Scholarly article on topic 'Corporate social responsibility, coordination and profit distribution in a dual-channel supply chain'

Corporate social responsibility, coordination and profit distribution in a dual-channel supply chain Academic research paper on "Economics and business"

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{Dual-channel / CSR / "Product compatibility" / Coordination}

Abstract of research paper on Economics and business, author of scientific article — Nikunja Mohan Modak, Shibaji Panda, Shib Sankar Sana, Manjusri Basu

Abstract The dual-channel supply chain model has become increasingly popular in the industry and describes a scenario in which a firm, in addition to selling through the traditional supply chain of manufacturer and retailer, opens a direct channel to the customer through Internet sales. However, in the current global business environment, corporate social responsibility (CSR) is a determining factor of choices of the customers. Based on the above important factors, this article introduces a corporate social responsibility two-echelon dual-channel supply chain. In addition to operating an online channel, the manufacturer intends to increase stakeholders' welfare by exhibiting CSR. The pricing decisions for both the cases of the decentralized and centralized scenarios are studied analytically as well as numerically. The paper also examines the effect of the degree of concern of the manufacturer regarding CSR on product compatibility and discusses feasibility of the successful operation of a dual-channel supply chain. Finally, channel coordination through all unit quantity discounts with the agreement of a franchise fee and surplus profit division through bargaining is discussed analytically.

Academic research paper on topic "Corporate social responsibility, coordination and profit distribution in a dual-channel supply chain"

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Pacific Science Review xx (2015) 1 — 15

www.elsevier.com/locate/pscr

Corporate social responsibility, coordination and profit distribution

in a dual-channel supply chain

Q4 Nikunja Mohan Modak a, Shibaji Panda b, Shib Sankar Sana c *, Manjusri Basu a

a Department of Mathematics, University of Kalyani, Kalyani, 741235, West Bengal, India Department of Mathematics, Bengal Institute of Technology, 1. No. Govt. Colony, Kolkata, 700150, India c Department of Mathematics, Bhangar Mahavidyalaya, Bhangar, 743502, South 24 Parganas, India

Received 26 March 2015; revised 12 May 2015; accepted 14 May 2015

Abstract

The dual-channel supply chain model has become increasingly popular in the industry and describes a scenario in which a firm, in addition to selling through the traditional supply chain of manufacturer and retailer, opens a direct channel to the customer through Internet sales. However, in the current global business environment, corporate social responsibility (CSR) is a determining factor of choices of the customers. Based on the above important factors, this article introduces a corporate social responsibility two-echelon dual-channel supply chain. In addition to operating an online channel, the manufacturer intends to increase stakeholders' welfare by exhibiting CSR. The pricing decisions for both the cases of the decentralized and centralized scenarios are studied analytically as well as numerically. The paper also examines the effect of the degree of concern of the manufacturer regarding CSR on product compatibility and discusses feasibility of the successful operation of a dual-channel supply chain. Finally, channel coordination through all unit quantity discounts with the agreement of a franchise fee and surplus profit division through bargaining is discussed analytically.

Copyright © 2015, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and Hosting by Elsevier B.V. All rights reserved.

Keywords: Dual-channel; CSR; Product compatibility; Coordination

Introduction

Currently, an impressive growth of e-commerce in the highly competitive global market drives

* Corresponding author.

E-mail addresses: nikunja.modak@gmail.com (N.M. Modak), shibaji.panda@gmail.com (S. Panda), shib_sankar@yahoo.com (S.S. Sana), Manjusri_basu@yahoo.com (M. Basu).

Peer review under responsibility of Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University.

manufacturers to introduce online channels. A manufacturer captures the markets situated in geographically diverse locations through an online channel via the Internet that reduces the time consumption for purchasing, and hence it can also increase market share. In Western Europe, e-commerce spending hit 128 billion Euros in 2013, up 14.3% from that in 2012. In 2010, the Czech Republic earned 24% of the country's total turnover through online channels. Global e-commerce sales topped 1 trillion for the first time in 2012 [23]. It is forecasted that e-commerce spending in 2017 will

http://dx.doi.org/10.1016/j.pscr.2015.05.001

1229-5450/Copyright © 2015, Far Eastern Federal University, Kangnam University, Dalian University of Technology, Kokushikan University. Production and Hosting by Elsevier B.V. All rights reserved.

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reach 191 billion Euros in Western Union, a compound annual growth rate of approximately 11% [24]. Ecommerce sales in the US were increased by 15.8% in 2013 compared to the year 2011. It is observed that consumers prefer alternatives and choose the one that is better suited to their needs, which compels manufacturers to restructure their traditional brick-and-mortar channels by engaging in direct sales through Internet channels [48].

Corporate Social Responsibility (CSR) can be defined as a doctrine that promotes the expansion of social stewardship by businesses and organizations. The CSR approach is holistic and integrated with the core of the business strategy by addressing social and environmental impacts of the businesses. CSR suggests that corporations embrace responsibilities toward a broader group of stakeholders, such as customers, employees, etc., besides their regular financial obligations to stockholders [20]. In the current global business environment, CSR is now a determining factor in consumers' and clients' choices that cannot be ignored by companies. The companies that fail to maximize their adoption of a CSR strategy will be left behind. Recently, empirical evidence has shown that customers are willing to pay a higher price for products with CSR attributes and that CSR programmes influence 70 per cent of all consumers' buying decisions [4,10]. As a result, many leading international brands, such as Walmart, Nike, Adidas and Gap, have been compelled to incorporate CSR in their complex supply chains via a code of conduct [3].

Several research works have been conducted in the area of supply chain coordination. Many of them concentrate on the direct collaboration between two individual members, whereas the models dealing with resolving channel conflict in dual-channel supply chains are notably fewer. The purpose of this present article is to incorporate CSR in a dual-channel supply chain comprising a manufacturer and a retailer. In addition to traditional retail channels, the manufacturer operates an online channel. The manufacturer, as the leader of the channel, considers stakeholders' welfare through CSR and influences the downstream channel members to behave socially. Instead of the manufacturer's CSR activity, we also incorporate the effect of CSR in the form of consumer surplus in its profit function. In a manufacturer-Stackelberg game, setting apart the discussion of the effects of CSR in decentralized and centralized decision-making, we apply all unit quantity discounts with the agreement of a franchise fee to resolve channel conflict and to find out win—win profits of the channel members.

Literature review

In the recent trends of global business scenarios, the dual-channel supply chain has a significant importance in supply chain management. In addition to a retail channel, an Internet channel of the manufacturer has the potential to reduce retailers' dominance, addressing different customer segments in order to gain a higher profit margin. For instance, with the popularity of the Internet, many top manufacturers, such as IBM, Cisco, Nike and Estee Lauder, have started selling online directly. Several electronics manufacturers, including Sony, PalmOne and Samsung, have setup boutiquestyle outlets in upscale locations. The largest English-language publisher, Random House, has publicly declared that it may sell books directly to the readers, putting them in direct competition with Barnes and Noble and Amazon.com [49].

Meanwhile, traditional companies are expanding their business through online access at retail stores. Dell has installed kiosks in shopping malls and now sells its computers through Costco [30]. These studies suggest that more consumers are embracing multiple channels to satisfy their shopping needs [47]. Some customers prefer purchasing online, whereas others prefer shopping in retail stores. As a result, manufacturers redesign their traditional channel structures by engaging in direct sales to reach different customer segments that cannot be reached by the traditional retail channel, giving birth to dual channels. Several issues in dual-channel supply chains have been addressed by researchers. Hua et al. [21] analysed the effect of delivery lead-time on the pricing decisions in a dual-channel supply chain. Dan et al. [14] determined the optimal retail service and prices in a dual-channel supply chain. Chen et al. [8] developed a dual-channel supply chain and proposed pricing strategies that maximize decentralized dualchannel performance. Sharma and Mehrotra [46] claimed that the dual-channel setup increases channel conflict, though it has the potential to increase customers' demand. Yan [50] developed a dual-channel supply chain and analysed the effect of differentiated branding. Chiang et al. [9] proposed a model that demonstrates that a dual-channel supply chain can be used to control retailers' prices. Panda et al. [39,42] analysed pricing and replenishment decisions in a dual-channel supply chain considering continuous unit cost decrease. All of the proposed models mentioned above have addressed pricing and replenishment policies, channel conflict and channel competition, mainly between brick-and-mortar and Internet channels, but they do not focus on corporate social responsibility.

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Corporate social responsibility is corporate self-regulation, which currently does not have a unique definition. Dahlsrud [15] analysed 37 definitions of CSR and developed five dimensions of CSR: environmental, social, economic, stakeholder, and volun-tariness. Dyllick and Hockert [17] defined CSR as "meeting the needs of a firm's direct and indirect stakeholders (e.g., shareholders, employees, clients, pressure groups, communities etc.), without compromising its ability to meet the needs of future stakeholders as well." Applications of CSR in supply chains have emerged in the last two decades. Considering a socially responsible supply chain, Murphy and Poist [32] suggested a total responsibility approach by adding social issues to the traditional economy. Carter and Jennings [7] explained the necessity of CSR consideration in supply chain decision-making through a case study and survey research. Analysing a French sample data set, Ageron et al. [1] derived several conditions for successful sustainable supply chain management. Cruz [11] traced the equilibrium condition for an environmentally responsible supply chain network by using a multi-criteria decision-making approach. Cruz and Wakolbinger [13] extended the model to a multi-period setting for measuring long-term effects of CSR. Considering a socially responsible supply chain network, Hsueh and Chang [25] showed that social responsibility sharing through monetary transfer leads to channel optimization. Cruz [12] developed a decision support system framework for modelling and analysis of a CSR supply chain network. Ni et al. [35] developed a two-tier CSR supply chain by assuming the dominant upstream channel member's CSR cost, which is shared by the downstream channel member through a wholesale price contract. Ni and Kevin [34] investigated a two-echelon supply chain by assuming individual CSR costs for each channel member. They examined the effects of strategic interactions between the channel members via a game theoretical approach. Panda [36] and Panda et al. [38] considered CSR supply chains and used different contracts to resolve channel conflict. They used a Nash bargaining product to divide surplus profit between the channel members.

Coordination among channel members is imperative for improving channel-wide performance because it neutralizes the difference between the decentralized and centralized outcomes. The main objective of a coordination mechanism is the transfer of money from one channel member to another while they act coherently. Existing literature has rich content in this regard for two-echelon supply chains. Quantity

discounts [38], two-part tariffs [26], revenue sharing [36], mail-in-rebates [45], buyback [16], disposal cost sharing [37,43], profit sharing [31], etc. are used to resolve double marginalization in a two-tier supply chain. However, there are a few papers that have focused on cutting out channel conflict in dualchannel supply chains. Chen et al. [8] used wholesale prices and manufacturers' direct channel price contracts for channel coordination. They also suggested that two-part tariffs and profit sharing in a range coordinates the channel and that the channel members' profits follow a win—win strategy. Agrawal et al. [2] showed that sales effort resolves channel conflict when the channels do compete with each other. Cai [6] proposed a hybrid revenue sharing and linear online retail prices relationship to cut out channel conflict and examined the influence of channel coordination on the supplier. Panda [40,41] used revenue sharing contracts and Nash bargaining for channel coordination and under quantity-price and time-price dependent demand. Boyacci [5] showed that revenue sharing, buyback and wholesale price contracts are unable to resolve double marginaliza-tion. He mentioned that a penalty contract can coordinate a dual-channel supply chain, though it is difficult to implement. However, CSR in the modelling of channel coordination has not been considered in the models reported above.

The research reported in this paper differs from the prior works in many aspects, as follows. First, unlike the natural intention of maximizing the channel members' profits, the objectives of the channel members are to engage in CSR and to find the effects of CSR on the dual-channel supply chain. The outcomes of the paper indicate that the profits of the members of the chain are always higher than their individual pure profits when the channel members concentrate more on CSR. Second, the paper discusses the effect of CSR on the pricing issues of a product. Third, the paper analyses the effect of customers' channel preference on the channel competition for optimal prices. Fourth, it examines the effect of CSR on product compatibility and discusses feasibility for successful operation of a dualchannel supply chain. Fifthly, the paper uses all unit quantity discounts with agreement of franchise fees as the contract mechanism to resolve channel conflict. It cuts out channel conflict but is unable to depict win—win profits for the channel members. Sixthly, the paper uses a Nash bargaining product to divide the surplus profit between the channel members, where integrated profits of all of the members of the chain are win—win.

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We consider a dual-channel supply chain comprising a manufacturer and a retailer. The manufacturer produces and sells products through retail as well as e-tail/online channels. Here, the price-demand relationship is deterministic and known. Following Yue and Liu [49], Kurata et al. [28] and Huang and Swaminathan [22], we assume that, for model simplicity, the channel demand functions in the two channels are linear in self-price and cross-price effects. The forms of the demand functions in retail and e-tail (online) channels are

Dr = 0a - bipr + a(pd - pr) (1)

Dd =(1 - 9)a - b2pd + a(pr - pd)

where a > 0 is the market potential. The parameter 0 (0 < 0 < 1) is the compatibility of the product with the retail channel. How the product is perceived within the context of the customers' lifestyles choices is dependent on the compatibility of the product. When the product closely matches the needs, wants, beliefs, values and consumptions patterns of the customers, it can be considered highly compatible with the consumers' choices. The percentage of the primary demand that goes to the retail channel is 0, and, when the value of 0 is greater, the product's compatibility with the retail channel is larger and more consumers purchase the product from the retail channel. Computer-related products, books, information, magazines and digital products have more compatibility with the direct channel than products such as water, rice, gasoline and milk. Here, b1(>0) and b2(>0) are the price sensitivity factors in the retail channel and online channel, respectively. The parameter a(>0) is the cross-price effect, which reflects the degree of price competition between the channels. Quite often, the selling price in the online channel is higher than the manufacturer's wholesale price, i.e., pd > wm. Otherwise, the retailer would purchase the product through the online channel rather than from the manufacturer. Additionally, for the profitability of the retailer, the selling price of the retailer is higher than the manufacturer's wholesale price, i.e., pr > wm.

Many leading brands face intense pressure for socially responsible supply chain management [3]. A commonly noted response to this pressure is to maintain the code of conduct given to the business partners who are socially responsible [44]. For quantitative

analysis, the paper considers only the effect of CSR in the form of consumer surplus rather than the CSR activities, which are performed by the socially responsible channel members. It is well established that a firm's social responsibility is accounted for through the consumer surplus that is accrued from its stakeholders [18,19,27,29,34,35]. The consumer surplus is the difference between the maximum price that the consumers are willing to pay for a product and the market price that they actually pay for the product. Thus, in the present model, the consumer surplus can be found as Q1

Pr/mkt

Drdpr +

Vd/mkt

2(b + a) 2(b2 + a)

where pr/mkt = (da + apd — Dr)/ (h + a) and pd=mkt = ((1 — d)a + apr — Dd)/(b2 + a) denote the market prices of the product in retail and online channels, respectively, and pr/max = (da + apd) / (bj + a) and Pd/max = ((1 — d)a + apr )/(b2 + a) denote the maximum prices that consumers are willing to pay for a product in retail and online channels, respectively.

If t (0<t < 1) is the degree of CSR that is the socially responsible manufacturer's concern, then it incorporates tCS as the consumer surplus in its profit. The value of t = 0 implies that the manufacturer is the pure profit maximizer, and t = 1 represents that the manufacturer is the perfect welfare maximizer. Because the manufacturer is socially responsible, its profit function consists of pure profit that is received by selling the product and consumer surplus through CSR practices. Under this setting, we first derive the centralized and decentralized decisions of the channel members.

Decentralized decisions

In decentralized decision-making, the channel members operate independently and optimize their individual goals. Interactions between the manufacturer and the retailer are considered as a Stackelberg game. The manufacturer acts as the Stackelberg leader of the channel, and the retailer is its follower. In a Stackelberg game, the leader makes the first move, and the follower then reacts by playing the best move consistent with the available information. In this way, the manufacturer first announces the wholesale price

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and selling price of the product in the online channel. Based on the manufacturer's decision, the retailer determines the retail price. The profit function of the retailer is

Note that dpr = -2(bi + a) < 0. That is, pr is a concave function of pr. Substituting the value of pr into the total profit function of the manufacturer and the

Pr = 0r - wm)(0 a - b1 pr + a(pd - pr))

necessary conditions mization of vm yields

Vvm Swm

Vvm Vpd

0 I for opti-

'4/5ib2(b2 ca + b1cß2 + a(a + b20)) + a(b2a + bib2)(a 2b1cb2 + a((a + b2c)a)(3b2 + 2a)+ab2(4b2 + 3a) 0)+ b1 ß2(ca(5b2 + 2 a) + a(4b20 + a(3 + 0)))

(b2a + b1b2)(2 - t)(b2(4a + b1(4 - t)) - b2at)

4b1 b2(b2ca + b1cb2 + a(b1 - b1q)) + a(b2a b1 (c (b2 + 2a )(b2« + b ß2)+ a (5 b1 ß2 -a(b2 a 2 + 5 b? b2 + 3 b1 a(2b2

(b2a + b1b2)(2 - t)(^2(4a + b1(4

The pure profit function of the manufacturer is

Pm = (wm - c)(0 a - b1 pr + a(pd - pr)) + (pd - c)

X ((1 - 0)a - b2 pd - a(pd - pr))

The total profit function of the manufacturer is

vm = Pm + t CS (6)

where 0 < t < 1.

where b1 = (b1 + a) and b2 = (b2 + a). The optimal solutions will maximize the manufacturer's total profit function if the profit function is concave with respect to its decision variables. To check the concavity of the total profit function of the manufacturer, we take the second-order partial derivatives of the profit function, which are as follows

-4ab2 + b1b2( - 4 +1 ) + a(b2 + 2a)t

92vm vpd

-4 b1 b (2b1 b + a (2b2 + a )) + (4 b\ b2 + b1 ab2(8 b2 + 5 a)+ a2 (4b2 + 5 b2a + 2a2) )

Differentiating pr with respect to pr and equating it to zero, we have

0 a +(b1 + a)wm + apd " 2(b1 + a)

m [a (3b1b2 + a (3b2 + 2a ))t] a--

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Clearly, Vft < 0 and < 0 for any t e [0, 1]. Now, the necessary condition for concavity of vm is

92Vm X 2

For any re [0,1],

> 0, and thus

dwl VP2d \VwmPd

= (b2a + bjfc) (2 - r )(4afr + frfo(4 - r )-b2«r )

b?cfr + b1ca(3b 2 + 2a) + a(2(a + b2c)a + 3ab20 ) -a(b2a + bib2)(a + b2q)r

vwm Vpd l Vwmpd the profit function of the manufacturer is a concave function of pd and wm. Using (8) and (9) in (7) and simplifying, we obtain the optimal retail price of the product with decentralized decisions as follows

(b2a + b^) (82 (4a + ^(4-

From (8), (9) and (13), we have the optimal demands of the product in retail and online channels, the profit of the retailer, and the pure and total profit of the manufacturer with decentralized decisions as follows

(2ab20 — ^cP2(2 — t )+b2 cat — a(a + b 20)t )

(2 - r)(fr(4a + b1(4 - r )) - b2ar)

ß2(c ( - 2b1(2b2 + a) - b2a (4 - r )+ b1b2r )+ a (b1 (1 - 0 )(4 - r)+ a(4 - 20 - r))) (2 - r )(fr (4a + b1(4-

[ß1(2afr0 - b1 cb2(2 - r)+ b2car - -a(a + b20)r)"

(2 -r)(fr(4a + b1 (4 - r )) - b2ar)

(b (c(2b1(2b2 + a)-

2ab2 q + b1cb2(2 - r) --b2a (4 - r ) -b1^2r ) ■

b2car + a (a + b2q )r)F1+ -a(b1(1 - q )(4 - r )+ a (4-

■2 0 - r)))F2)

((b2 a + b1b2)(2 - r)2(fr(4a + b1 (4 - r)) - b2ar)2

2a2b2 [2b2 - 4b1b1q + (b1 (2b 1 + b2) + (b1 + b2)a)q2] -a2(frM + a(b2 + 2a)) + 2fr foa - b^^ + (b2fr + b2fr)r+ 2ac(b2a + b1 b2)(2fr( - 2fr + b1q) + (181 (b2 + 2a) - (b - b2)aq)r)+ c2(b2a + b1b2)(2b^b2 + 2b2a + 2^82) - (81 + fr)(b2a + b^r)

(2(b2 a + b1b2)(2 - r)(b2(4a + b1 (4 - r)) - b2ar))

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F1 = 4bib2(b2ca + b:cb2 - a(a + b20 ))

+ (b2a + b1 b2)(b2ca + b1cb2 - a(a + b20))r2 + ( - 4b2cb2 + a ((a - b2c)a (3b2 + 2a) + ab2(4b2 + 3a)0) + buS2( - ca(7b2 + 2a) + a (4b20 + a (3 + 0 ))))r

F2 = c(b2a + b^) (a (2a(2 - r)+ b2(4 - r)(1 - r)) + b1(a(2 - r)2 + b2(4 - r)(1 - r))) + a (b1b2( - 1 + 0)(4 - r)(1 - r) + a2(2a( - 2 + r)-ba(4 + r(-5 + 0 + r)))) + ab1a(4b2(-2 + 0) + (1Ob2 + 7a - 3(2b2 + a)0)r +( - a + b2(-2 + 0))r2)

Here, the consumer can buy the product from both retail and online channels. The retailer operates its channel in competition with the online channel. The retailer has to buy the product from the manufacturer and then sell it to the consumers, and, in doing so, it makes a profit. Thus, the concept of dual channels will be feasible only when the selling prices in both retail and online channels are higher than the wholesale price of the manufacturer. That is, the optimal pricing strategy of the decentralized system is acceptable to the channel members only when p* > w*m and p*d > w^,. Now, p* > w*m if q < dmax, where

three values of t, only b bb1+b+a+b2a 2 (0, 1), and hence it is acceptable because r 2 (0, 1). That is, dmax > dmin

t. From the above discussion,

if t2 0' b1b21-bb1«++b2a

we have the following proposition.

Proposition 1. The pricing policy of the decentralized socially responsible dual-channel supply chain can be operated successfully if the product compatibility parameter 62(6min, dmax) and the degree of social concern of the manufacturer

(0; b^CX«) .From Fig. 1, one can observe

that, to operate the dual-channel successfully, the manufacturer cannot set its degree of social concern, i.e., the value of t, above the threshold b1b2 +b1"

because, whenr e

b1b2+b1a

b1b2+b1a+b2a qmax < qmin ?

b1b2 +b1«+b2 a'

i.e., the pricing policy of the dual channels becomes infeasible. Thus, from Proposition 1, we can conclude that the manufacturer cannot show CSR concern over a threshold to operate a decentralized dual-channel supply chain. It also indicates that the customer's channel preference is one of the determining factors for operating an online channel in addition to the traditional retail channel. When 6 < 6min, the retailer cannot do business because its selling price is less than the manufacturer's wholesale price. Alternately, for 6 > 6max, the manufacturer cannot set the optimal selling price as the online price exists.The online selling price is higher than the wholesale price. This does not ensure that the

b2c(b1 + 2a)(b2a + b1b2) r + a (b2b2(4 - r)(1 - r) - 2b2a2r + b1 a(4a(1 - r)+ b2(4 - (7 - r)r)))

" a24(bT^

and p* > wm if

b1cb2(2 - r) + (a - b2c)ar 2ab2 - ab2r

Note that, both 6min and 6max depend on t, i.e., on the degree of social concern of the manufacturer. It is observed that this range will be valid until 6max > 6min, and, solving 6max - 6min = 0, we have three values of

retailer will participate in the profit-making retail/e-tail channel; the retailer will participate in the dual channels only when its demand in the retail channel is positive, i.e., D* > 0, i.e., if

b1cb2(2 - r ) + (a - b2 c) a r

2 - a b2r

t, ^ 2

b1b2+b1a b!b2+b!a+b2a'

4 (b1b2+b1a+b2a+a2) b1b2+b1a+b2a

. Among these

Note that 6r = 6min. Alternately, the manufacturer will operate the online channel until the demand in the online channel is positive, i.e., D* > 0, i.e., if

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Fig. 1. Graphical representation of Smin and Smax with respect to t.

aß1 (4 - r) - b2c a(4 - r) - b1c(4 b2 + 2 a - b2r)

optimal online selling price

decreases with

a(2 a + b1 (4 - r))

Eqs. (21) and (22) suggest that the manufacturer can successfully operate a profitable dual-channel supply chain when the customer's retail channel preference lies between 6min and min{6m, 6max}. This result is quite obvious because the manufacturer will operate the online channel only when both the channels are profit-able.Thus, another proposition is as follows. Proposition 2. The manufacturer can operate a profitable retail-online channel when the customers' retail channel preference 6 e(6min, min{6m, dmax}). Further, comparing selling prices of retail and online channels, we have p* > p*d if 6 > q1, where

increasing product compatibility, whereas the optimal retail price (pr*) increases with increasing product compatibility. The optimal online selling price coincides with the retail price when d = d1. In the next subsection, we shall study the centralized decisions of the socially responsible dual-channel supply chain when the channel members act as a single entity.

Centralized decisions

When the channel members cooperate and find the decision that maximizes the supply chain performance, it requires a centralized decision-making process. It may be assumed that there is a single decision-maker who produces and sells the product to the customers. The total profit of the channel is the sum of the pure

c(b2a + b1b2)(2 b1b2 - (b1 - b2)ar) + a(b2fr(4 - r)(1 - r) " -b2a2r + b1a(a(4 - 3r)+ b2(4 +( - 6 + r) r)))

a(b2b2(4 - r)( 1 - r) + b2a(6a + b2(3 - r)(2 - r) - 4ar) ' " +b^6b2 - (b2 + 2a)(5b2 + 2a)r + b2(b2 + 2a)r2))

Now, combining the above results with Proposition 1, we obtain the following proposition.

Proposition 3. In a socially responsible decentralized dual-channel supply chain, the optimal retail price is higher than the online selling price if

profit (pc) and the consumer surplus (CSc) that the channel accrues from the stakeholders. The profit function of the channel is

vc= Pc + CSc

q e(q1

i{qm, qmaxg), and the reverse may be

Pc2 = (Pr - c)Dr + (pd - c)D,

noted for q e(qmin, q1).From Fig. 2, one may note that p* > w*m if q > qmin and p* > w*m if < qmax. The

CSc = jjbr + The necessary conditions dvc/dpr and dvc/dpd = 0, for the existence of the optimal solution yield the optimal values of the selling prices as

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follows

2b1b2(b2ca + b^fr + a(a + b20 )) + a(b2a + bnö2)(a + b20)r2-82 ( b1cb2 + b1ca(3b 2 + 2a) + a(2(a + b2 c) a + 3ab2q) + ab1 (3b2q + a(2 + q)))r

(b2a + b182) ^(b2(2 - r)2 + 4a(1 - r)) + ^82(2 - r)2)

28182(b2ca + b1cb2 + a(b1 - b10)) + a (b2a + ^82X81 - b10 )r2-b1(c(b2 + 2a)(b2a + b^) + a(3b182(1 - q) + a(3b2 + 2a - b2q)))r

(b2a + b^2) (a (b2(2 - r)2 + 4a(1 - r)) + ^82(2 - r)2)

To check the concavity of the total centralized channel profit function, we take the second-order partial derivatives of the total centralized channel profit function, which are as follows

vc b ^ , I , , (b2 + 2a)t^

— =—b1(2 — t) + a( — 2 +

Clearly, ^ < 0, ^ < 0 and 2

j p2 pd p2

S2 vc S2 vc

-b2(2 - r) + a : 2a(1 - r).

b2 + a (b1 + 2a) r b1 + a

for all t 2 [0, 1]. Thus, the total profit function of the centralized channel (vc) is a concave function of pd and pr. Hence, the optimal selling prices (prc and& pdc) provide the global maximum to (24). From (25) and (26), we obtain the optimal values of the demand of the product in the retail and online channels for the centralized decision, which are as follows

Hence, we have

Fig. 2. Graphical representation of optimal decentralized prices with respect to 0.

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b1(2ab20+b1 cß2(-2+r)+b2car - a(a+b 20 )r )

a( b2 (2 - r )2+4a(1 - r)) + b^(2 - r )2

then the manufacturer's decision to open an online channel is not profitable because its online demand is negative in this case. However, there must be competition between the retail channel and the online channel in the centralized process even though the channel

b2( - 2b1(b2c + a( - 1 + 0)) + (b2coc - + bcfe + ab10 )r ) " a2b2(2 - r )2 + 4a(1 - r)) + b^(2 - r )2

The optimal pure and total profits of the centralized channel are as follows

P* = (Prc - c)Drc + (pdc - c)Ddc and

v* = (prc - c)Drc + (pdc - c)Ddc + r

'DL + Dd-2b1 2^2.

In the context of centralized decision-making, the manufacturer would be interested in opening the online

members co-operate. The channel members make decisions jointly, but the market potential remains the same. When the manufacturer operates an online channel, some customers switch to the online channel; as a result, the retailer's demand decreases, and it earns less profit. In addition to the selling prices of the retail and online channels, the customers' channel preference determines the divisions of the potential market demand. Thus, like in the decentralized decision-making process, here also the selling prices of the retail channel may be higher than the online channel, i.e., prc >pdc, i.e., if q > q2, where

_2ab1^1^2 - ((b1 - b2)ca(b2a + b^) + a^1 (b2a + 3b^2))r + ab1 (b2a + b^) r2

a22(b1 + b2)b1b2 - 23b?b2 + b1 (b2 + 2 a)(3b2 + 2 a)+ b2a (3 b2 + 4 a))r + (b1 + b2)(b2 a + b1 b2)r2

channel only when the online channel demand is positive, i.e. Ddc > 0, which, after simplification, yields

aß1 (2 - r) - 2b2cß1 + c(b2a + b1ß2)r 1 - ab1 r

Alternately, the minimum level of product compatibility for operating a centralized retail channel can be found from Drc > 0. This, after simplification, yields

b1cß2(2 - r) + (a - b2c)ar ab2r

Although the manufacturer and the retailer cooperate and make decisions jointly in the centralized channel, the product compatibility has an impact on the manufacturer's decision to open the online channel. In the i-th replenishment cycle, if the customers' retail channel preference is higher than the threshold qj^,

From the above discussion, we have the following proposition.

Proposition 4. The manufacturer can operate a centralized dual-channel supply chain if 62 (6cmin, 6cmax)- The online selling price is higher than the retail price for any 62(6cmin, 62), and the retail price is higher than the online price for any 62 (62, 6cmax, ).Proposition 4 demonstrates that, when the channel members cooperate and make decisions jointly, the manufacturer's decision to open an online channel is profitable only when the customers' retail channel preference lies between 6min and& 6cmax. Interestingly, between these thresholds of the product compatibility, there exists a price competition between the retail channel and the online channel. If the customers' retail channel preference is within (6cmin, 62), then the online price will be higher than the retail price, and the reverse is true for 02 (02, 0^, ). Fig. 3 also

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02 0.4 0.6 0.8

Fig. 3. Graphical representation of optimal centralized prices with respect to 0.

justifies our analytical findings. Thus, for a profitable centralized retail/online channel, the channel will set the selling prices according to the customers' channel preference.Observe that both dcmin and 0^ depend on the degree of the manufacturer's social concern, i.e., on t. A centralized dual-channel supply chain will be

feasible only when dCmin < dCmax. Solving dmax — d<min = 0 for t, we obtam_t^ values for t,

V2bTb2/(Vbb2 — a) and VWfrAVbfr + a). Clearly, both values are greater than 1 because Vbrb2> a. However, t 2 (0, 1), hence we have the following proposition.

Proposition 5. A centralized dual-channel supply chain will he feasible for any degree of the manufacturer's social concern.Proposition 5 shows the feasibility of a centralized dual-channel supply chain, i.e., that positive demands in both channels exist in the centralized scenario for any degree of the manufacturer's social concern. This is in contrast to the decentralized scenario, for which the manufacturer cannot exhibit CSR above a certain threshold. Hence, channel coordination is essential not only for profit enhancement but also for the performance of a high level of social responsibility. In the next section, we shall analyse the issue of channel coordination.

Coordination through all unit quantity discount contracts

Coordination among the channel members is essential to optimize system performance. Thus, a key issue in supply chain management is to develop mechanisms that can align channel members and objectives and coordinate their activities to obtain

centralized channel profit. To implement a centralized pricing policy, the manufacturer offers to the retailer that online selling prices will be adjusted according to a centralized policy, as well provides all unit quantity discounts as an incentive to the retailer. The online selling price of the manufacturer under the coordinated scenario is (pd — R), and the discounted wholesale price of the manufacturer is w*m (4 2(0, 1)). Under this mechanism, the profit function of the retailer and total profit function of the manufacturer are, respectively, as follows

Prco = (pr — 4 w*m) (6a — b1pr + a(pd — R — pr )) (34)

vmco = [yWm — c) (0a — Vr + a0d — R — pr))

+ (p — R — c)((1 — 0 )a — b2(pd — R) + a(pr — pd + R))

0a — b1pr + a(pd — R — pr))2

((1 - 0 )a - b2(pd - R) + a(pr - pd + R))2

In a decentralized dual-channel supply chain for a given wholesale price (w*m) of the manufacturer and price for the online channel (pd — R), prco is concave in pr, hence solving dprco/dpr = 0, and we get

pd a — Ra + ad + w*mb14

The channel will be coordinated only if the retailer's self-optimized selling price (prco) under the all unit

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quantity discount contract coincides with the centralized retail price, i.e., prco = prc. Solving prco - prc = 0 for the fraction of the wholesale price discount 4, we get

= (4coWm - c)Drc

+JDLJDk

+ N1 + 2ß2

+ (pdco - Rco - c)Dd,

2ß1ß2 (b2ca + b1 cß2 + a(a + b20)) + a(b2a + b1ß2 )(a + b20)r2

2(pda - Ra + a0)

wm(b2a + b1ß2) ^(b2(2 - r)2 + 4a(1 - r)) + b1ß2(2 - r)2) 2ß^b^cß2 + b1ca (3b2 + 2a) + a(2(a + b2c)a + 3ab20) + ab1 (3b20 + a(2 + 0)))r

Thus, the retailer will agree to sell the product at the centralized retail price if 4 = qco. However, one may note that qco depends on the online selling price (pd ) of the manufacturer. In the second stage, in response to the retailer's decision, the manufacturer will optimize its total profit function. Hence, by solving vmco/dpd = 0, the online selling price (pdco) of the manufacturer can be determined. In contrast, the manufacturer has to adjust its online price for channel coordination. Thus, the adjustment in the online selling price that the manufacturer will consider, is given by Rco = (pdco - pdc), which yields

Here, vm

* * P = v ,

rco c '

which means that the total

channel profit under the proposed contract mechanism is exactly equal to the total centralized channel profit, and we have the following proposition.

Proposition 6. The all unit quantity discount with the set of contracts (Rco, 4co ) of the manufacturer can coordinate a socially responsible dual-channel supply chain.The above analysis shows that our proposed all

aß1 (2aß20 + bcß2( - 2 + r)+ b2car - a(a + b20)r) (b1 ß2 + a(b2 + 2a)) 2a2b2(2 - r)2 + 4a(1 - r)) + b1 ß2(2 - r)2) ( - 2 + r)

Thus, profits of the retailer and the manufacturer are as follows

ß1 (2aß20 + b1cß2( - 2 + r)+ b2car - a(a + b20)r)2

unit quantity discount can coordinate the supply chain and allows the manufacturer to earn a positive profit. Note that the difference in total profit of the manufacturer between coordinated and decentralized scenarios is as follows

b2(2 - r)2 + 4a(1 - r^ + b1ß2(2 - r)2)

2ß1 (2aß2 + b1ß2(2 - r) - b2ar)(2aß20 - b1cß2(2 - r)+ b2car - a(a + b20)r)2 2a2b2(2 - r)2 + 4a(1 - r)) + b1ß2(2 - r)2)2(2 - r)(4aß2 + b^(4 - r) - b2ar)

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Thus, comparing the profits of the channel members with their respective decentralized profits, we find that, due to coordination, profits of the retailer are enhanced significantly, which improves the dual-channel supply chain efficiency but fails to provide benefit to the manufacturer.Next, we shall discuss the implementation of the contract with a complementary agreement between the manufacturer and the retailer that not only coordinates the dual-channel supply chain but also ensures a win-win strategy for both members of the chain.

All unit quantity discount with the agreement of franchise fees

In the previous section, we have already shown that an all unit quantity discount contract can coordinate the channel, but it cannot provide a win—win condition for the manufacturer. Thus, for successful implementation of the contract, suppose that the manufacturer charges a franchise fee F to the retailer. When a franchise fee F satisfies p*co — F > p*, the retailer will accept a (Rco, 4co, F) contract, which yields

F < p*Co - p** = F

Alternately, the minimum franchise fee charged by the manufacturer to the retailer is given by

F v* v* F

— m mco —

Thus, we have the following proposition.

Proposition 7. The all unit quantity discount with the agreement of franchise fees can coordinate a two-level socially responsible dual-channel supply chain and provide a win-win opportunity for the channel members for the franchise fee F if it satisfies the inequality F < F < F. Proposition 7 suggests that a higher F benefits the manufacturer, whereas a lower F benefits the retailer. The value of F depends heavily on the bargaining power of the retailer in the supply chain. In the next subsection, we shall discuss the outcomes of bargaining.

Determination of franchise fees through bargaining

Bargaining refers to situations where two or more players who have the opportunity to collaborate form mutual benefit in more than one way. To determine the exact value of franchise fees and profits of respective channel members, we use the generalized asymmetric Nash bargaining solution [33]. Nash proposed a basic

framework to construct a negotiation model among players. Suppose the manufacturer and the retailer have bargaining powers of, respectively, g and 1 — g (g 2 (0, 1)). Let Dm and Dr denote the surplus profit share of the manufacturer and the retailer, respectively. The functional forms of Dm and Dr are as follows

Dm(F)= ^o + F - v*m) = Xm + F Dr (F) = (p*co - F - p**) = Xr - F

where Xm v*m

vm and Xr = p*

The total surplus profit generated through cooperation is equal to Dm + Dr = Xm + Xr. According to generalized asymmetric Nash bargaining, we must maximize the following function

xF<F<F AmAr

The equilibrium solution of the above Nash bargaining product can be obtained by solving ^^ = 0 and is found as follows

Fb = gXr - (1 - g )Xm

Using the bargaining solution of franchise fees, we secure the profit of the manufacturer and the retailer after bargaining as follows

vbmco = v*m + g(Xm + Xr)

<o = p** +(1 - g)(Xm + Xr)

Note that, in particular, if all players involved in the bargaining procedure have equal bargaining power, i.e., g = 1/2, then each and every one obtains an equal share ((Xm + Xr)/2) of the total surplus. From the above results, we have the following proposition.

Proposition 8. (i) The bargaining outcome of franchise fees depends on channel members' bargaining power. (ii) The surplus profit of the channel generated through coordination is distributed between the channel members according to the ratio of their bargaining power. -Thus, the all unit quantity discount contract combined with the adjustment of the online selling price achieves channel coordination but fails to provide benefit to the manufacturer. However, with the agreement of the franchise fee, a win-win opportunity is provided to both members. Finally, through Nash asymmetric

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bargaining, the members find their equilibrium profit within the win-win range depending on their bargaining power.

Summary and concluding remarks

In this paper, the analysis of a dual-channel socially responsible supply chain has been conducted. In a Stackelberg setting, the manufacturer, the leader of the channel, exhibits CSR. While formulating the model, we have incorporated only the effect of CSR in the form of consumer surplus in the socially responsible firm's profit function rather than the activities that it performs. The paper explores the pricing decision through both decentralized and centralized channels. The effect of CSR on the successful operation of dual channels is analysed. To coordinate the channel and obtain profit equal to the integrated system, a hybrid coordination mechanism is developed. The coordination mechanism not only coordinates the channel but also achieves a win—win outcome for the channel members. Finally, the manufacturer and the retailer share the surplus profit through a Nash bargaining solution.

This paper makes contributions to many aspects. First, the paper considers the effect of CSR on the dual-channel supply chain. Second, the paper develops decentralized and centralized models considering the effect of CSR on consumer surplus. Third, it examines the effect of CSR on product compatibility and discusses the feasibility of the successful operation of dual channels for both decentralized and centralized supply chains. It is analytically shown that the feasibility of a centralized dual-channel supply chain exists for any degree of the manufacturer's social concern. In the decentralized scenario, the manufacturer cannot exhibit CSR above a certain threshold and still operate the dual channels successfully. Fifth, an all unit quantity discount with the agreement of a franchise fee not only cuts out channel conflict but also provides a win—win opportunity for the channel members. Sixth, through Nash bargaining, the members find their equilibrium profit within the win—win range in the ratio of their bargaining powers. As far as the authors are aware, such a discussion within a single model has not yet been studied for supply chains.

Although the proposed model provides some ideas about a socially responsible supply chain that can be managed in the sense of pure profit maximization, it has some limitations. First, the demand is assumed to be deterministic and linear in price. This model can be extended immediately for uncertain price-dependent

demand. Second, the CSR has a great impact on the channel members' pure profits. Under the present model settings, a threshold of CSR for the non-negative pure profit of the manufacturer is identified. However, detailed investigation is required to find a specific range of it. Third, the paper applies a transfer pricing policy for channel coordination and then uses a Nash bargaining product for profit division. Instead, strategic bargaining may be used for the same purpose, as indicated. These variations make the model robust and may discover a variety of characteristics of a socially responsible supply chain. Moreover, manufacturing disruptions due to reliability of the manufacturing system, asymmetric information, supply disruptions, cases of imperfect quality products, environmental issues for production, etc. are neglected here. These may be included in an extension of the proposed model in the future.

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