i=1..n−m
n−m
Y
i=1
(λiq(Pi−θici−vi)−bqcoop∗2)
From the Pareto optimality property of the Nash Bargaining solution, the respective maxi-
mums of the Nash product will occur at qA∗and qB∗such that
qA∗∈arg max
q∈QX
i∈A
((λiq(Pi−θici−vi)−2bq∗2),
qB∗∈arg max
q∈QX
i∈B
((λiq(Pi−θici−vi)−bqcoop∗2).
25
where Qis the set of all feasible quantities. Since the threat options are given , these conditions
reduce to
qA∗∈arg max
q∈QX
i∈A
λiq(Pi−θici−vi), qB∗∈arg max
q∈QX
i∈B
λiq(Pi−θici−vi).(32)
for symmetry of the Nash bargaining solution we again end up with the following condition
for both coalitions
λi(Pi−θici−vi) = λj(Pj−θjcj−vj), j ̸=i, i, j ∈A, B (33)
Now consider that coalition B is the ‘breakaway’ coalition. The buyer produces the product
which demands an assembly operation. Hence, the weighted quantities from all suppliers must
be same - or there can be a single quantity of the final product produced. We take qnew∗
as the quantity of final product. Therefore, all members of both coalitions produce the exact
quantity needed, and by the above condition, get exactly the same contributions from business.
Utilizing the conditions of (33), the result from the first stage in equation (23) and the condi-
tions of equation (32), we get, after some algebra,
Pi=
1
3mλia−vm−Pm
j=1,j̸=iλjθjcj−Pm
j=1,j̸=iλjvj+ (3m−1)λi(θici+vi), i ∈A
1
3(n−m)λia−vm−Pn−m
j=1,j̸=iλjθjcj−Pn−m
j=1,j̸=iλjvj+ (3(n−m)−1)λi(θici+vi), i ∈B
(34)
(b) Now
qnew∗=
a−vm−1
3mPm
i=1 (a−vm−Pm
i=1 λiθici−Pm
i=1 λivi+ 3m(λiθici+λivi)) −
1
3(n−m)Pn−m
i=1 a−vm−Pn−m
j=1,j̸=iλjθjcj−Pn−m
j=1,j̸=iλjvj+ (3(n−m)−1)λi(θici+vi)
2b
= (a−vm−Pn
i=1 λi(θici+vi)
6b)
Also
Πraw =q
n
X
i=1
λiθi(ci−cr)
so, n
X
i=1
λiθici=a−vm+ 4 Pn
i=1 λi(θicr−vi)
8(35)
therefore
qnew∗=a−vm−Pn
i=1(λiθici+λivi)
6b=q∗(n+ 1)
3(36)
and the results follow. For (c) and (d), note that the profits made by a member of any of the
groups is
ΠA,B
i=λiqnew∗(Pi−θici−vi), i ∈A, B
= (qnew∗)2
after some algebra from equations (34) and (36). Since qnew∗< qcoop∗,the results follow.
26
Proof of Proposition 7
Hands-off RM Management
Utilizing Cournot competition analysis, we get the Nash equilibrium quantities for the two
buyers as
xj=1
3ba−2Xn
i=1 λiPij +Xn
i=1 λiPie
j−2vm1+vme
j(37)
From (37) and first order conditions of (17), we get after some rearrangement
a−2Xn
i=1 λiPij +Xn
i=1 λiPie
j−2vmj +vme
j=λiPie
j+λiθici−λivie
j+2λi(Pij −vij ) (38)
Summing up over iin (38), and rearranging, we get
Xn
i=1 λiPij =1
n+ 1(Xn
i=1 λi(θici+vij )−nvmj +na) (39)
The above is a system of nequations in nunknowns, and has a symmetric solution - the Nash
equilibrium Pij . Putting in expressions for buyer’s price and quantity, we get the equilibrium
quantities as
Pij =θici+vij +1
(n+ 1)λi
(a−vmj −Xn
i=1 λi(θici+vij )) (40)
The last equation is obtained using (39). Add (37), combined with (39), we get
x1+x2=1
3(n+ 1)b2a−(vm1+vm2)−Xn
i=1 λi(2θici+vi1+vi2)(41)
Now the first order conditions for the profit maximization by RM supplier for its problem in
(18) gives
n
X
i=1
λiθici=1
42a−(vm1+vm2)−Xn
i=1 λi(−2θicr+vi1+vi2),whence (42)
Π∗
raw = 3(x1+x2)2(n+ 1)b= 3X2(n+ 1)b.
Recalculate (37) using (40),
xj=1
12b(n+ 1)[2a−2
n
X
i=1
λiθicr−7
n
X
i=1
λivij +5
n
X
i=1
λivie
j−7vmj +5vme
j].(43)
Therefore we can get after some algebra,
Πi=1
(n+ 1) x1(3b(n+ 1)x1+b(n+ 1)(x2−x1))
+x2(3b(n+ 1)x2+b(n+ 1)(x1−x2)) !
and the results follow. Again, the firm level profit function for buyer firm 1is
Π∗
1m=−bx1(x1+x2)+ x1
4(n+ 1) 2a−3vm1+vm2−3
n
X
i=1
λivi1+
n
X
i=1
λivi2−2
n
X
i=1
λiθicr!
27
using (39) and 42. Using (43), we have
2a−3vm1+vm2−3
n
X
i=1
λivi1+
n
X
i=1
λivi2−2
n
X
i=1
λiθicr
=(x1+x2)6(n+ 1)b+ 2(x1−x2)(n+ 1)b
and the results follow.
RM Supply
The supplier profit function for supplier iis in (14), and for the RM suppliers is in (15). In
this game, the RM supplier and component suppliers move simultaneously to determine their
price levels. Plugging in (37) to (15), we get from first order conditions for firm j, j = 1,2
and e
j= 3 −j,
(−4cj+ 2ce
j)Xλiθi+crXλiθi+a−2XλiPij +XλiPie
j−2vmj +vme
j= 0
whence,
ci=1
2Pλiθi
(a+crXλiθi−XλiPi1−vmi).(44)
Also, using (37) in (14), we get from first order conditions,
2λi(Pij −vij )−λ(Pie
j−vie
j) = a+ (ce
j−2cj)Xλiθi+XλiPie
j−2Pij −2vmj +vme
j
(45)
whence
Pij =vij +1
λi
(a−cjXλiθi−XλiPij −vmj ) (46)
and therefore we get
XλiPij =1
(n+ 1) Xλivij +na −ncjXλiθi−nvmj (47)
Thus we can recalculate (44) as
ci=1
(n+ 2) Pλiθia−vmi −Xλivij + (n+ 1)crXλiθi(48)
Plugging in (48) and (47), (46) can be rewritten as
Pij =1
(n+ 2)λi a−vmj + (n+ 2)λivij −
n
X
i=1
λivi−cr
n
X
i=1
λiθi!(49)
Recalculating (47)
XλiPij =1
(n+ 1) Xλivij +na −n1
(n+ 2) a−vmj −Xλivij + (n+ 1)crXλiθi−nvmj
=1
(n+ 2) 2Xλivij +na −ncrXλiθi−nvmj
28
Recalculate (37) using the above result, we get
xj=a−2vmj +vme
j−crPn
i=1 λiθi−2Pn
i=1 λivij +Pn
i=1 λivie
j
3b(n+ 2) (50)
Note that by (50),
a−vmj −Xλivij −crXλiθi=b(n+ 2)(2xj+xe
j),and
Pij −vij =1
(n+ 2)λi a−vmj −
n
X
i=1
λivi−cr
n
X
i=1
λiθi!=b
λi
(2xj+xe
j)
whence the results follow.
Supplier Cooperation
Utilizing Cournot competition analysis, we get for buyer j, j = 1,2and e
j= 3 −jthe Nash
equilibrium quantities,
xj=1
3b a−2
n
X
i=1
λiPij +
n
X
i=1
λiPie
j−2vmj +vme
j!,whence (51)
n
X
i=1
λiPij =a−2bxj−bxe
j−vmj .(52)
The supplier profit function for supplier iis
Πi= max
Pi1,Pi2
λi(x1(Pi1−θici−vi1) + x2(Pi2−θici−vi2)) −X2
j=1 Fij (53)
For the concave three stage problem of the RM supplier, we get
x∗
j=1
12b(n+ 1)[2a−2
n
X
i=1
λiθicr−7
n
X
i=1
λivij + 5
n
X
i=1
λivie
j−7vmj + 5vme
j],
Now, the component suppliers bargain cooperatively. Note that Π∗
i= 2b(x∗2
1+x∗
1x∗
2+x∗2
2)−
P2
j=1 Fij .Proceeding as in the proof for Proposition 2, we get the Nash product as
N= max
Pi1,Pi2,i=1..n
n
Y
i=1 λi(x1(Pi1−θici−vi1) + x2(Pi2−θici−vi2))
−2b(x∗2
1+x∗
1x∗
2+x∗2
2)!(54)
From the Pareto optimality property of the Nash Bargaining solution, the maximum of the
Nash product will occur at (xcoop∗
1, xcoop∗
2)such that
(xcoop∗
1, xcoop∗
2) = argmax
(x1,x2)∈Q
n
X
i=1 λi(x1(Pi1−θici−vi1) + x2(Pi2−θici−vi2))
−2b(x∗2
1+x∗
1x∗
2+x∗2
2)!
(55)
where Qis the set of all feasible quantities. Since the threat options are given, this condition
reduces to
(xcoop∗
1, xcoop∗
2) = argmax
(x1,x2)∈Q
n
X
i=1
λi(x1(Pi1−θici−vi1) + x2(Pi2−θici−vi2)) (56)
29
which can be rewritten as follows, using (52),
(xcoop∗
1, xcoop∗
2) = argmax
(x1,x2)∈Q
2
X
j=1
xj a−2bxj−bxe
j−vmj −
n
X
i=1
λi(θici+vij )!
,
whence, from first order conditions, a−Pn
i=1 λi(θici+vij )−4bxj−2bxe
j−vmj = 0,and
therefore
xcoop∗
j=1
6b a−2
n
X
i=1
λi(θici+vij ) +
n
X
i=1
λiθici+vie
j+vme
j−2vmj !.
Now, for the RM supplier, Πraw = (xcoop∗
1+xcoop∗
2)Pn
i=1 λiθi(ci−cr)where cris the
production cost of the RM supplier. We get from first order condition
n
X
i=1
λiθici=2a−vm1−vm2+Pn
i=1 λi(2θicr−vi1−vi2)
4, so
xcoop∗
j=1
24b 2a−2
n
X
i=1
λiθicr−7
n
X
i=1
λivij + 5
n
X
i=1
λivie
j−7vmj + 5vme
j!(57)
For symmetry of the Nash bargaining solution we must have
Πi(xcoop∗
1, xcoop∗
2)−Π∗
i= Πj(xcoop∗
1, xcoop∗
2)−Π∗
j, j ̸=i(58)
which gives us the condition that
λi
2
X
j=1
xcoop∗
j(Pij −θici−vij ) = λk
2
X
j=1
xcoop∗
j(Pkj −θkck−vkj ), k ̸=i(59)
Hence,
nλi(xcoop∗
1(Pi1−θici−vi1) + xcoop∗
2(Pi2−θici−vi2))
=
2
X
j=1
xcoop∗
j a−2bxcoop∗
j−bxcoop∗
e
j−vmj −
n
X
i=1
λi(θici+vij )!(60)
The last equation is obtained using (52). From (57), we have
a−vmj −
n
X
i=1
λi(θici+vij )=2b(2xcoop∗
j+xcoop∗
e
j) (61)
Now rewrite (60) as
nλi(xcoop∗
1(Pi1−θici−vi1) + xcoop∗
2(Pi2−θici−vi2))
= 2bxcoop∗
1(2xcoop∗
1+xcoop∗
2)+2bxcoop∗
2(xcoop∗
1+ 2xcoop∗
2)
The results follow.
30
