Designing coordinating contracts for the consignment channel: Integrating manufacturer-greening and retailermarketing efforts
Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
International Conference on Marketing in the Connected Age (MICA-2018), October 6th, 2018
Danang City, Vietnam
Designing Coordinating Contracts for the Consignment
Channel: Integrating Manufacturer-Greening and Retailer-
Marketing Efforts
Dinh Anh Phana*, Hoa T. L. Vob, Hong Quang Duongc
aUniversity of Economics – The University of Danang, 71 Ngu Hanh Son Street, Danang City, Vietnam
aPhD Student, IGR-IAE, University of Rennes 1, France
bAssociate Professor in Production and Operations Management at IGR-IAE, University of Rennes 1, France
cFPT School of Business and Technology, Vietnam
A B S T R A C T
In this paper, we study the sustainable coordination of a consignment channel that arises due to simultaneous
consideration of Greening and Marketing initiatives undertaken by channel agents. We investigate a green
channel where the manufacturer (M) is responsible for greening and the retailer (R) undertakes marketing
efforts. Therefore, the market demand is affected by retail price, R’s marketing and M’s greening efforts. Using
M-led Stackelberg game to model the decision-making of the two firms in the channel, we analyze the
decentralized channel under our four proposed sharing contracts, namely Revenue – Production cost sharing
(RP), Revenue – Production cost and Marketing cost sharing (RPM), Revenue – Production cost and Greening
cost sharing (RPG), and Revenue – Production cost – Marketing cost and Greening cost sharing (RPMG). For
each sharing contract, we first consider the scenario that the sharing fraction is determined by either R or M
who dominates the green channel and then envisage the possibility of negotiation between R and M on the
sharing fraction which forms the basis of division of costs and revenues. Our analytical results show that the
cooperation between M and R via sharing contracts improves the greening level of the products and the overall
profitability of channel. In addition, both M and R get higher profits in the coordination state. From managerial
insights, our research could help channel managers to improve greening level as well as the overall
performance of channel.
Keywords: marketing effort; consignment channel; green channel; coordinating contract
1. Introduction
The development of industrial technology and the focus of manufacturers on their growth and profit had
adverse effects on the environment and society (Hsueh, 2015) and considering Greening within supply chain
(channel) management has become an inevitable requirement for improving the competitiveness of
manufacturers (Xiao and Yang, 2008). In recent times, green supply chain management is becoming increasingly
attention among scholars and practitioners who are integrating environmentally sound choices into supply chain
management research and practice (Yenipazarli, 2017; Babbar et al., 2017). From business practice, increasingly
regulatory pressures and as well as rising public environmental protection awareness have forced the M giants to
work with upstream and downstream companies to build green supply chains (Sancha et al., 2016). The
manufacturers are asked to provide evidence of their operations meeting relevant environmental requirements
and, in some cases evidence of ISO14001 certification (Swami et al., 2013). Therefore, M can invest funds for
new product research and development (R&D) to develop green products (Song and Gao, 2018) that reduce
environmental impact of production process and meet the increasing consumer demand for these products. As an
* Corresponding author. E-mail address: dinhanhdhkt@gmail.com
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example, Adidas, a leading M of athletic wear, uses Eco-Grip technology to reduce harmful substances from
materials used in manufacturing to minimize the manufacturing impact on environment. Similarly, World's
largest beverage company Coca-Cola has made significant efforts in measuring and reducing its carbon
footprints. In another example, PepsiCo mandates her suppliers to implement green technology to reduce the
carbon footprint in their businesses. An increase in greening performance may lead to greater market demand but
requires higher greening investment cost (Raj et al., 2018). Therefore, firms are only willing to adopt green
technology if they enhance their profitability (Yang et al., 2017). In addition to M’s greening efforts, R who are
more likely to face the public directly can exploit the sales channel to promote the market demand and boost
sales (Wang and Hu, 2011). R’s sales channel includes different types of “marketing efforts” such as local
advertising, on-site shopping assistance, rebates and post-sales service. However, these activities may constitute
a significant portion of firm’s operating expenses (Xiao et al. 2005). As a result, if the M does not provide
sufficient incentives, then R will have no motivation to enhance marketing effort level (Krishnan et al., 2004).
It is also well known that when the channel member’s decisions on efforts are made separately and each party
pays the associated costs of efforts to maximize their own profit, these strategies lead to a suboptimal level of
efforts which may lower total profit of the whole channel. In the past decades, the issues of coordinating the
green channel have received a great deal of research attention since it improves the profit both of the channel and
of the individual channel member. Readers may refer to Raj et al. (2018) for a summary of the reviewed
literature in the context of green supply chain (channel) management literature. Coordinating contracts provide
incentives to induce channel members to behave in ways that are best for the whole channel while maximizing
their own profit. This situation leads to a coordination of the channel. However, some coordinating contracts only
reach the cooperation state (Pareto improvement) where the channel members are better off with the coordinating
contract than any other different contracts (Chakraborty et al., 2015). In this paper, we propose an effective
contract to coordinate the green channel through the combination of revenue-sharing and cost-sharing contracts
and based on two common channel practices: consignment channel and Vendor Managed Inventory (VMI).
Under the VMI system complemented by a consignment contract (VMI-CC), the vendor (i.e., M) manages the
R's inventory levels and makes periodic replenishment decisions in terms of quantity and frequency (Wong et al,
2009) while retaining ownership of the inventory (Chen et al. 2010). VMI-CC has been adopted by many
industries such as personal computer and automobile. Readers may refer to Chen et al. (2010) for more examples
of the VMI-CC. The coordination of a green channel using a revenue - sharing contract has been widely studied
in the literature. Qian and Guo (2014) developed a revenue-sharing bargaining model between an Energy Service
Company (ESCO) and an Energy-Using Organization (EU). Their research show that the greater the probability
of adverse circumstances is, the higher is the revenue share (of the EU) and the more disadvantageous is the
ESCO’s position in the game. Arani et al. (2016) proposed a mixed revenue-sharing option contract to coordinate
the channel and modeled that using a game theoretic approach. Song and Gao (2018) established a green channel
game model with two kinds of revenue-sharing contracts: the retailer-led- and the bargaining- revenue sharing
contract. Their results proved that the revenue-sharing contracts can effectively improve the greening level of the
products and the overall profitability of the channel. Besides, the cost-sharing contract has recently been used in
coordinating a green channel (Ghosh and Shah., 2015; Arda., 2017; Raj et al., 2018). However, no study has
addressed the coordination issues in a consignment channel with the presence of both M’s greening and R’s
marketing efforts. Therefore, in this paper, we examine the problem of designing coordinating contract for a
green consignment channel, focusing on how to share the channel’s revenue and costs between the channel
members to achieve the best performance for such a channel. For doing this, we propose four kinds of sharing
contracts namely RP, RPM, RPG, RPMG which are based on the combination of revenue-sharing and cost-
sharing contract in VMI-CC. We study the efficiency of each sharing contract in a two-echelon channel where
the market demand is affected by retail price, R’s marketing and M’s greening effort. In this context, we model
the decision-making of the two firms in the decentralized channel as the M-Stackelberg game and carry out
equilibrium analysis with consideration of wholesale price contract (WP) and four kinds of sharing contracts. We
use the results of decentralized channel under WP as a benchmark for the evaluation of channel cooperation with
the sharing contracts. We also develop a corresponding model for centralized channel and use the optimal results
to investigate channel coordination.
Our work contributes to the extant literature in two folds. First, we develop an analytical model dealing with
channel coordination issues for the different decisions impacting on the channel performance including not only
the operational choices (quantity, price) and marketing decisions of the firms but also the green channel
management. Therefore, our study address a business practices which so far has not been studied. Secondly, we
propose the coordination schemes for the green consignment channel through the combination of revenue-
sharing and cost-sharing contracts under VMI system.
This paper is organized as follows: after this introductory section, we describe the problem setting with
notations and assumptions in Section 2. Section 3 focuses on analyzing a centralized model and a decentralized
model. In Section 4, we analyze the impact of bargaining power on the implementation of sharing contract and
the channel performance. We next conduct numerical studies to validate the proposed models in Section 5. A
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summary of the findings, the managerial insights, and suggested directions for future research are described in
the last section. To save place, all of proof, some tables and analyses are put in the Appendix and available upon
request from the authors
2. Model formulation
We consider a two-echelon distribution channel consisting of a M (he) and a R (she), in which M produces the
green product and sells it through R who then sells the products to the final consumers. We assume that the
consumers are sensitive towards environment friendly characteristic of a product as well as marketing efforts
undertaken by R. We consider a deterministic linear demand function faced by a R in the market as follows: 퐷 =
푎 − 푏푝 + 푒 + , 푎 > 0, 푏 > 0, > 0, > 0 and a-bc>0 are assumed for the demand function, where, a is
overall market potential, b is price sensitivity, p is retail price, is greening level of product, e is marketing
effort level, and are consumer sensitivity to greening and marketing effort levels respectively. (In Table 1,
we present all relevant notations used in this paper). This type of demand function form has been widely used to
incorporate the price, marketing and green effort impacting on the demand (Ma et al, 2013; Ghosh and Shah,
2015; Arda, 2017; Raj et al., 2018). Here, the demand is decreasing in the retail price, increasing in both the R’s
Marketing effort and product’s greening level. We further assume a quadratic functions to formulate R’s
marketing and M’s green product R&D costs. The cost of green product R&D is entirely borne by M and is
represented by 2/2 where > 0 is the green investment parameter (Banker et al., 1998; Song and Gao, 2018).
Similarly, the cost of the marketing efforts at level e is 휂푒2/2 where 휂 > 0. This type of marketing cost function
has been widely used in the literature (Krishnan et al., 2004; Ma et al, 2013). Assumption of cost nonlinearity
represents the diminishing rate of returns for greening and marketing related activities. We also assume that both
M and R possess full and symmetric information regarding costs and demand.
The trade between M and R can be either a WP or a sharing contract. We define a sharing contract as being
the combination of the revenue-sharing and cost-sharing between M and R embedded in the VMI-CC. Under
such a contract, M retains the ownership of the consignment stock, decides on the retail price and manages the
inventory at R (i.e., decides on stocking quantity). The sharing contract also specifies the sharing parameters to
allocate the channel’s costs and revenue. For simplicity, we assume in our original model that the same sharing
terms for revenue are used to share the costs. Therefore, in our proposed sharing contracts, if one kind of cost is
shared, the fraction of cost sharing is equal to that of revenue sharing and we call it the sharing fraction for short.
Further, we will extend our model using different sharing parameters for efforts costs. Under a sharing contract,
the decision on the level of sharing fraction has to be made before deciding on the level of efforts meaning that M
and R are engaged in a long-term commitment to share their costs and revenues. By contrast, the sharing fraction
would have no impact on M’s greening and R’ marketing efforts. Therefore, when firms determine the level of
their efforts, they know the share of investment cost on efforts will be undertaken by the other firm and their
decision on the effort level would accommodate this sharing fraction. Once the investment in effort has been
made, the upfront cost is divided between M and R according to this sharing fraction. As a consequence, R is free
to determine the marketing effort level and M is free to determine the product’s greening level to maximize their
own profit under the sharing contract. In particular, we propose the following four kinds of sharing contract to
coordinate a green channel:
Contract RP: The revenue and Production cost sharing contract
Contract RPM: The revenue - Production cost and Marketing cost sharing contract
Contract RPG: The revenue - Production cost and Greening cost sharing contract
Contract RPMG: The revenue - Production cost - Marketing cost and Greening cost sharing contract
In the RP contract, the inventory at R is owned by M, R does not pay M upon receipt of the stocks (i.e., green
products) but shares the sales revenue on units sold. For each unit of any sold stock, R keeps a fraction (0, 1)
of the revenue for herself and shares a fraction 1 − of her revenue with M, and R incurs a fraction of
production cost for each unit of stock.
In the RPM contract, R keeps a fraction ∈(0, 1) of her revenue, incurs a fraction of production cost for
each unit of stock and M is willing to bear a fraction 1 − of R’s marketing cost.
In the RPG contract, R keeps a fraction ∈(0, 1) of her revenue, incurs a fraction of production cost for
each unit of stock and R is willing to share a fraction of the M's upfront cost of greening investment.
In the RPMG contract, R keeps a fraction ∈(0, 1) of her revenue, incurs a fraction of production cost for
each unit of stock and R and M share their costs of marketing and greening with each other according to a
fraction , i.e., R absorbs a fraction of the M’s greening cost while M absorbs a fraction 1 − of R’s
marketing cost.
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Table 1. Notations used.
Notations
Explanation
Notations
Explanation
p
w
Unit retail price
M’s wholesale price
Product’s greening level
Coefficient of greening effort cost
Indicator of firm, i=m (M), r (R)
Indicator of the sharing contract, j=RP,
RPM, RPG, RPMG
The optimal decisions for centralized
channel
The optimal decisions for decentralized
channel under WP
The optimal decisions for decentralized
channel under sharing contract
M’s, R’s and channel’s profit under WP
i
j
(푝푐∗, 푒푐∗, ∗푐)
e
c
a
R's marketing effort level
Unit production cost for M
Market scale parameter
(푝푊∗ 푃, 푒푊∗ 푃, ∗푊푃
)
(푝푗∗, 푒∗, 푗∗):
푗
푊푚푃, 푊푟 푃, 푊푐 푃
푚푗 , 푟푗, 푐푗
b
Price elasticity of the demand
Consumer sensitivity to
marketing effort
M’s, R’s and channel’s profit under
sharing contract j
Consumer sensitivity to green
improvements
Coefficient of marketing effort
cost
Centralized channel’s profit
c
Sharing fraction
3. Modeling centralized and decentralized channels
3.1. The centralized channel model
We first investigate the integrated channel which is considered as a single system operating under a global
optimization strategy. In this setup, all relevant decisions are taken by a central planner who possesses all the
relevant information. The central planner decides the optimal retail price, production quantity, greening level,
and marketing effort level for the entire channel. Therefore, the optimization problem of the central planner is
given by
2
2
(
)
max 푐(. ) = 푝 − 푐 퐷 − 휂푒 /2 − /2
(1)
푝,푒,
From the problem of (1), we impose a restriction of 푏 > 훾2/2휂 and 휅 > where = 휂휆2/(2푏휂 − 훾2) to
ensure the Hessian matrix of Πc is a negative definite. The same expression of this condition is presented by 0 <
훾2/휂 + 휆2/휅 < 2푏. Under this restriction, the profit of the centralized channel is jointly concave in p, e, and ,
therefore, the optimal decisions of retail price 푝푐∗, marketing effort level 푒푐∗, and product greening level ∗푐 can be
obtained through the first order optimality conditions.The results of optimal decisions are listed in Table 2 (in the
following section). Substituting (푝푐∗, 푒푐∗, 푐∗)into Eq. (1), we obtain the optimal profit of the centralized channel
and present it in Table 3. From the optimal results: If market demand is not influenced by marketing efforts, then
휆 = 0 and 훾0, the channel turns into a greening only channel.Under such a scenario, we can calculate the
optimal values for a green channel using the limit 휆0. Similarly, if market demand is not influenced by
greening efforts, then 휆0 and 훾=0, the channel turns into a marketing only channel. In this case, we can
determine the optimal values for a marketing channel using the limit 0. If market demand is neither greening
nor marketing, then 휆 = 0 and 훾=0, we can obtain the optimal values for a channel without efforts using the
limit 0 and 휆0.We can also observe from the generalized results that the centralized channel orders more,
earns more profit, makes higher greening level and marketing level with a higher consumer sensitivity to
2
(
)
marketing and greening efforts.We further find that 푐 > 푙푖푚 푐 = 푎 − 푏푐 /4푏 under the concavity
condition of profit function. From this expression, the profit of→a0g,r→ee0n centralized channel is higher than that of
its profit only counterpart. This finding indicates that if the consumers are willing to pay higher for green
products and marketing effort, the firms will have motivations to invest more in green products and marketing
efforts.
3.2. Decentralized channel under WP
In a decentralized channel, the channel members make their own decisions based on their own costs to
maximize their own profits, but the decision making results are mutually influential. In a decentralized channel
under WP contract, we model the decision-making problems of the two channel members as a M-led Stackelberg
game (MS) in which the M takes the initiative and R as the follower1. The dynamic game order is as follows:
firstly M determines the greening level of products and the wholesale price w. Subsequently, R determines the
marketing effort level e, the retail price p and uses an order quantity equal to demand D to maximize her profit.
To obtain the optimal decisions and firm-level profits in equilibrium, we use backward induction method to solve
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Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
this sequential move game. We begin by characterizing the R’s best-response function. For a given {w,}, R’s
problem is max 푊푟 푃 = (푝 − 푤)퐷 − 휂푒2/2. Based on the R’s best response, M’s problem can be stated as
follows: max푝,푒푚푊푃 = (푤 − 푐)퐷 − 2/2. The equilibrium results for WP contract are presented in Tables 2 and
푤,
3. Some algebraic calculations verify that: ∗푐/푊∗ 푃 >2 and 푒푐∗/푒푊∗ 푃 >2. These results indicate that in a WP
contract, optimal greening and marketing effort levels are less than half of the corresponding values for a
centralized channel. This finding suggests that the channel agents need to puts higher efforts in greening and
marketing effort in a decentralized channel to get more profit. We further observe that 푊푐 푃/c < 3/4. This
observation implies that the double marginalization problem and suboptimal level of efforts of WP contract
generate a profit loss of channel that higher than 25%. Therefore, in the following subsections, we analyze four
sharing contracts to investigate the optimal performance of a decentralized channel and compare them with the
WP contract.
1
Remark : The interaction between M and R in a decentralized channel under WP contract is often
characterized by the power of decision making of the partners involved (Chakraborty et al., 2018). Three channel
structures including: (i) M-led Stackelberg (MS), (ii) R-led Stackelberg (RS) and (iii) vertical Nash (VN) have
been discussed in the literature (Ma et al., 2013). In the RS model, R is the Stackelberg leader, who anticipates
M's reaction on wholesale price and green effort, and then decides on its retail price and marketing effort level. In
the VN model, M's decisions and R's decisions are made independently. In our study, we address a channel
where M is a Stackelberg leader (MS model).
3.3. Decentralized channel under sharing contracts
As the description of the sharing contracts in Section 2, the sequence of events under the sharing contracts is
as follows: In the first step, both firms negotiate a sharing fraction . Then, in the second step, M decides the
retail price, the product’s greening level and chooses a stocking quantity equal to demand to maximize his own
profit. In the third step, R decides only on the marketing effort level to obtain her own profit maximization.2
Therefore, after the sharing fraction was chosen, the behavior of M and R under the sharing contracts can be
described by using M-led Stackelberg game setting where M as the leader and R as follower. Then, the
Stackelberg game corresponding to each sharing contract can be expressed as follows:
Contract
Stage 1
Stage 2
max 푅푚푃 = (푝 − 푐)(1 − )퐷 − 2/2
max 푅푟푃 = (푝 − 푐)퐷 − 휂푒2/2
RP
푝,
푒
max 푅푚푃푀 = (푝 − 푐)(1 − )퐷 − (1 − )휂푒2/2 − 2/2
max 푅푟푃푀 = (푝 − 푐)퐷 − 휂푒2/2
RPM
RPG
푝,
푒
2
max 푅푚푃퐺 = 푝 − 푐 (1 − )퐷 − (1 − ) /2
max 푅푟푃퐺 = (푝 − 푐)퐷 − 휂푒2/2 − 2/2
(
)
푝,
푒
(
)
1 −
2
max 푅푚푃푀퐺 = 푝 − 푐 1 − 퐷 −
휂푒2
(
)(
)
max 푅푟푃푀퐺 = (푝 − 푐)퐷 − 휂푒2/2 − 2/2
푝,
RPMG
푒
(1 − )
−
2
2
We solve the games by backward induction. The equilibrium results are listed in Tables 2 and 3.
Table 2. The optimal decisions for centralized and decentralized channel
Models/Contract
Centralized
Retail price
Marketing effort level (e)
greening level (θ)
(푎 − 푏푐)휂휅
−훾2휅 + 2푏휂휅 − 휂휆2
(푎 − 푏푐)(3푏휂 − 훾2)휅
(푎 − 푏푐)훾휅
−훾2휅 + 2푏휂휅 − 휂휆2
(푎 − 푏푐)훾휅
4푏휂휅 − 2훾2휅 − 휂휆2
(푎 − 푏푐)훼훾휅
(푎 − 푏푐)휂휆
−훾2휅 + 2푏휂휅 − 휂휆2
(푎 − 푏푐)휂휆
4푏휂휅 − 2훾2휅 − 휂휆2
(푎 − 푏푐)(1 − 훼)휂휆
푐 +
WP
RP
푐 +
푏(4푏휂휅 − 2훾2휅 − 휂휆2)
(푎 − 푏푐)휂휅
−2훼훾2휅 + 2푏휂휅 − 휂휆2 + 훼휂휆2
(푎 − 푏푐)휂휅
−훾2휅 + 2푏휂휅 − 휂휆2 + 훼휂휆2
(푎 − 푏푐)휂휅
−2훼훾2휅 + 2푏휂휅 − 휂휆2
(푎 − 푏푐)휂휅
푐 +
−2훼훾2휅 + 2푏휂휅 − 휂휆2 + 훼휂휆2
(푎 − 푏푐)훾휅
−훾2휅 + 2푏휂휅 − 휂휆2 + 훼휂휆2
(푎 − 푏푐)훼훾휅
−2훼훾2휅 + 2푏휂휅 − 휂휆2 + 훼휂휆2
(푎 − 푏푐)(1 − 훼)휂휆
−훾2휅 + 2푏휂휅 − 휂휆2 + 훼휂휆2
(푎 − 푏푐)휆
RPM
RPG
RPMG
푐 +
푐 +
−2훼훾2휅 + 2푏휂휅 − 휂휆2
(푎 − 푏푐)훾휅
−훾2휅 + 2푏휂휅 − 휂휆2
−2훼훾2휅 + 2푏휂휅 − 휂휆2
(푎 − 푏푐)휂휆
−훾2휅 + 2푏휂휅 − 휂휆2
푐 +
−훾2휅 + 2푏휂휅 − 휂휆2
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Table 3: M’s, R’s and channel’s profit under sharing contracts and WP
Models/
R's profit
M’s profit
Omitted
Total profit
Contract
(푎 − 푏푐)2휂휅
Centralized
WP
Omitted
2(−훾2휅 + 2푏휂휅 − 휂휆2)
(푎 − 푏푐)2휂(2푏휂 − 훾2)휅2
2(4푏휂휅 − 2훾2휅 − 휂휆2)2
(푎 − 푏푐)2훼휂(2푏휂 − 3훼훾2)휅2
(푎 − 푏푐)2휂휅
푎 − 푏푐 2휂휅(6푏휂휅 − 3훾2휅 − 휂휆2)
(
)
2(4푏휂휅 − 2훾2휅 − 휂휆2)
2(4푏휂휅 − 2훾2휅 − 휂휆2)2
푎 − 푏푐 휂휅( 2푏휂휅 − 휂휆 − 2훼 훾 휅 − 휂휆 − 훼 (훾 휅 + 휂휆 ))
2
2
2
2
2
2
2
푎 − 푏푐 2(1 − 훼)휂휅
(
)
(
)
(
)
(
)
2(2훼훾2휅 − 2푏휂휅 + 휂휆2 − 훼휂휆2)2
RP
2(2훼훾2휅 − 2푏휂휅 + 휂휆2 − 훼휂휆2)2
(푎 − 푏푐)2훼휂(2푏휂 − 훾2)휅2
2(훾2휅 − 2푏휂휅 + 휂휆2 − 훼휂휆2)2
(푎 − 푏푐)2훼휂휅(2푏휂휅 − 3훼훾2휅 − 휂휆2)
−4훼훾2휅 + 4푏휂휅 − 2휂휆2 + 2훼휂휆
푎 − 푏푐 2(1 − 훼)휂휅
−2훾2휅 + 4푏휂휅 − 2휂휆2 + 2훼휂휆2
(푎 − 푏푐)2휂휅(훾2휅 + 휂(−2푏휅 + ( − 1)2휆2))
−2(훾2휅 − 2푏휂휅 + 휂휆2 − 훼휂휆2)2
(푎 − 푏푐)2휂휅(−2훼훾2휅 − 훼2훾2휅 + 2푏휂휅 − 휂휆2)
(
)
RPM
푎 − 푏푐 2(1 − 훼)휂휅
(
)
RPG
2(2훼훾2휅 − 2푏휅 + 휆2))2
−4훼훾2휅 + 4푏휅 − 2휆2
2(2훼훾2휅 − 2푏휅 + 휆2)2
(푎 − 푏푐)2휂휅
(1 − )(푎 − 푏푐)2휂휅
(푎 − 푏푐)2휂휅
RPMG
2(−훾2휅 + 2푏휂휅 − 휂휆2)
2(−훾2휅 + 2푏휂휅 − 휂휆2)
2(−훾2휅 + 2푏휂휅 − 휂휆2)
4. Analytical results for channel performance
4.1. Bargaining power and cooperation
The channel contract terms can be decided overwhelmingly by one of the parties (R or M) depending on their
bargaining power. Therefore, in this section, we first investigate the case that the sharing fraction in each
sharing contract is determined by R. In this case, R is the dominant player and offers a take-it-or-leave-it sharing
contract to M. Conversely, when M has more bargaining power than that of R, he embodies the channel power
and offers a take-it-or-leave-it sharing contract to R and stipulates a sharing fraction which maximizes his profit.
In some cases, the negotiation between R and M could be made to allocate the cost of efforts and/or revenues
between these two parties (Arda, 2017). Therefore, we also investigate the cases where the sharing fraction is
determined through the negotiation between R and M. In particular, we use the bargaining structure proposed by
Nash to determine the optimal sharing fraction in this scenario. In a Nash bargaining game, two players have
equal power and cooperatively decide on how the surplus generated by their interaction should be divided
between them. In the next subsection, we analyze the impact of bargaining power on channel member’s profit.
4.2. The impact of bargaining power on the channel member’s profit
From the results in the Table 3, 푖푗 is a function of sharing fraction (). By examining the sign of the
functions 휕푖푗/휕 with the condition of 푖푗 > 0 that assure positive profits for each partner in the channel, we
drive the impact of bargaining power on the profit of M and R though the selection of in each sharing contract.
We summarize with the following proposition.
Proposition 1. When M is the dominant player and embodies the channel power, the equilibrium level of
sharing fraction j* which maximizes M’s profit in the sharing contract j are as follow: (1) In the RP contract: as
푏 > 훾2/, 푅푃∗ = 0, otherwise, 푅푃∗ = 2푏휂/3훾2. (2) In the RPM contract: 푅푃푀∗ = 0. (3) In the RPG contract:
as 휂 > 2훾2휅/(2푏휅 − 휆2), 푅푃퐺∗ = 0, otherwise, 푅푃퐺∗ = (2푏휂휅 − 휂휆2)/3훾2휅. (4) In the RPMG contract;
푅푃푀퐺∗ = 0.
From Proposition 1, we makes the following observations: In the RP contract, as 푏 > 훾2/ and M has more
contractual power than R, he will choose a value of approaching zero to attain the highest profit. Conversely,
when 푏 < 훾2/, M’s profit increases with for any in the range of (0, 2푏휂/3훾2). Thus, M chooses a value of
approaching 2푏휂/3훾2 to attain the highest profit. (2) In the RPM contract: M’s profit always decreases in .
Therefore, M achieves the highest profit if approaches zero. (3) In the RPG contract: as 휂 is higher than a
threshold level, i.e., 휂 = 2훾2휅/(2푏휅 − 휆2), the smaller the selection of , the more profits M gets. This implies
that M obtains the highest profit if the value of approaches zero. Otherwise, M should raise the value of
approach (2푏휂휅 − 휂휆2)/3훾2휅 to attract the highest profit. (4) In the RPMG contract: M’s profit always
decreases with . Therefore, M attains the highest profit if approaches zero.
Proposition 2. When R is the dominant player and embodies the channel power, the equilibrium level of
sharing fraction j* which maximizes R’s profit in the sharing contract j are as follow: (1) In the RP contract: as
휅 > (3훾2휆2 − 2푏휂휆2)/(4푏훾2 − 2푏2휂), 푅푃∗ = 1, otherwise, 푅푃∗ = (2푏2휂휅 − 푏휂휆2)/(4푏훾2휅 − 3훾2휆2 +
푏휂휆2). (2) In the RPM contract: as 휅 < 2, 푅푃푀∗ = (−훾2휅 + 2푏휂휅 − 휂휆2)/휂휆2, otherwise, 푅푃푀∗ = 1. (3) In
the RPG contract: as 휂 = 4훾2휅/(2푏휅 − 휆2) then 푅푃퐺∗ = 1, otherwise, 푅푃퐺∗ = (2푏휂휅 − 휂휆2)/4훾2휅. (4) In
the RPMG contract: 푅푃푀퐺∗ = 1.
By Proposition 2, we show the impact of bargaining power on R’s profit with the following observations: (1)
In the RP contract: as is higher than a threshold level, ie, 휅 > (3훾2휆2 − 2푏휂휆2)/(4푏훾2 − 2푏2휂), R’s profit
increases with (0,1). This suggests that if R has more contractual power than M, she increases the value of
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approaching one to attract the highest profit. This also means that R should incur most of the production costs
and extract most of the channel sales to maximize her profit. By contrast, R attains the highest profit if
approaches (2푏2휂휅 − 푏휂휆2)/(4푏훾2휅 − 3훾2휆2 + 푏휂휆2). (2) In the RPM contract: as is higher than a threshold
level, i.e, 휅 = 2, R’s profit increases with (0,1), therefore, R increases the value of 훼 to approach one to
attract the highest profit. Conversely, R raises to approach (−훾2휅 + 2푏휂휅 − 휂휆2)/휂휆2 to maximize her profit.
(3) In the RPG contract: As is higher than a threshold level, i.e, 휂 = 4훾2휅/(2푏휅 − 휆2), R increases the value
of to approach one to attract more profit. On the contrary, R raises 훼 to approach (2푏휂휅 − 휂휆2)/4훾2휅 to
attain the highest profit. (4) In the RPMG contract: R’s profit always increases with the value of . Therefore, R
attains the highest profit if approaches one.
We next examine the case when the sharing fraction is endogenously determined by both R and M. By using
the Nash bargaining structure in which M has the same bargaining power to that of R, we identify the optimal
profit allocation schemes for the problem of 푚푎푥 푚푗 ∗ 푟푗. We summarize the equilibrium level of sharing
fraction in the following proposition.
Proposition 3. The equilibrium solution of sharing fraction j∗ to the Nash bargaining problem under the
sharing contract are as follow: (1) In the RP contract: 푅푃∗ = 퐴 − 1 퐵 so that 푅푃∗(0, 2) where 퐴 =
2
3
휆
2
2
2
2
2
2
4
2
2
3
2
3
2
4
4
2
4
2
2
2
2
3
2
3
4
2
4
2
4
2
3
4
2
4
4
2푏훾 휂휅+4푏
휂
휅−3훾 휂휆
28푏
√
훾
휂
휅
−40푏
훾
휂
휅
+16푏
휂
휅
−24푏훾
휂
휅휆 +28푏
훾
휂
휅휆 −8푏
휂
휅휆 +9훾
휂
휆
−12푏훾
휂
+4푏
휂
and 퐵 =
휆 . (2) In
4
2
2
2
2
2
4
2
2
2
2
2
2
2(−3훾 휅+7푏훾 휂휅−3훾 휂휆 +푏휂
휆
)
(3훾 휅−7푏훾 휂휅+3훾 휂휆 −푏휂
휆
)
2
4
2
2
2
2
2
2
2
2
2
2
2 4
the RPM contract: 푅푃푀∗
=
−훾 휅+2푏휂휅 − √훾 휅 −4푏훾 휂휅 +4푏 휂 휅 +훾 휂휅휆 −2푏휂 휅휆 +휂 휆 so that 푅푃푀∗(0, 1). (3)
2
2
4
휂휆
휂 휆
2
2
2
2
2
2
2
2
2
2
2 4
2
2
2
4
2
2
2
2
2 2
−2푏훾 휂휅 −4푏
휂
휅
+훾 휂휅휆 +4푏휂 휅휆 −휂
휆
휂
√
(−2푏휅+휆
)
(7훾
휅
+5훾 휂휅(−2푏휅+휆 )+휂 (−2푏휅+휆 ) )
In the RPG contract:
푅푃퐺∗
=
−
so that
2
2
2
4
2
2
2
2
훾
휅(6훾 휅−14푏휂휅+7휂휆
)
훾
휅
(6훾 휅+7휂(−2푏휅+휆 ))
1
푅푃퐺∗(1 , 2). (4) In the RPMG contract: 푅푃푀퐺∗ = .
4
3
2
Proposition 3 shows that when the level of sharing fraction is determined through bargaining, the R obtains at
most 75 percent of channel’s gross profit if she undertakes all of her marketing cost and does not bear M’s
upfront cost of greening investment. In the case that R shares the gross profit margin of channel and cost of
marketing efforts with M, R undertake at most 50 percent of her marketing costs. By contrast, when R decides to
bear a proportion of M’s upfront greening cost, she absorbs at least 25 percent and at most 67 percent of that. In
the case that R and M share all of the marketing, greening investment and production costs, firms agree on that
the channel profit is split equally.
4.3. The impact of on the channel’s profit
We further investigate the impact of negotiation between the R and M on the total profit of the channel. With
this aim, similar to Cachon (2003), we define the efficiency of the decentralized channel with respect to the
centralized channel, as the ratio of the channel's profit in the decentralized channel to that in the centralized
channel, i.e., 퐸푗 = 푐푗/푐. By examining the sign of the functions 푗 = 휕퐸푗()/휕 with the conditions of
푐
푖푗 > 0, we summarize the impact of on the profit of the channel in the decentralized system through the
following results: (1) The decentralized channel with the RP contract generates the highest profit when is
2
2
2
2푏훾 휂휅−훾 휂휆
chosen at 훼푐푅푃
=
2. Furthermore, the profit of the decentralized channel in the RP
2
2훾 휅+2푏훾 휂휅−4훾 휂휆 +2푏휂 휆
4
2
2
2
contract is always less than that of the centralized channel. (2) The channel efficiency of the RPM contract
2
2
훾 휅−2푏휂휅+휂휆
always decreases in , approaches one as approaches zero and approaches
as approaches
2
훾 휅−2푏휂휅
one. (3) The decentralized channel with the RPG contract generates the highest profit when is chosen at
2
2푏휂휅−휂휆
훼푐푅푃퐺
=
2. However, the profit of the decentralized channel under the RPG contract is always less
2
2훾 휅+2푏휂휅−휂휆
than that of the centralized channel. (4) The decentralized channel with the RPMG contract generates the same
profit as that of the centralized channel and the channel efficiency of the RPMG contract does not depend on the
selection of .
From the above analysis, we observe that the channel efficiency is highest in the RPMG contract and the
RPMG contract perfectly coordinates the channel while the RP, RPM and RPG contracts do not coordinate the
channel. Note that when = 0 in the RPM contract, the channel efficiency is equal to one, thus RPM can lead a
perfectly coordinated channel. However, M captures all the channel profits while R obtains zero profit in this
situation. Therefore, R has no incentive to accept an RPM contract with the sharing fraction equal to zero.
4.4. Channel cooperation and greening-performance
The aim of the channel cooperation is to determine a channel profit allocation scheme among its members.
However, both R and M are willing to accept the optimal profit allocation schemes only if it can generate more
profits than those derived in a non-collaborative channel (i.e., in the WP contract). Let 푗(푗, ̅푗) represent a
Pareto-improving region where both members of channel earn higher profit in the sharing contract compared to
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Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
WP contract, i.e., 푅푗∗ > 푊∗ 푃 and 푀푗∗ > 푊∗ 푃. Thus, both the R and M will be motivated to adopt the shairng
contract when the sharing fraction was choosen within these values. In the propositions 4-7, we identify the
upper (̅푗) and lower bounds (푗) of the Pareto-improving region and investigate the greening performance level
of channel in this region corresponding to each sharing contract.
Proposition 4: In the RP contract:
푅푃
(1) When 푏 > 훾2/휂 and > 휅 then 푅푃 = 0.5푢 − 푣 ; ̅ = 0.5,
√
1
1
3
2
2
4
2
2
4
2
2
2
2
휂(16푏 휂 휅 +2훾 휅휆 −훾 휂휆 +(푏휂휆 −4푏 휂휅)(2훾 휅+3휂휆 ))
where 푢1 =
,
6
2
3
4
4
2
2
2
2
2
2
4
4훾 휅 +푏휂 휆 +4훾 휂휅(2휆 −5푏휅)+훾 휂 (24푏 휅 −16푏휅휆 +휆 )
2
2
2
2
2
2
4
3
2
2
2
2
2
2
4
휂 (훾 −푏휂)(2훾 휅−4푏휅+휆 ) (3훾 휆 −16푏 휂휅 +8푏 휅(훾 휅+2휂휆 )−푏(8훾 휅휆 +5휂휆 ))
and 푣1 =
.
6
2
3
4
4
2
2
2
2
2
2
4
2
(4훾 휅 +푏휂 휆 +4훾 휂휅(2휆 −5푏휅)+훾 휂 (24푏 휅 −16푏휅휆 +휆 ))
∗
(2) 푅푃 > ∗푊푃 when 푅푃 < < ̅ and the conditions of part (1) are satisfied.
푅푃
Proposition 5: In the RPM contract:
푅푃푀
(1) When 푏 > 훾2/2휂 and 휅 > 휅 then 푅푃푀 = 푢 + 푣 ; ̅
= 0.5, where 푢2 = (4훾4휅2 + 2훾2휂휅(3휆2 −
√
2
2
2
2
2
2
4
2
4
2
2
8푏휅) + 휂 (16푏 휅 − 12푏휅휆 + 3휆 ))/2휂 휆 and 푣2 = ( 2훾 휅 − 4푏휅 + 휆 2(4훾4휅2 + 8훾2휂휅(휆2 − 2푏휅) +
(
)
휂2(16푏2휅2 − 16푏휅휆2 + 5휆4)))/휂4휆8.
∗
∗
푅푃푀
(2) 푅푃푀 > 푊푃 when 푅푃푀 < < ̅
and the conditions of part (1) are satisfied.
2
2
2
2
2
2
4
2
2
휂 (2푏휅−휆 )(16푏 휂휅 +4훾 휅휆 +휂휆 −8푏휅(훾 휅+휂휆 ))
Proposition 6: In the RPG contract, let 푢3 =
,
2
4
2
2
2
2
2
2
훾 휅(8훾 휅 +3휂 (휆 −4푏휅) +4훾 휂휅(3휆 −10푏휅))
2
2
2
2
2
2
4
2
2
2
2
2
2
2
2
2 4
1
훾 휂 휆
휂휆
푣3 = 휂 (휆 −2푏휅) (2훾 휅−4푏휅+휆 ) (8훾 휅 +4훾 휂휅(휆 −6푏휅)+휂 (휆 −4푏휅) ), 1 = √(2푏휂−훾 )(훾 −푏휂)
−
; and
4
2
4
2
2
2
2
2
2
2
2
2
2
2
훾 휅 (8훾 휅 +3휂 (휆 −4푏휅) +4훾 휂휅(3휆 −10푏휅))
4
4(훾 −푏휂)
2
2
2
4
3 4
1
휂휆
2 = √−훾 휂 휆 −푏휂 휆
−
, we have :
2
3
2
4
(훾 −푏휂)
4(훾 −푏휂)
(1) When 훾2/ < 푏 ≤ 5훾2/2, 1 < 휅 ≤ 2 or when 푏 > 5훾2/2, 휅 < 휅 < 2 then 푅푃퐺 = 0.5(푢3 −
푅푃퐺
푅푃퐺
푣 ); ̅
= 0.5(푢 + 푣 ). Otherwise, when 푏 > 훾2/, 휅 > then 푅푃퐺 = 0.5(푢 − 푣 ); ̅
=
√
√
√
3
3
3
2
3
3
(2훾2휅 − 2푏휂휅)/(4훾2휅 − 4푏휂휅 + 휂휆2).
∗
∗
푅푃퐺
(2) 푅푃퐺 > 푊푃 when 푅푃퐺 < < ̅
and the conditions of part (1) are satisfied.
Proposition 7: In the RPMG contract:
2
2
2
2
(훾 −2푏휂)휅(훾 휅−2푏휂휅+휂휆 )
(훾 −2푏휂)휅
푅푃푀퐺
(1) When 푏 > 훾2/2휂 and 휅 > 휅 then 푅푃푀퐺
=
; ̅
and the conditions of part (1) are satisfied.
(3) 푅∗ 푃푀퐺 = ∗푐, 푒푅∗푃푀퐺 = 푒푐∗, 푝푅∗푃푀퐺 = 푝푐∗, 푚푅푃푀퐺 = (1 − )푐 and 푅푟푃푀퐺 = 푐 for any 0 < < 1.
=
.
2
2
2
2
2
(2훾 휅−4푏휂휅+휂휆 )
2훾 휅−4푏휂휅+휂휆
∗
(2) 푅푃푀퐺 > ∗푊푃when 푅푃푀퐺 < < ̅
푅푃푀퐺
Part 1 of Proposition 4-7 indicates that there exists a Pareto optimal solution under each sharing contract
through which channel members can maximize their profits. We also observe from Part 1 of Proposition 4 and 6
that in RP and RPG, a win-win scenario for both channel members can be reached only when the effect of price
on the market demand is relatively high i.e., 푏 > 훾2/휂. By contrast, from Part 1 of Proposition 5 and 7, RPM
and RPMG always bring the channel to such a scenario regardless of the impact of price on market demand. We
can further observe from Part 1 of Propositions 4 and 5 that RP and RPM only reach the cooperation state if R
shares less than 50% of the production cost with M. From Part 2 of Proposition 4-7, the collaboration through
bargaining between R and M under sharing contracts achieves the win–win-win situation, namely, R and M earn
more profit; the environment is less affected by the M’s production process. Moreover, part 3 of Proposition 7
shows that the profit of channel in the RPMG can be maximized and that of M and R will be arbitrarily allocated
based on each player’s bargaining power.
5. Numerical analysis
In this Section, we numerically illustrate our results and gain further insights. We fix the parameter values as
follows: a=101, b=3, c=10, γ = 0.9, λ=1, =0.8 and =1.6. These parameter values have been chosen for two
reasons. First, these values guarantee that the profit of the centralized channel is jointly concave in p, e, and ,
hence, the optimal decision of retail price 푝푐∗, marketing effort level 푒푐∗, and product greening level ∗푐 exists and
is unique. Second, the parameters of a, b, c satisfy that the market demand is positive when the retail price is
equal to the production cost, i.e., p=c.
5.1. The sharing contracts use the same sharing rule (original model)
Table 4 gives the numerical example results for the optimal decisions and the profit of the centralized channel
and the decentralized channel under WP. The results of two models serve as benchmarks for the evaluation of the
performance of sharing contracts.
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Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
Table 4. The optimal decisions under centralized channel and WP
w
p
q
e
E
m
r
c
Model
Centralized
channel
10.17
2
26.27
5
48.82
5
18.30
9
-
-
-
577.765
1
22.62
4
30.21
8
22.78
1
0.71
5
4.746
8.543
269.572
143.796
413.368
WP
From Tables 4, the production quantity, the marketing effort and the greening effort level of the decentralized
channel under WP are lower than those of the centralized channel. These results lead to a lower profit for whole
channel under WP. We next compute M's and R’s optimal decisions and profit in the decentralized channel under
sharing contracts corresponding to the values of in the range of [0.01, 0.99]. We present the results of jm, 푟푗
and 퐸j in Table 5. Furthermore, we also present the optimal decision of M on product’s greening level in this
table to verify whether the greening level of channel is improved in the cooperation state.
Table 5. Computational results of original model
RP
RPM
RPG
E
RPMG
E
m
r
E
m
r
E
m
r
m
r
0.01
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.99
465.5
433.3
395.8
356.1
314.1
269.6
222.3
172.0
118.5
61.3
5.2
0.81
0.84
0.87
0.89
0.90
0.91
0.92
0.91
0.89
0.86
0.82
8.19
7.63
6.97
6.27
5.53
4.75
3.91
3.03
2.09
1.08
0.11
571.2
512.6
449.3
387.8
327.9
269.6
212.8
157.5
103.7
51.2
6.6
1.00
1.00
0.99
0.99
0.98
0.96
0.95
0.93
0.92
0.90
0.88
10.06
9.03
7.91
6.83
5.77
4.75
3.75
2.77
1.83
0.90
0.09
466.0
438.6
405.7
370.1
331.3
288.9
242.4
191.1
134.2
71.0
4.7
0.81
0.84
0.87
0.90
0.92
0.94
0.96
0.96
0.96
0.94
0.91
8.29
572.0
520.0
462.2
404.4
346.7
288.9
231.1
173.3
115.6
57.8
5.8
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
10.17
10.17
10.17
10.17
10.17
10.17
10.17
10.17
10.17
10.17
10.17
52.4
64.2
47.8
8.58
57.8
104.7
156.7
208.1
258.4
307.2
353.8
397.6
437.6
469.3
124.9
182.2
236.4
287.6
336.1
381.9
425.3
466.4
501.6
97.3
8.93
115.6
173.3
231.1
288.9
346.7
404.4
462.2
520.0
572.0
148.5
201.3
255.4
310.4
366.0
421.2
474.8
520.2
9.31
9.72
10.17
10.67
11.21
11.82
12.49
13.17
6.3
5.1
7.5
5.8
We display the results of 푚푗 and 푟푗 in Table 5 through Figure 1 to demonstrate that R’s profit increases and
M’s profit decreases with sharing fraction in all the sharing contracts.
RP
RPM
RPG
RPMG
1(a)
1(b)
Fig. 1. (a) M’s profit, (b) R’s profit changes with sharing fraction
We next display the value of 퐸j in Table 5 through Figure 2 to evidence that the channel efficiency is concave
in sharing fraction () under RP and RPM contracts whereas it decreases in under RPM contract and remains
stable at one under RPMG contract. We can also determine the value of that maximizes the channel efficiency
푅푃
푀푎푥
푅푃푀
푀푎푥
under each sharing contract. Namely, 퐸
= 0.916 at =0.582, 퐸푀푅푃푎퐺푥 = 0.964 at =0.726 and 퐸
approach one when approaches to zero. These numerical results demonstrate that the RP, RPM and RPG
contracts cannot coordinate the channel while the RPMG contract perfectly coordinates the channel.
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Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
RP
RPM
RPG
RPMG
Fig. 2. 퐸푗 changes with sharing fraction
We further observe from Table 5 that if the beforehand negotiated is at 0.3, 0.4 and 0.5 respectively, 푚푗 >
푊푚푃 and 푟푗 > 푟푊푃. This means that both R and M earn greater profits under the sharing contracts than under
WP if the sharing faction was chosen at 0.3, 0.4 and 0.5 respectively. Thus, the Pareto improvements can be
achieved if the sharing fraction was chosen at these values. From Proposition 1-4, we can determine the exact
value of in the Pareto-improving region which leads to a win-win outcome, namely, 훼푅푃(0.275, 0.5),
훼푅푃푀(0.232, 0.5), 훼푅푃퐺(0.291, 0.543) and 훼푅푃푀퐺(0.249, 0.533). Moreover, from observing the value of
column , we find that the greening performance of the channel under each sharing contract is higher than those
in WP for all values within the Pareto-improving region. (For example, when =0.3, the greening level of
product under RP, RPM, RPG and RPMG are 6.27, 6.83, 9.31 and 10.17 respectively. These levels of greening
are higher than that under WP (i.e., 4.746).
5.2. The sharing contracts with different sharing parameters for effort costs
So far, our analysis results in original model depending heavily on the assumption that the firms use the same
sharing rule for all costs. We now extend our analysis using different the sharing parameters for costs. We denote
such a contract as (, , ) where ∈[0, 1] is the fraction of the gross profit (i.e., the total revenue minus the
production cost of sold stocks) that R receives, ∈ [0, 1] is the fraction of R’s marketing cost that R undertakes;
and ∈ [0, 1] is the fraction of M’s greening effort costs which R agrees to share with M. Under this setting, the
equilibrium results can be derived by following backward induction. However, we obtained complex results that
is difficult to analytically following the same procedure used in Section 4. Thus, we use numerical methods to
illustrate the Pareto-improving region for this case.
The Pareto-improving region is plotted in Figure 3 (a) with respect to and for the RPM contract with
differentiating between the sharing rule for gross profit share, , and the sharing rule for the Marketing cost, φ
(i.e., the sharing contract as (, , 0)). Every pair (, ) in this region presents a feasible solution to the
bargaining problem that leads to higher profits of both channel members. Similarly, Figure 3 (b) illustrates the
Pareto-improving region with respect to and for the RPG contract with differentiating between the sharing
rule for gross profit, , and the sharing rule for the greening effort cost, (i.e., the sharing contract as (, 1, )).
Compared to the results of original model, we find that the use of different sharing coefficients will expand more
the feasible region. However, the negotiable range values for gross profit sharing do not change significantly
compared to the original model. This result implies that regardless of efforts cost sharing, the adoption of a
cooperative program on efforts is never feasible when most of the gross profits go to either M or R. Further, M is
willing to implement a cooperative program on marketing efforts only when R bears marketing cost higher than a
threshold (i.e., 13,6%). Whereas, R is willing to implement a cooperative program on greening efforts only when
R incurs greening investment cost lower than a threshold, about 80%. This result is quite intuitive; the increase in
cost share borne by the partner leads a decrease in benefits for the party who handles the activities and makes the
implementation of a cooperative program on efforts difficult to be feasible.
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Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
Fig. 3. The Pareto-improving region in the RPM (a), RPG (b) contract with different sharing parameters for
effort costs
6. Conclusions, limitations and Future Research
6.1. Conclusion
In this paper, we studied the channel collaboration issues through coordinating contracts on efforts invested in
order to promote the market demand and reduce the negative environmental impact of the channel. We study a
two-echelon channel wherein the upstream manufacturer is responsible for product greening, a downstream
retailer undertakes marketing activities and the market demand is affected by retail price, R’s marketing and M’s
greening effort. These complex settings represent a realistic business practices for firms dealing with channel
collaboration issues for the different decisions impacting on the channel performance including not only the
operational choices (quantity, price) and marketing decisions of the firms but also the sustainable channel
management. Therefore, we integrate M’s greening and R’s marketing efforts into the sustainable coordination of
channel and propose the coordination schemes for the channel through the combination of revenue-sharing and
cost-sharing contracts under a VMI-CC system. Through analytical model, we first analyze the impact of power
structure on the implementation of sharing contracts, as well as the economic and environmental aspects in the
channel. We then prove that the cooperation between M and R in a VMI-CC via sharing contracts is beneficial to
channel agents, leads to higher profitability and results in higher levels of the environmental performance. From
managerial insights, the channel managers can increase the greening level of product to meet the expectations of
consumers while optimizing their economic performances by adopting sharing contracts.
6.2. Limitations and Future Research
Although the proposed model provides some ideas about how a green channel can be managed in the sense of
profit maximization, there exist still some limitations that can be tackled in future research. First, for simplicity
of analysis the demand is assumed as deterministic linear in price. Future research may be developed by
considering the case of stochastic demand. Second, we don't take the joint impact of marketing and greening
effort on the consumers’ behavior into consideration. In contrast, prior researchers show that potential types of
customer benefits resulting from environmentally friendly consumption (i.e, Self-benefit value and societal
benefit value) that depends not only on the green investment cost but also the interactions between firms and
customers through marketing strategy (i.e., advertising appeals for the product, Green and Peloza, 2014).
Therefore, future research can examine the case that the elasticity of greening investment on the customers’
preference depends on the marketing strategy (i.e., advertising level and advertising appeals). Third, our study
considers a channel in which both M and R have sufficient budget to make any decisions, however, in the real
world, the capital constraints are a great challenge for many firms. Therefore, it might be interesting to examine
our sharing contracts in a green channel where the capital constraints exist. Finally, as another opportunity for
future investigation, researchers can explore the cases of asymmetric information. For example, the cost of green
product R&D is the private information of M whereas R can be more knowledgeable about the cost of exerting
marketing effort and the demand.
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Dinh Anh Phan, Hoa T. L. Vo, Hong Quang Duong/ MICA 2018 Proceedings
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