- Email: [email protected]
Coordination of a sustainable supply chain contributing in a cause-related marketing campaign
Accepted Manuscript Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign
J. Heydari, Zeynab Mosanna PII:
S0959-6526(18)32028-6
DOI:
10.1016/j.jclepro.2018.07.055
Reference:
JCLP 13509
To appear in:
Journal of Cleaner Production
Received Date:
26 September 2017
Accepted Date:
06 July 2018
Please cite this article as: J. Heydari, Zeynab Mosanna, Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign, Journal of Cleaner Production (2018), doi: 10.1016/j.jclepro.2018.07.055
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(Manuscript Word count: 6421)
Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign J. Heydari (corresponding Author) School of Industrial Engineering College of Engineering, University of Tehran, Iran E-mail: [email protected]
Tel: +98 21 82084489
Zeynab Mosanna Department of Industrial Engineering, Alborz Campus, University of Tehran, Iran E-mail: [email protected]
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Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign
Abstract: This paper investigates a two-echelon supply chain coordination problem in presence of consumer social awareness (CSA) when SC contributes in a cause-related marketing campaign. The channel consists of a manufacturer and a retailer where the manufacturer contributes in a CM campaign by donating a sum per sold item to the CM campaign. Two scenarios are analysed: (1) In the first scenario, the donation size as a portion of retail price is the only decision variable and paid by the manufacturer (2) In the second scenario, in addition to the donation size, retail price is a decision variable. In the first scenario, a cost sharing contract is proposed to improve channel performance while in the second scenario a collaborative model is developed to coordinate decisions of channel members. The numerical investigations illustrate that the proposed collaborative model not only increases the channel/members profit, but also creates a more socially concerned SC with lower retail prices. Moreover, the developed model helps supply chain managers to more effectively contribute in a CM campaign by making decision correctly on donation size. Key words: Social supply chain coordination; Sustainable supply chain; Cooperate social responsibility; Cause-related marketing; Consumer social awareness 1. Introduction Development of industrial technology and the only focus of companies on their growth and profit had adverse effects on the environment and society (Nigam, 2014). By increasing
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these effects on the world, the concepts of sustainability and sustainable development have emerged (Hutchins & Sutherland, 2008) and the companies were expected by customers and stakeholders to be more responsible and consider corporate social responsibility (CSR) in their business operations (Hsueh, 2014). The importance of the social pillar of sustainability is admitted by the concept of CSR and there are strong links between these concepts (Hutchins & Sutherland, 2008). By increasing consumer social awareness (CSA), SCs are forced to be more responsible toward the society. Nowadays, governments, competitors, and employees pressure downstream firms to distribute and sell social products (Letizia & Hendrikse, 2016). AS a result of increasing pressure on companies to be more socially responsible, cause related marketing (CM) has been applied frequently as a popular marketing tool (He et al., 2016). CM is a form of CSR ( Lii & Lee, 2012) defined by Varadarajan and Menon (Varadarajan & Menon, 1988) as marketing activities in which the firm donates a specified amount to a designated cause. In CM, companies promise to donate a proportion of sales revenue to a cause every time a consumer makes a purchase. CM has been officially used in 1983 when American Express created a campaign for Statue of Liberty restoration and donated a few cents each time its customers used their American Express cards (Lafferty et al., 2016). Since then, hundreds of brands have participated in CM campaigns such that in 2017, $2.05 billion have been allocated for CM in U.S. alone1. As a case of CM campaign, Paksan Co., a detergent producer in Iran, spent 10% of Pril-labelled products sales revenue to support and empower unskilled women. In another CM campaign, Starbucks donated $1 for every pound of sold East Africa Blend coffee to support AIDS sufferers in Africa (Müller et al., 2014). For more detailed data see: http://www.sponsorship.com/Report/2018/02/05/The-Most-Active-Sponsors-OfCauses.aspx 1
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Donation size as a design element of a CM campaign is a key success factor of a SC contributing in a CM campaign which is directly controlled by SC managers. Müller et al., (2014) found that donation size has a positive effect on brand choice if consumers have no choice between a CM product and a same product at a discount, i.e. the increase of donation size can increase consumers’ demand when customers are socially aware. Controlling donation size, the SC can earn profit from CM campaign participation by absorbing more socially aware customers. However, as donation volume is a decision made by the manufacturer, decided value does not maximize the whole SC profit when we face a decentralized SC where each member has a myopic approach to maximize own profit regardless of other channel members (Shukla et al., 2016). As a result, a coordination mechanism is required to ensure maximum profit for the whole SC following by a profit sharing mechanism to ensure higher profitability for all channel members. In this paper, a two-echelon SC including one manufacturer and one retailer in presence of socially aware customers is investigated. The manufacturer contributes in a CM campaign in order to absorb socially aware consumers. In the first case demand is assumed as a function of donation size. According to related literature (e.g. Baghi et al., 2009), consumers are absorbed if related causes described more clearly. Therefore, donation size, as a portion of retail price or an absolute amount per sold item, is decided by the manufacturer and announced on the product label. The problem is to optimize the donation size provided that the whole SC profit is maximized and at the same time ensure for more profit for both channel members after participating in the CM campaign. The model is then extended to include both the donation size and pricing decisions simultaneously where the retailer has the authority to decide on retail price. 3
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Main contribution of this paper with respect to the previous literature is bringing the concept of CM into the quantitative models by deciding on donation size mathematically. Although, several researches have been conducted in SC coordination area to improve the overall performance of SC (e.g. Ambilikumar et al., 2015) through different contracts, they have never used in SCs with a CM strategy. The concept of social SC is rarely investigated in the literature of SC coordination. Almost all previous works in this area have used an abstract factor as “social responsibility investment cost” to develop the mathematical models while in the current study, it is clearly defined that the cost is spent as donation for the CM campaign. As the first paper in the field, in this study we quantitatively explore and optimize participation of a SC in charitable activities (i.e. CM campaign). The rest of the article is organized as follows. In section 2 the relevant literature is reviewed. Section 3 introduces problem statement. Sections 4 and 5 present the proposed decision models. Section 6 discusses on results and managerial implications. All proofs of theorems and lemmas are presented in appendix. 2. Literature Review The extensive scope and complex nature of social issues makes it difficult to measure social responsibility and it is hard to measure its aspects all (Pishvaee et al., 2012). Some researchers proposed quantitative social sustainability indicators to evaluate the social supply chains (Ahi and Searcy, 2015; Popovic, et al., 2018) and some considered CSR level or social responsibility investment in quantitative models to measure social aspect of sustainability in supply chains. Ni et al. (2010) assumed that the upstream's CSR cost is shared by the other channel member by a wholesale price contract in a two-echelon SC. Ni and Li (2012) considered a 4
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two-tire SC that each channel member incurs its individual CSR cost. They have examined the effects of strategic interactions between the channel members under game theoretic setting and wholesale price contracts. Georing (2012) considered a two-echelon SC consists of a manufacturer and a retailer where the retailer to be socially concerned in one case, and the manufacturer to be so in another and a two-part tariff set by the manufacturer to coordinate the channel. Hsueh (2014) proposed a revenue sharing contract to coordinate CSR in a two-stage SC. Hsueh (2015) developed the study of Hsueh (2014) and considered a bi-level programming model in order to analyze a CSR collaboration problem in a threeechelon SC to maximize the profit of whole SC. Panda (2014) and Panda et al. (2016) considered a manufacturer–retailer SC where one of the firms, either the manufacturer or the retailer, is socially responsible. They used revenue sharing and quantity discount contracts to resolve channel conflicts. Modak et al. (2014) analysed a two-layer dualchannel SC where the manufacturer sells through an online channel in company with a traditional retail channel and intends to enhance social activities by exhibiting CSR. They analytically discussed channel coordination using quantity discounts along with an agreement on franchise fee and surplus profit division. Following that, Modak et al. (2016a) explored channel coordination in a two-tire SC consists of a socially responsible manufacturer and two competing retailers. They found that two-part tariff contract removes channel conflicts and provides win–win result for specific values of the franchise fee. Panda et al. (2015) and Modak et al. (2016b) considered a three-layer SC where the manufacturer invests on CSR and use a wholesale price discount-Nash bargaining and a new revenue sharing contracts to remove channel conflicts. Panda et al. (2017) developed a revenue sharing scheme to coordinate a two-tire socially responsible closed-loop SC with 5
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product recycling by use of Nash bargaining for dividing surplus profit. Raj et al. (2018) coordinated a two-echelon supply chain consists of a responsible supplier for greening and a buyer with social responsibility through 5 different contracts. Considering cause-related marketing, many previous researches have studied the effect of CM campaign characteristics (for an overview, see Fries, 2010) and identified a wide range of CM success factors. Donation size is one of these factors that some researches have evaluated its effect on CM Success (Human & Terblanche, 2012; Muller et al., 2014; Olsen et al., 2003; Strahilevitz, 1999). Lafferty et al. (2016) also reviewed the empirical studies in cause-related marketing. 2.1.
Research Gap
The related studies concentrated on socially responsible SC coordination are presented in Table 1. These studies all considered a CSR channel and some of them considered the effect of social activities on demand function. In socially responsible supply chains investigated by previous researches, CSR investment level was considered to evaluate the effect of the supply chain social activities. This factor is mainly assumed independent of the product sales while the donation amount paid for a special cause in a CM campaign, which is assumed in this study, completely depends on the product sales and it is consistent with the mission of SC to sell more product (i.e. more sales, more donations). Moreover, the donation size and consumer social awareness, which are two critical factors defined by the current study, affect CM success and the market demand. The influence of these factors has not been formulated in any previous demand function. Even though the use of coordination contracts to deal with channel conflict in social responsible SCs has been developed in recent decade, Cause-related Marketing as a form of social responsibility has never been 6
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taken into account in SC coordination to cut out double marginalization. Double marginalization exists in decentralized supply chains when there are two marginal profits from the manufacturer and the retailer and they make decision independently according to their own marginal profits without considering entire supply chain marginal (He et al., 2009). While cause related marketing as a popular form of CSR (Nan & Heo, 2007) is widely considered in empirical and conceptual marketing researches, previous studies in the field of SC optimization and SC coordination never modeled it as a social activity of the SC. By considering this point, in this study, for the first time, donation amount (per each sold item) paid by SC to a CM campaign is optimized and appropriate contracts are developed to share earnings.
Table 1. Comparison of previous researches with the proposed model
Wholesale Price
Ni & Li (2012)
Two
Wholesale Price
Goering (2012)
Two
Two-part tariff
Hsueh (2014)
Two
Revenue sharing
Panda (2014)
Two
Revenue sharing
Modak et al. (2014)
Two
Quantity discount & bargaining
Hsueh (2015)
Three
Collaboration model
Panda et al. (2015)
Three
Wholesale price
7
Donation size
CSR level
Two
CSR level
Ni et al. (2010)
CSR effort
Retail price
Donation size
Greening level
Wholesale price
Demand pattern Recycling factor
CSR investment
Marketing effort
Decision variables
mechanism
Greening level
Coordination
Order quantity
Echelons
Retail Price
Study
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discount & bargaining Panda et al. (2016)
Two
Modak et al. (2016a)
Two
Modak et al. (2016b)
Three
Ma et al., (2017)
Three
Panda et al., (2017) Nematollahi et al. (2017)
Two Two
Quantity discount &
bargaining Two-part tariff & bargaining Revenue sharing Wholesale price and two-part tariff Revenue sharing & bargaining
Collaboration model
Wholesale price Raj et al. (2018)
Two
Two-part tariff Greening cost sharing
Revenue sharing This study
Two
Cost sharing & Collaboration model
3. Supply chain model The models are developed in two cases. In the first case, we analyse a manufacturerretailer SC, where the manufacturer decides to participate in a CM campaign as a social activity to increase the sales volume from the socially aware customers. In this state, the manufacturer promises to donate a portion of retail price per each sold product to a social cause and clearly announces it to consumers with some labels stuck on their products. The manufacturer handles all the CM costs and therefore no increase in wholesale price w is occurred. The manufacturer supplies the products with the production unit cost 𝑐 and sell with wholesale price w where 𝑤 > 𝑐. The retailer sells the products at a given retail price 𝑝 where 𝑝 > 𝑤. In the second case, unlike the first case, we consider that the retailer decides
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on the retail price 𝑝 and therefore there are two decision variables in the second case: (1) donation size decided by the manufacturer (2) retail price decided by the retailer. According to Muller et al. (2014), increase of donation size can increase consumers demand. The demand function in the first case is considered as 𝐷1 = 𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝, where 𝐴 > 0 is the market potential, 𝑏 > 0 is the customers price sensitivity, 𝛾 > 0 is consumer social awareness (CSA) level and 𝛼 ≥ 0 is the portion of retail price donated (i.e. '𝛼𝑝' is the donation size) that decided by the manufacturer. Such a linear demand function is used frequently in various SC models especially green and social SCs in the literature.
𝑤
Decision Variables
Donated
𝑝
Manufacturer
Retailer
Case I
Donation Portion 𝛼
-
Case II
Donation Size 𝑑𝑠
Retail price
Consumer
Figure1. Supply chain model and decision variables in both cases As a real-world case, the manufacturer like Paksan Co. announces 𝛼 to consumers by labelling on the product. In the second case, the demand function considered as 𝐷2 = 𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠where 𝑑𝑠 ≥ 0 is the donation size which is an absolute value independent of retail price. As a real-world example for such a donation, Starbucks uses such an absolute amount (i.e. 1 $) as donation to CM campaign per one pound of sold East Africa Blend coffee. 9
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Notations: The following notations are used in developing the model. 𝑝
Retail price (Retailer’s decision variable in case II)
𝑤
Wholesale price (decided in cost sharing contract in case I)
𝑐
Unit production cost
𝐷1
Demand in case I
𝐷2
Demand in case II
𝐴
Market potential size
𝑏
Demand price sensitivity
𝛾
Consumer Social Awareness (CSA) level
𝛼
Portion of retail price donated (Manufacturer’s decision variable in case I)
𝑑𝑠
Donation size (Manufacturer’s decision variable in case II)
𝛱𝑚
Manufacturer profit function
𝛱𝑟
Retailer profit function
𝛱𝑆𝐶
Channel profit function
Superscripts ‘c’, ‘d’, ‘cs’, and ‘co’, indicate the centralized, decentralized, cost sharing contracts, collaboration scenario, respectively. Asterisk is used to represent optimum value of decision variables and profit functions.
4. Case I: Deciding only on donation size 4.1.
Decentralized decision
Under decentralized decision-making, the channel members make decision independently and optimize own profits. In this situation, the profit functions of channel members and SC are formulated as follows: 𝛱𝑚(𝛼) = 𝐷1(𝑤 ‒ 𝑐 ‒ 𝛼𝑝) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑤 ‒ 𝑐 ‒ 𝛼𝑝)
(1)
𝛱𝑟(𝛼) = 𝐷1(𝑝 ‒ 𝑤) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑝 ‒ 𝑤)
(2)
𝛱𝑠𝑐(𝛼) = 𝐷1(𝑝 ‒ 𝑐 ‒ 𝛼𝑝) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑝 ‒ 𝑐 ‒ 𝛼𝑝)
(3)
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In Eq. (1), term (𝑤 ‒ 𝑐 ‒ 𝛼𝑝) represents earned revenue for the manufacturer from selling each item where, 𝑤 ‒ 𝑐 is net profit from each sold item and 𝛼𝑝 is paid donation per each sold item. Theorem 1: The manufacturer profit function is concave in 𝛼 and optimal value of 𝛼 for the manufacturer is: 𝑑∗
𝛼
=
𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝑝 2𝛾𝑝
(4)
Lemma 1: To participate in CM campaign, the manufacturer’s unit marginal profit should be greater than
𝐴 ‒ 𝑏𝑝 . 𝛾
Substituting the optimal value of 𝛼 in Eqs. (1-3), we have: 𝑑∗
𝛱𝑚(𝛼
(
𝑑∗
𝛱𝑟 𝛼
(
)=(
𝑑∗
𝛱𝑠𝑐 𝛼 4.2.
𝐴 ‒ 𝑏𝑝 𝑤 ‒ 𝑐 2 ) = 𝛾( + ) 2𝛾 2
(5)
𝐴 ‒ 𝑏𝑝 𝛾(𝑤 ‒ 𝑐) + )(𝑝 ‒ 𝑤) 2 2
) = 𝛾(
(6)
𝐴 ‒ 𝑏𝑝 𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 2𝑝 ‒ 𝑤 ‒ 𝑐 + )( + ) 2𝛾 2 2𝛾 2
(7)
Centralized decision
Under centralized decision-making, it is assumed that a single decision maker decides on behalf of SC. Central decision maker intends to optimize the whole SC profit by deciding on 𝛼. Lemma 2: the optimal value of donation size 𝛼𝑝 under the centralized decision-making is 𝑐∗
𝛼
=
𝑝 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝑝 2𝛾𝑝
(8)
Lemma 3: The optimum value of 𝛼 under the centralized decision making is greater than 𝑐∗
the decentralized channel (i.e. 𝛼
𝑑∗
>𝛼
).
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Lemma 4: The manufacturer’s profit in centralized decision-making is less than the 𝑐∗
decentralized decision-making, i.e. 𝛱𝑚(𝛼
) < 𝛱𝑚(𝛼𝑑 ∗ ).
Lemma 5: The total profit of centralized channel is greater than the decentralized channel 𝑑∗
(i.e. 𝛱𝑠𝑐(𝛼
) < 𝛱𝑠𝑐(𝛼𝑐 ∗ )).
According to Lemma 5, centralized decision-making improves the performance of SC, even though the manufacturer’s profit decreases (Lemma 4). Therefore, if we have a decentralized channel, a side payment policy must be applied to persuade the manufacturer to change its decision in order to obtain the maximum channel performance.
4.3.
Channel coordination through Cost Sharing (CS) contract
The manufacturer contributes in a CM campaign to increase sales volume and at the same time participate in a social activity. According to Lemma 5, donation size decided by the manufacturer does not optimize the total channel performance. On the other hand, based 𝑐∗
on Lemma 4, the manufacturer profit is reduced if donation size is decided as 𝛼
.
Therefore, the retailer needs to persuade the manufacturer to change decision through an appropriate compensating scheme. A cost sharing (CS) contract is proposed to resolve the channel conflict. In the proposed CS contract, the retailer handle a fraction of CM cost and at the same time the manufacturer offers a new wholesale price. Therefore, the proposed contract has two 𝑐𝑠
parameters namely 𝑤
𝑐𝑠
and 𝜑; where 𝑤
is the modified wholesale price set by the
manufacturer and 𝜑 (0 < 𝜑 < 1) is the share of donation size undertaken by the retailer. Based on the suggested model, the SC members’ profit functions can be reformulated as:
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𝑐𝑠
𝑐𝑠
𝛱𝑚 (𝛼) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑤 ‒ 𝑐 ‒ (1 ‒ 𝜑)𝛼𝑝)
(9)
𝑐𝑠
𝑐𝑠
𝛱𝑟 (𝛼) = 𝐷1(𝑝 ‒ 𝑤 + 𝑟 ‒ 𝜑𝛼𝑝) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑝 ‒ 𝑤 ‒ 𝜑𝛼𝑝)
(10)
Under the CS contract, the manufacturer problem is to maximize its profit by deciding on 𝛼. 2
Since
𝑑 𝛱𝑚
𝛼
2
𝑐𝑠
=‒ 2𝛾(1 ‒ 𝜑)𝑝 < 0 ensures that 𝛱𝑚 is a concave function in 𝛼, the necessary
2
𝑑𝛼
condition 𝑐𝑠 ∗
𝑐𝑠
𝑑𝛱𝑚
𝑐𝑠
= 0 results in:
𝑑𝛼 𝑐𝑠
𝑤 ‒𝑐 𝐴 ‒ 𝑏𝑝 = ‒ 2(1 ‒ 𝜑)𝑝 2𝛾𝑝
(11)
The channel is coordinated if the manufacturer’s decision maximizes the whole channel 𝑐𝑠 ∗
profit, i.e. 𝛼
𝑐∗
=𝛼
. Therefore, we can calculate the following condition for the CS
contract parameters: 𝑐𝑠
(12)
𝑤 = 𝑝 ‒ 𝜑(𝑝 ‒ 𝑐) Lemma 6: The CS contract can coordinate channel members decisions if and only if
[
𝜑𝜖[𝜑,𝜑] = 2𝛾(𝑝 ‒ 𝑤)
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) (𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
,1‒ 2
(
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) 𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐)
)] 2
(13)
Lemma 7: There is at least one feasible value of 𝜑 to coordinate the channel through CS contract. Lemma 8: If the manufacturer chooses the wholesale price from the following closed interval, the channel will be coordinated. 𝜑𝜖[𝑤,𝑤] =
[
(
)]
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) 2 𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) 𝑐 + (𝑝 ‒ 𝑐) , 𝑝 ‒ 2𝛾(𝑝 ‒ 𝑐)(𝑝 ‒ 𝑤) 2 𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐) (𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
(
)
13
(14)
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5. Case II: Simultaneously pricing and donation size decisions In this case we extend the Case I by assuming that the retailer also has the authority to decide on retail price. In addition, donation size in Case II is considered as an absolute value independent of the retail price. As discussed earlier, such a donation mechanism is also used in real-world cases. 5.1.
Decentralized decision
Under decentralized decision-making, the channel members operate independently and optimize individual profits. In this case, interaction between players is assumed as a Stackelberg game. The manufacturer is supposed to be the leader of the channel. The manufacturer, as the leader, makes the first decision, and then the follower reacts by choosing its best move in accordance with the available information. In this way, at first, the manufacturer announces the donation size with some labels stuck on the product while the manufacturer is absolutely certain that the retailer determines the retail price in response to the manufacturer's decision. Therefore, we extract the optimal amount of retail price from the retailers’ profit function at first. Lemma 9: The retailer earns maximum profit if the retail price is determined as: ∗
𝑝 =
𝐴 + 𝑏𝑤 + 𝛾𝑑𝑠
(15)
2𝑏
Lemma 10: In a Stackelberg game, to earn maximum profit, the manufacturer as a leader of ∗
the channel chooses 𝑑 𝑠 as follows: ∗
𝑑𝑠 =
𝑤 ‒ 𝑐 2(𝐴 ‒ 𝑏𝑝) ‒ 3 3𝛾
(16)
Solving the system of two linear Eqs. (15-16) results in: ∗
𝑝 =
𝛾(𝑤 ‒ 𝑐) + 3𝑏𝑤 + 𝐴 4𝑏
(17) 14
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(𝑤 ‒ 𝑐) 𝐴 ‒ 𝑏𝑤 ‒ 2 2𝛾
∗
𝑑𝑠 =
(18)
Lemma 11: To participate in a CM campaign, the manufacturer’s unit marginal profit should be greater than
𝐴 ‒ 𝑏𝑤 . 𝛾
Substituting the optimal value of donation size and retail price from Eqs. (17-18) in demand function and profit functions, we have: ∗
∗
𝐷2(𝑝 ,𝑑 𝑠 ) = 𝛱𝑚(𝑝
∗
∗
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤
∗ ,𝑑 𝑠 ) = 2𝛾 ∗
( (
𝛱𝑟(𝑝 ,𝑑 𝑠 ) = 𝑏 ∗
∗
𝛱𝑠𝑐(𝑝 ,𝑑 𝑠 ) = 5.2.
(19)
4
(
)
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤 4𝛾
2
(20)
2
) )(
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤 4𝑏
(21)
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤 𝛾(𝑤 ‒ 𝑐) + 3𝑏𝑤 + 𝐴 𝛾(𝑤 ‒ 𝑐) + 𝑏𝑤 ‒ 𝐴 ‒𝑐‒ 4 4𝑏 2𝛾
)
(22)
Collaboration scenario
As discussed in Case I, the decentralized solution is unable to maximize the whole channel profit and remove the double marginalization effect due to pursuit of individual goals by each SC member. We propose a collaboration scenario by the aim of maximizing channel profit and ensuring for better position for both players. Under the proposed collaboration mechanism, both the players cooperate in order to maximize the profit of the whole channel provided that the profits of both members remain at least in the same level of the decentralized model. In this situation, the players have enough motivation to collaborate. Under the proposed collaboration model, a win-win solution is derived while each player is able to negotiate on its share from the earned surplus based on its market domination. In the proposed model, members’ market domination is represented by parameters ‘𝜃’, for the retailer, and ‘β’, for the manufacturer, where 0 < 𝜃+ 𝛽 ≤ 1. ‘𝜃’ and ‘β’ are the dominancy 15
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factors of the retailer and the manufacturer, respectively. Dominancy factor of stronger player takes a larger value closer to one and most of the earned surplus profit will be gained by him. In practice, indicators such as brand popularity, marker share, and privileged accesses are used to measure market dominancy/bargaining-power (Basiri & Heydari, 2017). The proposed collaboration model is formulated as a mathematical programming model to maximize the total channel profit as follow: 𝑀𝑎𝑥 𝛱𝑠𝑐(𝑝,𝑑𝑠) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑝 ‒ 𝑐 ‒ 𝑑𝑠)
(23)
s.t.
{
(
𝑐𝑜
𝑑
∗
∗
(
)
𝑑
(
∗
∗
𝛱 𝑟 = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑝 ‒ 𝑤) ≥ 𝛱 𝑟 𝑝 ,𝑑 𝑠 + 𝜃 𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐 𝑝 ,𝑑 𝑠 𝑐𝑜
𝑑
(
∗
∗
)
(
𝑑
(
)) ∗
(24) ∗
𝛱 𝑚 = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑤 ‒ 𝑐 ‒ 𝑑𝑠) ≥ 𝛱𝑚 𝑝 ,𝑑 𝑠 + 𝛽 𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐 𝑝 ,𝑑 𝑠 0<𝜃+𝛽≤1 𝐴 0 ≤ 𝑑𝑠 & 0 ≤ 𝑝 ≤ ( 𝑏)
))
(25) (26) (27)
Where, Eq. (23), as the objective function of collaborative decision-making, aims to maximize the channel profit. Constraints (24) and (25) ensure that the retailer and the manufacturer profits through collaboration strategy are at least equal to the decentralized 𝑑
∗
∗
decision-making profit, respectively. In other words, terms ‘𝜃(𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐(𝑝 ,𝑑 𝑠 ))’ and 𝑑
∗
∗
‘𝛽(𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐(𝑝 ,𝑑 𝑠 ))’ in the right-hand of the inequalities (24-25) guarantee enough motivations for the retailer and the manufacturer to participate in collaborative decisionmaking, respectively. Constraint (27) ensures that the solution is rational and finite. 5.3.
Numerical Experiments in Case II
To show the outcome of the proposed collaborative model numerically, a set of experiments are examined. Three numerical examples are tested to evaluate the proposed collaborative model numerically. The parameters and the decentralized decision results
16
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are presented in Table 2. All datasets satisfy the requirements and assumptions of the proposed models and are consistent with literature in this area.
Table 2: Three numerical examples datasets and decentralized decision results Parameters
Decentralized Decision ∗
∗ 𝑑𝑠
𝐷2
𝛱𝑚
𝛱𝑟
𝛱𝑆𝐶
𝐴
𝑏
𝛾
𝑐
𝑤
Ex. 1
50
2.0
1.0
10
21
23.38
1.50
4.75
45.13
11.28
56.41
Ex. 2
100
0.8
0.7
28
80
102.64
0.29
18.10
936.03
409.51
1345.54
Ex. 3
150
1.5
0.5
40
85
92.50
0.00
11.25
506.25
84.38
590.63
𝑝
The results of running the proposed collaborative model for various amount of 𝜃 on the three investigated examples are presented in Table 3. In all experiments it is assumed that 𝜃 = 1 ‒ 𝛽. According to Table 3, the retail price and donation size will increase simultaneously by increasing 𝜃 which result in a fixed demand for all combinations of 𝜃 and 𝛽. Furthermore, as expected, by increasing 𝜃, profit of the retailer increases while the profit of the manufacturer decreases. For all combinations of 𝜃 and 𝛽 both the retailer and the manufacturer have a better position than the decentralized decision model. Test problems show that when 𝜃 decreases, the model creates higher profit for the whole channel and manufacturer while the retailer’s share decreases. By comparing Tables 2 and 3, one can conclude that in all test problems the collaboration model is more profitable for the SC and both SC members and therefore participating in the collaborative decision making is guaranteed. We expected this result according to the previous proposed collaborative models (e.g. Basiri & Heydari, 2017). The results also
17
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approve the conceptual researches in cause-related marketing (Müller et al., 2014) that participation in a CM campaign can help business economics by increasing sales volume. Comparing Tables 2 and 3 shows that, in all test problems, the proposed collaboration model results in a greater demand amount than the decentralized model. While the realized demands for three investigated examples are 4.75, 18.1, and 11.25 in decentralized model, demands increase to 9.5, 36.2, and 22.5 in collaborative model, respectively. In addition, in all experiments, the collaboration model results in a higher donation size (than the decentralized model) from one side and lower prices (than the decentralized model) from the other side. This means the proposed collaboration model causes a more socially concerned SC with lower price offered to the customers. Table 3: Collaboration model results under various 𝜃 𝒄𝒐 ∗
𝜽 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
𝒑 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3
22.19 91.31 88.75 22.40 92.59 89.69 22.58 93.83 90.36 22.74 95.03 90.86 22.87 96.20 91.25 22.98 97.35 91.56 23.08 98.46 91.82 23.17 99.54 92.03 23.24 100.59 92.21
𝒄𝒐 ∗
𝒅𝒔
3.88 13.21 11.25 4.31 14.67 14.06 4.67 16.09 16.07 4.97 17.46 17.58 5.23 18.81 18.75 5.46 20.11 19.69 5.66 21.38 20.45 5.83 22.62 21.09 5.99 23.82 21.63
𝒄𝒐
𝒄𝒐
𝒄𝒐
𝑫𝟐
𝜫𝒎
𝜫𝒓
𝜫𝒔𝒄
9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50
67.69 1404.04 759.38 63.59 1351.31 696.09 60.17 1300.04 650.89 57.27 1250.18 616.99 54.79 1201.66 590.63 52.46 1154.44 569.53 50.77 1108.46 552.27 49.11 1063.67 537.89 47.63 1020.03 525.72
11.28 409.51 84.38 13.33 455.65 105.47 15.04 500.52 120.54 16.49 544.15 131.84 17.72 586.60 140.63 18.80 627.92 147.66 19.74 668.15 153.41 20.57 707.34 158.20 21.31 745.52 162.26
78.97 1813.55 843.76 76.92 1806.96 801.56 75.21 1800.56 771.43 73.76 1794.33 748.83 72.51 1788.26 731.26 71.26 1782.36 717.19 70.51 1776.61 705.68 69.68 1771.01 696.09 68.94 1765.55 687.98
18
Total paid Donation 36.81 478.36 253.12 40.92 531.09 316.41 44.33 582.36 361.61 47.23 632.23 395.51 49.71 680.74 421.88 51.85 727.97 442.97 53.73 773.95 460.23 55.39 818.73 474.61 56.87 862.37 486.78
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0.9 1.0
Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3
23.31 101.62 92.37 23.38 102.63 92.50
6.13 25.00 22.10 6.25 26.14 22.50
9.50 36.20 22.50 9.50 36.20 22.50
46.31 977.50 515.29 45.13 936.03 506.25
21.97 782.74 165.74 22.56 819.03 168.75
68.28 1760.24 681.03 67.69 1755.06 675.00
58.19 904.90 497.21 59.38 946.37 506.25
6. Conclusions This paper considers a social channel coordination in a two-echelon SC consist of a manufacturer, who contributes in a cause-related marketing campaign by donating a portion of sales revenue to support a social cause, and a retailer. Based on previous researches in the effect of donation size on consumer's demand and willingness to pay, demand is considered as a linear function of donation size. The channel is analyzed in two cases. In Case I the manufacturer decides on donation size in presence of a given retail price, while in Case II the manufacturer decides on donation size and at the same time the retailer determines the retail price. In Case I, a cost sharing contract is proposed to improve channel performance and depicts a win-win outcome for both players. In Case II a collaborative model is developed to improve decision making process. The numerical examples show that the suggested collaborative mechanism is capable of improving whole channel performance. Indeed, the solution experiences a Pareto-improvement in which the whole channel profit better off without making no player worse off than the decentralized decision making. In addition, numerical study reveals that the proposed collaborative model increases donation size and decrease the retail price at the same time which means a more socially concerned SC and more satisfied customers. Though the academic researches on CM grew in recent years, they only studied this strategy conceptually. Moreover, the previous researches on social supply chains evaluated the effect of social activities by 19
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considering CSR investment or CSR level in quantitative models. However, in this study we formulated social activities through donation size as a key success factor in a CM campaign. Indeed, the main contribution of this paper is considering the concept of cause-related marketing in the quantitative models. In addition, unlike the previous studies in modeling of social supply chains, we introduce and apply the concept of consumer social awareness (CSA) and its impact on stimulating market demand. The managerial implication of our proposed coordination contract and collaboration model is helping the SC mangers to design an optimal CM strategy in alignment with the whole supply chain profitability where the SC not only earns more profit, but also enhances its social reputation. Although this paper provides interesting ideas about how a social supply chain with causerelated marketing strategy can be managed to achieve maximum profit, as a first research in this area, it has some limitations which we leave them for future researches. For example, for the sake of simplicity, the demand is assumed as a deterministic linear function in both the investigated cases which can be further investigated by considering a stochastic donation size dependent demand. Moreover, two-echelon supply chain considered in this paper can be expanded and a competitive environment can be investigated in future studies instead of the considered dyadic SC.
Acknowledgements We would like to appreciate the two anonymous reviewers for their valuable comments which have helped us to enhance the quality of paper. The financial support of University of Tehran for this research under grant number 29917-01-01 is also appreciated.
20
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Appendix: proofs Proof of Theorem 1: Differentiating 𝛱𝑚 with respect to 𝛼, as the only decision variable of 𝑑∗
the manufacturer and equating it to zero, results in 𝛼
=
𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 2𝑝
given that 𝛱𝑚is a
2
concave function of 𝛼 as
𝑑 𝛱𝑚 2
𝑑𝛼
2
2
2
=‒ 𝛾𝑝 ‒ 𝛾𝑝 =‒ 2𝛾𝑝 < 0. 𝑑∗
Proof of lemma 1: The manufacturer participates in CM campaign if 𝛼 results in 𝑤 ‒ 𝑐 >
> 0, which
𝐴 ‒ 𝑏𝑝 . 𝛾 2
Proof of lemma 2: As
𝑑 𝛱𝑠𝑐 2
𝑑𝛼
2
=‒ 2𝛾𝑝 < 0 ensures that 𝛱𝑠𝑐 is a concave function in 𝛼, 𝑐∗
results in optimal value for 𝛼 as 𝛼
=
𝑑𝛼
=0
𝑝 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 . 2𝑝
Proof of lemma 3: The rational decision on retailer price (𝑝 > 𝑤) results in 𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 2𝑝
𝑑𝛱𝑠𝑐
𝑝 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 > 2𝑝
which results in a greater donation size under the centralized decision making
than the decentralized decision making.
(
𝑐∗
Proof of lemma 4: Substituting Eq. (8) in Eq. (1) results in 𝛱𝑚 𝛼
) = 𝛾(𝐴 2𝛾‒ 𝑏𝑝 + 𝑝 2‒ 𝑐)
(𝐴 2𝛾‒ 𝑏𝑝 + 2𝑤 ‒2𝑝 ‒ 𝑐). Replacing (𝑝 ‒ 𝑐) by (𝑝 ‒ 𝑤) + (𝑤 ‒ 𝑐) in the first parentheses of (𝛼𝑐 ∗ )
(𝑝 ‒2 𝑤)
𝑐∗
and some simplifications we have 𝛱𝑚(𝛼 2
> 0, therefore, 𝛾
((
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 𝑝‒𝑤 2 ‒ + ( ) 2𝛾 2 2
)=𝛾
) < 𝛾(
)
((
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 𝑝‒𝑤 2 ‒ + ( ) 2𝛾 2 2
)
𝐴 ‒ 𝑏𝑝 𝑝‒𝑐 2 + ) . 2𝛾 2
). Since
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 . + 2𝛾 2
)
Proof of lemma 5: Substituting Eq. (8) in the SC profit function leads to
(
𝛱𝑚
𝑐∗
𝛱𝑠𝑐(𝛼
)=𝛾
Moreover, if we replace (𝑤 ‒ 𝑐) in the first parenthesis of Eq.(7) with (𝑝 ‒ 𝑐)
21
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𝑑∗
‒ (𝑝 ‒ 𝑤), then 𝛱𝑠𝑐(𝛼
)=𝛾
((
𝐴 ‒ 𝑏𝑝 𝑝‒𝑐 2 𝑝‒𝑤 2 ‒ + 2𝛾 2 2
) ( ))
. Since
𝑝‒𝑤 2 > 0, 2
( )
therefore, 𝛱𝑠𝑐
(𝛼𝑑 ∗ ) < 𝛱𝑠𝑐(𝛼𝑐 ∗ ). Proof of lemma 6: The manufacturer and the retailer both accept CS contract when CS contract results in a greater or at least equal profit for them than respective decentralized 𝑐𝑠
𝑐𝑠
profits, i.e., 𝛱𝑚 ≥ 𝛱𝑚 and 𝛱𝑟 ≥ 𝛱𝑟. In other words, (
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 + ) 2𝛾 2
and
𝜑 𝐴 ‒ 𝑏𝑝 𝐴 ‒ 𝑏𝑝 𝛾(𝑤 ‒ 𝑐) 𝛾(𝑝 ‒ 𝑐) 2 ≥ 2 + 2 + 𝛾 2 2
) (
(
(1 ‒ 𝜑) 𝐴 ‒ 𝑏𝑝 𝛾(𝑝 ‒ 𝑐) 2 ( + ) ≥𝛾 𝛾 2 2
)(𝑝 ‒ 𝑤).
Simplifying
these
inequalities, a range of CS fraction 𝜑 for achieving a win-win situation can be extracted as Eq. (13). Proof of lemma 7: We must prove that the interval [𝜑,𝜑] is non-empty interval. In other words, we must show that: 2𝛾(𝑝 ‒ 𝑤)
2
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐)
(𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
2
≤1‒
‒ 𝑐) . We use proof (𝐴𝐴 ‒‒ 𝑏𝑝𝑏𝑝 ++ 𝛾(𝑤 𝛾(𝑝 ‒ 𝑐) )
by contradiction and suppose that the above interval is empty. Hence, we have: 2𝛾(𝑝 ‒ 𝑤)
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) (𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
2
2>1‒
‒ 𝑐) . Simplifying this inequality results in 𝑤 > 𝑝 (𝐴𝐴 ‒‒ 𝑏𝑝𝑏𝑝 ++ 𝛾(𝑤 𝛾(𝑝 ‒ 𝑐) )
that is not true. Therefore, the proof by contradiction is invalid and the interval [𝜑,𝜑]is a non-empty interval. Proof of lemma 8: Substituting 𝜑 and 𝜑 from Eq. (13) into Eq. (12) results in 𝑤 and 𝑤, respectively. Proof of lemma 9: Differentiating 𝛱𝑟(𝑝,𝑑𝑠) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑝 ‒ 𝑤) with respect to 𝑝 and ∗
equating it to zero results in 𝑝 =
𝐴 + 𝑏𝑤 + 𝛾𝑑𝑠 2𝑏
2
given that
function in 𝑝.
22
𝑑 𝛱𝑟 2
𝑑𝑝
= ‒ 2𝑏 < 0 and 𝛱𝑟 is a concave
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∗
Proof of lemma 10: Substituting the value of 𝑝 into the manufacturer profit function 𝛱𝑚 (𝑝,𝑑𝑠) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑤 ‒ 𝑐 ‒ 𝑑𝑠), necessary conditions ∗
𝑑𝑠 =
𝑑𝛱𝑚 𝑑𝑑𝑠
= 0 yields:
𝑤 ‒ 𝑐 2(𝐴 ‒ 𝑏𝑝) ‒ 3 3𝛾 2
Note that 𝛱𝑚 is a concave function in 𝑑𝑠 as
𝑑 𝛱𝑚 2
𝑑𝑑𝑠
=‒ 𝛾 ≤ 0.
Proof of lemma 11: According to Eq. (18), if 𝑤 ‒ 𝑐 >
𝐴 ‒ 𝑏𝑤 𝛾
∗
then 𝑑 𝑠 > 0 that means
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Varadarajan, P. R., & Menon, A. (1988). Cause-related marketing: A coalignment of marketing strategy and corporate philanthropy. The Journal of Marketing, 58-74.
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Highlights:
Contributing a SC in a Cause-related Marketing campaign is optimized Donation size and price decisions in a SC contributing in a CM campaign are coordinated A cost sharing mechanism is developed to create a win-win solution A collaborative decision model is proposed to coordinate donation size and retail price The proposed models result in less prices and higher donation sizes
J. Heydari, Zeynab Mosanna PII:
S0959-6526(18)32028-6
DOI:
10.1016/j.jclepro.2018.07.055
Reference:
JCLP 13509
To appear in:
Journal of Cleaner Production
Received Date:
26 September 2017
Accepted Date:
06 July 2018
Please cite this article as: J. Heydari, Zeynab Mosanna, Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign, Journal of Cleaner Production (2018), doi: 10.1016/j.jclepro.2018.07.055
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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(Manuscript Word count: 6421)
Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign J. Heydari (corresponding Author) School of Industrial Engineering College of Engineering, University of Tehran, Iran E-mail: [email protected]
Tel: +98 21 82084489
Zeynab Mosanna Department of Industrial Engineering, Alborz Campus, University of Tehran, Iran E-mail: [email protected]
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Coordination of a Sustainable Supply Chain contributing in a cause-related marketing campaign
Abstract: This paper investigates a two-echelon supply chain coordination problem in presence of consumer social awareness (CSA) when SC contributes in a cause-related marketing campaign. The channel consists of a manufacturer and a retailer where the manufacturer contributes in a CM campaign by donating a sum per sold item to the CM campaign. Two scenarios are analysed: (1) In the first scenario, the donation size as a portion of retail price is the only decision variable and paid by the manufacturer (2) In the second scenario, in addition to the donation size, retail price is a decision variable. In the first scenario, a cost sharing contract is proposed to improve channel performance while in the second scenario a collaborative model is developed to coordinate decisions of channel members. The numerical investigations illustrate that the proposed collaborative model not only increases the channel/members profit, but also creates a more socially concerned SC with lower retail prices. Moreover, the developed model helps supply chain managers to more effectively contribute in a CM campaign by making decision correctly on donation size. Key words: Social supply chain coordination; Sustainable supply chain; Cooperate social responsibility; Cause-related marketing; Consumer social awareness 1. Introduction Development of industrial technology and the only focus of companies on their growth and profit had adverse effects on the environment and society (Nigam, 2014). By increasing
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these effects on the world, the concepts of sustainability and sustainable development have emerged (Hutchins & Sutherland, 2008) and the companies were expected by customers and stakeholders to be more responsible and consider corporate social responsibility (CSR) in their business operations (Hsueh, 2014). The importance of the social pillar of sustainability is admitted by the concept of CSR and there are strong links between these concepts (Hutchins & Sutherland, 2008). By increasing consumer social awareness (CSA), SCs are forced to be more responsible toward the society. Nowadays, governments, competitors, and employees pressure downstream firms to distribute and sell social products (Letizia & Hendrikse, 2016). AS a result of increasing pressure on companies to be more socially responsible, cause related marketing (CM) has been applied frequently as a popular marketing tool (He et al., 2016). CM is a form of CSR ( Lii & Lee, 2012) defined by Varadarajan and Menon (Varadarajan & Menon, 1988) as marketing activities in which the firm donates a specified amount to a designated cause. In CM, companies promise to donate a proportion of sales revenue to a cause every time a consumer makes a purchase. CM has been officially used in 1983 when American Express created a campaign for Statue of Liberty restoration and donated a few cents each time its customers used their American Express cards (Lafferty et al., 2016). Since then, hundreds of brands have participated in CM campaigns such that in 2017, $2.05 billion have been allocated for CM in U.S. alone1. As a case of CM campaign, Paksan Co., a detergent producer in Iran, spent 10% of Pril-labelled products sales revenue to support and empower unskilled women. In another CM campaign, Starbucks donated $1 for every pound of sold East Africa Blend coffee to support AIDS sufferers in Africa (Müller et al., 2014). For more detailed data see: http://www.sponsorship.com/Report/2018/02/05/The-Most-Active-Sponsors-OfCauses.aspx 1
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Donation size as a design element of a CM campaign is a key success factor of a SC contributing in a CM campaign which is directly controlled by SC managers. Müller et al., (2014) found that donation size has a positive effect on brand choice if consumers have no choice between a CM product and a same product at a discount, i.e. the increase of donation size can increase consumers’ demand when customers are socially aware. Controlling donation size, the SC can earn profit from CM campaign participation by absorbing more socially aware customers. However, as donation volume is a decision made by the manufacturer, decided value does not maximize the whole SC profit when we face a decentralized SC where each member has a myopic approach to maximize own profit regardless of other channel members (Shukla et al., 2016). As a result, a coordination mechanism is required to ensure maximum profit for the whole SC following by a profit sharing mechanism to ensure higher profitability for all channel members. In this paper, a two-echelon SC including one manufacturer and one retailer in presence of socially aware customers is investigated. The manufacturer contributes in a CM campaign in order to absorb socially aware consumers. In the first case demand is assumed as a function of donation size. According to related literature (e.g. Baghi et al., 2009), consumers are absorbed if related causes described more clearly. Therefore, donation size, as a portion of retail price or an absolute amount per sold item, is decided by the manufacturer and announced on the product label. The problem is to optimize the donation size provided that the whole SC profit is maximized and at the same time ensure for more profit for both channel members after participating in the CM campaign. The model is then extended to include both the donation size and pricing decisions simultaneously where the retailer has the authority to decide on retail price. 3
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Main contribution of this paper with respect to the previous literature is bringing the concept of CM into the quantitative models by deciding on donation size mathematically. Although, several researches have been conducted in SC coordination area to improve the overall performance of SC (e.g. Ambilikumar et al., 2015) through different contracts, they have never used in SCs with a CM strategy. The concept of social SC is rarely investigated in the literature of SC coordination. Almost all previous works in this area have used an abstract factor as “social responsibility investment cost” to develop the mathematical models while in the current study, it is clearly defined that the cost is spent as donation for the CM campaign. As the first paper in the field, in this study we quantitatively explore and optimize participation of a SC in charitable activities (i.e. CM campaign). The rest of the article is organized as follows. In section 2 the relevant literature is reviewed. Section 3 introduces problem statement. Sections 4 and 5 present the proposed decision models. Section 6 discusses on results and managerial implications. All proofs of theorems and lemmas are presented in appendix. 2. Literature Review The extensive scope and complex nature of social issues makes it difficult to measure social responsibility and it is hard to measure its aspects all (Pishvaee et al., 2012). Some researchers proposed quantitative social sustainability indicators to evaluate the social supply chains (Ahi and Searcy, 2015; Popovic, et al., 2018) and some considered CSR level or social responsibility investment in quantitative models to measure social aspect of sustainability in supply chains. Ni et al. (2010) assumed that the upstream's CSR cost is shared by the other channel member by a wholesale price contract in a two-echelon SC. Ni and Li (2012) considered a 4
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two-tire SC that each channel member incurs its individual CSR cost. They have examined the effects of strategic interactions between the channel members under game theoretic setting and wholesale price contracts. Georing (2012) considered a two-echelon SC consists of a manufacturer and a retailer where the retailer to be socially concerned in one case, and the manufacturer to be so in another and a two-part tariff set by the manufacturer to coordinate the channel. Hsueh (2014) proposed a revenue sharing contract to coordinate CSR in a two-stage SC. Hsueh (2015) developed the study of Hsueh (2014) and considered a bi-level programming model in order to analyze a CSR collaboration problem in a threeechelon SC to maximize the profit of whole SC. Panda (2014) and Panda et al. (2016) considered a manufacturer–retailer SC where one of the firms, either the manufacturer or the retailer, is socially responsible. They used revenue sharing and quantity discount contracts to resolve channel conflicts. Modak et al. (2014) analysed a two-layer dualchannel SC where the manufacturer sells through an online channel in company with a traditional retail channel and intends to enhance social activities by exhibiting CSR. They analytically discussed channel coordination using quantity discounts along with an agreement on franchise fee and surplus profit division. Following that, Modak et al. (2016a) explored channel coordination in a two-tire SC consists of a socially responsible manufacturer and two competing retailers. They found that two-part tariff contract removes channel conflicts and provides win–win result for specific values of the franchise fee. Panda et al. (2015) and Modak et al. (2016b) considered a three-layer SC where the manufacturer invests on CSR and use a wholesale price discount-Nash bargaining and a new revenue sharing contracts to remove channel conflicts. Panda et al. (2017) developed a revenue sharing scheme to coordinate a two-tire socially responsible closed-loop SC with 5
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product recycling by use of Nash bargaining for dividing surplus profit. Raj et al. (2018) coordinated a two-echelon supply chain consists of a responsible supplier for greening and a buyer with social responsibility through 5 different contracts. Considering cause-related marketing, many previous researches have studied the effect of CM campaign characteristics (for an overview, see Fries, 2010) and identified a wide range of CM success factors. Donation size is one of these factors that some researches have evaluated its effect on CM Success (Human & Terblanche, 2012; Muller et al., 2014; Olsen et al., 2003; Strahilevitz, 1999). Lafferty et al. (2016) also reviewed the empirical studies in cause-related marketing. 2.1.
Research Gap
The related studies concentrated on socially responsible SC coordination are presented in Table 1. These studies all considered a CSR channel and some of them considered the effect of social activities on demand function. In socially responsible supply chains investigated by previous researches, CSR investment level was considered to evaluate the effect of the supply chain social activities. This factor is mainly assumed independent of the product sales while the donation amount paid for a special cause in a CM campaign, which is assumed in this study, completely depends on the product sales and it is consistent with the mission of SC to sell more product (i.e. more sales, more donations). Moreover, the donation size and consumer social awareness, which are two critical factors defined by the current study, affect CM success and the market demand. The influence of these factors has not been formulated in any previous demand function. Even though the use of coordination contracts to deal with channel conflict in social responsible SCs has been developed in recent decade, Cause-related Marketing as a form of social responsibility has never been 6
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taken into account in SC coordination to cut out double marginalization. Double marginalization exists in decentralized supply chains when there are two marginal profits from the manufacturer and the retailer and they make decision independently according to their own marginal profits without considering entire supply chain marginal (He et al., 2009). While cause related marketing as a popular form of CSR (Nan & Heo, 2007) is widely considered in empirical and conceptual marketing researches, previous studies in the field of SC optimization and SC coordination never modeled it as a social activity of the SC. By considering this point, in this study, for the first time, donation amount (per each sold item) paid by SC to a CM campaign is optimized and appropriate contracts are developed to share earnings.
Table 1. Comparison of previous researches with the proposed model
Wholesale Price
Ni & Li (2012)
Two
Wholesale Price
Goering (2012)
Two
Two-part tariff
Hsueh (2014)
Two
Revenue sharing
Panda (2014)
Two
Revenue sharing
Modak et al. (2014)
Two
Quantity discount & bargaining
Hsueh (2015)
Three
Collaboration model
Panda et al. (2015)
Three
Wholesale price
7
Donation size
CSR level
Two
CSR level
Ni et al. (2010)
CSR effort
Retail price
Donation size
Greening level
Wholesale price
Demand pattern Recycling factor
CSR investment
Marketing effort
Decision variables
mechanism
Greening level
Coordination
Order quantity
Echelons
Retail Price
Study
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discount & bargaining Panda et al. (2016)
Two
Modak et al. (2016a)
Two
Modak et al. (2016b)
Three
Ma et al., (2017)
Three
Panda et al., (2017) Nematollahi et al. (2017)
Two Two
Quantity discount &
bargaining Two-part tariff & bargaining Revenue sharing Wholesale price and two-part tariff Revenue sharing & bargaining
Collaboration model
Wholesale price Raj et al. (2018)
Two
Two-part tariff Greening cost sharing
Revenue sharing This study
Two
Cost sharing & Collaboration model
3. Supply chain model The models are developed in two cases. In the first case, we analyse a manufacturerretailer SC, where the manufacturer decides to participate in a CM campaign as a social activity to increase the sales volume from the socially aware customers. In this state, the manufacturer promises to donate a portion of retail price per each sold product to a social cause and clearly announces it to consumers with some labels stuck on their products. The manufacturer handles all the CM costs and therefore no increase in wholesale price w is occurred. The manufacturer supplies the products with the production unit cost 𝑐 and sell with wholesale price w where 𝑤 > 𝑐. The retailer sells the products at a given retail price 𝑝 where 𝑝 > 𝑤. In the second case, unlike the first case, we consider that the retailer decides
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on the retail price 𝑝 and therefore there are two decision variables in the second case: (1) donation size decided by the manufacturer (2) retail price decided by the retailer. According to Muller et al. (2014), increase of donation size can increase consumers demand. The demand function in the first case is considered as 𝐷1 = 𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝, where 𝐴 > 0 is the market potential, 𝑏 > 0 is the customers price sensitivity, 𝛾 > 0 is consumer social awareness (CSA) level and 𝛼 ≥ 0 is the portion of retail price donated (i.e. '𝛼𝑝' is the donation size) that decided by the manufacturer. Such a linear demand function is used frequently in various SC models especially green and social SCs in the literature.
𝑤
Decision Variables
Donated
𝑝
Manufacturer
Retailer
Case I
Donation Portion 𝛼
-
Case II
Donation Size 𝑑𝑠
Retail price
Consumer
Figure1. Supply chain model and decision variables in both cases As a real-world case, the manufacturer like Paksan Co. announces 𝛼 to consumers by labelling on the product. In the second case, the demand function considered as 𝐷2 = 𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠where 𝑑𝑠 ≥ 0 is the donation size which is an absolute value independent of retail price. As a real-world example for such a donation, Starbucks uses such an absolute amount (i.e. 1 $) as donation to CM campaign per one pound of sold East Africa Blend coffee. 9
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Notations: The following notations are used in developing the model. 𝑝
Retail price (Retailer’s decision variable in case II)
𝑤
Wholesale price (decided in cost sharing contract in case I)
𝑐
Unit production cost
𝐷1
Demand in case I
𝐷2
Demand in case II
𝐴
Market potential size
𝑏
Demand price sensitivity
𝛾
Consumer Social Awareness (CSA) level
𝛼
Portion of retail price donated (Manufacturer’s decision variable in case I)
𝑑𝑠
Donation size (Manufacturer’s decision variable in case II)
𝛱𝑚
Manufacturer profit function
𝛱𝑟
Retailer profit function
𝛱𝑆𝐶
Channel profit function
Superscripts ‘c’, ‘d’, ‘cs’, and ‘co’, indicate the centralized, decentralized, cost sharing contracts, collaboration scenario, respectively. Asterisk is used to represent optimum value of decision variables and profit functions.
4. Case I: Deciding only on donation size 4.1.
Decentralized decision
Under decentralized decision-making, the channel members make decision independently and optimize own profits. In this situation, the profit functions of channel members and SC are formulated as follows: 𝛱𝑚(𝛼) = 𝐷1(𝑤 ‒ 𝑐 ‒ 𝛼𝑝) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑤 ‒ 𝑐 ‒ 𝛼𝑝)
(1)
𝛱𝑟(𝛼) = 𝐷1(𝑝 ‒ 𝑤) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑝 ‒ 𝑤)
(2)
𝛱𝑠𝑐(𝛼) = 𝐷1(𝑝 ‒ 𝑐 ‒ 𝛼𝑝) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑝 ‒ 𝑐 ‒ 𝛼𝑝)
(3)
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In Eq. (1), term (𝑤 ‒ 𝑐 ‒ 𝛼𝑝) represents earned revenue for the manufacturer from selling each item where, 𝑤 ‒ 𝑐 is net profit from each sold item and 𝛼𝑝 is paid donation per each sold item. Theorem 1: The manufacturer profit function is concave in 𝛼 and optimal value of 𝛼 for the manufacturer is: 𝑑∗
𝛼
=
𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝑝 2𝛾𝑝
(4)
Lemma 1: To participate in CM campaign, the manufacturer’s unit marginal profit should be greater than
𝐴 ‒ 𝑏𝑝 . 𝛾
Substituting the optimal value of 𝛼 in Eqs. (1-3), we have: 𝑑∗
𝛱𝑚(𝛼
(
𝑑∗
𝛱𝑟 𝛼
(
)=(
𝑑∗
𝛱𝑠𝑐 𝛼 4.2.
𝐴 ‒ 𝑏𝑝 𝑤 ‒ 𝑐 2 ) = 𝛾( + ) 2𝛾 2
(5)
𝐴 ‒ 𝑏𝑝 𝛾(𝑤 ‒ 𝑐) + )(𝑝 ‒ 𝑤) 2 2
) = 𝛾(
(6)
𝐴 ‒ 𝑏𝑝 𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 2𝑝 ‒ 𝑤 ‒ 𝑐 + )( + ) 2𝛾 2 2𝛾 2
(7)
Centralized decision
Under centralized decision-making, it is assumed that a single decision maker decides on behalf of SC. Central decision maker intends to optimize the whole SC profit by deciding on 𝛼. Lemma 2: the optimal value of donation size 𝛼𝑝 under the centralized decision-making is 𝑐∗
𝛼
=
𝑝 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝑝 2𝛾𝑝
(8)
Lemma 3: The optimum value of 𝛼 under the centralized decision making is greater than 𝑐∗
the decentralized channel (i.e. 𝛼
𝑑∗
>𝛼
).
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Lemma 4: The manufacturer’s profit in centralized decision-making is less than the 𝑐∗
decentralized decision-making, i.e. 𝛱𝑚(𝛼
) < 𝛱𝑚(𝛼𝑑 ∗ ).
Lemma 5: The total profit of centralized channel is greater than the decentralized channel 𝑑∗
(i.e. 𝛱𝑠𝑐(𝛼
) < 𝛱𝑠𝑐(𝛼𝑐 ∗ )).
According to Lemma 5, centralized decision-making improves the performance of SC, even though the manufacturer’s profit decreases (Lemma 4). Therefore, if we have a decentralized channel, a side payment policy must be applied to persuade the manufacturer to change its decision in order to obtain the maximum channel performance.
4.3.
Channel coordination through Cost Sharing (CS) contract
The manufacturer contributes in a CM campaign to increase sales volume and at the same time participate in a social activity. According to Lemma 5, donation size decided by the manufacturer does not optimize the total channel performance. On the other hand, based 𝑐∗
on Lemma 4, the manufacturer profit is reduced if donation size is decided as 𝛼
.
Therefore, the retailer needs to persuade the manufacturer to change decision through an appropriate compensating scheme. A cost sharing (CS) contract is proposed to resolve the channel conflict. In the proposed CS contract, the retailer handle a fraction of CM cost and at the same time the manufacturer offers a new wholesale price. Therefore, the proposed contract has two 𝑐𝑠
parameters namely 𝑤
𝑐𝑠
and 𝜑; where 𝑤
is the modified wholesale price set by the
manufacturer and 𝜑 (0 < 𝜑 < 1) is the share of donation size undertaken by the retailer. Based on the suggested model, the SC members’ profit functions can be reformulated as:
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𝑐𝑠
𝑐𝑠
𝛱𝑚 (𝛼) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑤 ‒ 𝑐 ‒ (1 ‒ 𝜑)𝛼𝑝)
(9)
𝑐𝑠
𝑐𝑠
𝛱𝑟 (𝛼) = 𝐷1(𝑝 ‒ 𝑤 + 𝑟 ‒ 𝜑𝛼𝑝) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝛼𝑝)(𝑝 ‒ 𝑤 ‒ 𝜑𝛼𝑝)
(10)
Under the CS contract, the manufacturer problem is to maximize its profit by deciding on 𝛼. 2
Since
𝑑 𝛱𝑚
𝛼
2
𝑐𝑠
=‒ 2𝛾(1 ‒ 𝜑)𝑝 < 0 ensures that 𝛱𝑚 is a concave function in 𝛼, the necessary
2
𝑑𝛼
condition 𝑐𝑠 ∗
𝑐𝑠
𝑑𝛱𝑚
𝑐𝑠
= 0 results in:
𝑑𝛼 𝑐𝑠
𝑤 ‒𝑐 𝐴 ‒ 𝑏𝑝 = ‒ 2(1 ‒ 𝜑)𝑝 2𝛾𝑝
(11)
The channel is coordinated if the manufacturer’s decision maximizes the whole channel 𝑐𝑠 ∗
profit, i.e. 𝛼
𝑐∗
=𝛼
. Therefore, we can calculate the following condition for the CS
contract parameters: 𝑐𝑠
(12)
𝑤 = 𝑝 ‒ 𝜑(𝑝 ‒ 𝑐) Lemma 6: The CS contract can coordinate channel members decisions if and only if
[
𝜑𝜖[𝜑,𝜑] = 2𝛾(𝑝 ‒ 𝑤)
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) (𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
,1‒ 2
(
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) 𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐)
)] 2
(13)
Lemma 7: There is at least one feasible value of 𝜑 to coordinate the channel through CS contract. Lemma 8: If the manufacturer chooses the wholesale price from the following closed interval, the channel will be coordinated. 𝜑𝜖[𝑤,𝑤] =
[
(
)]
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) 2 𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) 𝑐 + (𝑝 ‒ 𝑐) , 𝑝 ‒ 2𝛾(𝑝 ‒ 𝑐)(𝑝 ‒ 𝑤) 2 𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐) (𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
(
)
13
(14)
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5. Case II: Simultaneously pricing and donation size decisions In this case we extend the Case I by assuming that the retailer also has the authority to decide on retail price. In addition, donation size in Case II is considered as an absolute value independent of the retail price. As discussed earlier, such a donation mechanism is also used in real-world cases. 5.1.
Decentralized decision
Under decentralized decision-making, the channel members operate independently and optimize individual profits. In this case, interaction between players is assumed as a Stackelberg game. The manufacturer is supposed to be the leader of the channel. The manufacturer, as the leader, makes the first decision, and then the follower reacts by choosing its best move in accordance with the available information. In this way, at first, the manufacturer announces the donation size with some labels stuck on the product while the manufacturer is absolutely certain that the retailer determines the retail price in response to the manufacturer's decision. Therefore, we extract the optimal amount of retail price from the retailers’ profit function at first. Lemma 9: The retailer earns maximum profit if the retail price is determined as: ∗
𝑝 =
𝐴 + 𝑏𝑤 + 𝛾𝑑𝑠
(15)
2𝑏
Lemma 10: In a Stackelberg game, to earn maximum profit, the manufacturer as a leader of ∗
the channel chooses 𝑑 𝑠 as follows: ∗
𝑑𝑠 =
𝑤 ‒ 𝑐 2(𝐴 ‒ 𝑏𝑝) ‒ 3 3𝛾
(16)
Solving the system of two linear Eqs. (15-16) results in: ∗
𝑝 =
𝛾(𝑤 ‒ 𝑐) + 3𝑏𝑤 + 𝐴 4𝑏
(17) 14
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(𝑤 ‒ 𝑐) 𝐴 ‒ 𝑏𝑤 ‒ 2 2𝛾
∗
𝑑𝑠 =
(18)
Lemma 11: To participate in a CM campaign, the manufacturer’s unit marginal profit should be greater than
𝐴 ‒ 𝑏𝑤 . 𝛾
Substituting the optimal value of donation size and retail price from Eqs. (17-18) in demand function and profit functions, we have: ∗
∗
𝐷2(𝑝 ,𝑑 𝑠 ) = 𝛱𝑚(𝑝
∗
∗
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤
∗ ,𝑑 𝑠 ) = 2𝛾 ∗
( (
𝛱𝑟(𝑝 ,𝑑 𝑠 ) = 𝑏 ∗
∗
𝛱𝑠𝑐(𝑝 ,𝑑 𝑠 ) = 5.2.
(19)
4
(
)
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤 4𝛾
2
(20)
2
) )(
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤 4𝑏
(21)
𝐴 + 𝛾(𝑤 ‒ 𝑐) ‒ 𝑏𝑤 𝛾(𝑤 ‒ 𝑐) + 3𝑏𝑤 + 𝐴 𝛾(𝑤 ‒ 𝑐) + 𝑏𝑤 ‒ 𝐴 ‒𝑐‒ 4 4𝑏 2𝛾
)
(22)
Collaboration scenario
As discussed in Case I, the decentralized solution is unable to maximize the whole channel profit and remove the double marginalization effect due to pursuit of individual goals by each SC member. We propose a collaboration scenario by the aim of maximizing channel profit and ensuring for better position for both players. Under the proposed collaboration mechanism, both the players cooperate in order to maximize the profit of the whole channel provided that the profits of both members remain at least in the same level of the decentralized model. In this situation, the players have enough motivation to collaborate. Under the proposed collaboration model, a win-win solution is derived while each player is able to negotiate on its share from the earned surplus based on its market domination. In the proposed model, members’ market domination is represented by parameters ‘𝜃’, for the retailer, and ‘β’, for the manufacturer, where 0 < 𝜃+ 𝛽 ≤ 1. ‘𝜃’ and ‘β’ are the dominancy 15
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factors of the retailer and the manufacturer, respectively. Dominancy factor of stronger player takes a larger value closer to one and most of the earned surplus profit will be gained by him. In practice, indicators such as brand popularity, marker share, and privileged accesses are used to measure market dominancy/bargaining-power (Basiri & Heydari, 2017). The proposed collaboration model is formulated as a mathematical programming model to maximize the total channel profit as follow: 𝑀𝑎𝑥 𝛱𝑠𝑐(𝑝,𝑑𝑠) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑝 ‒ 𝑐 ‒ 𝑑𝑠)
(23)
s.t.
{
(
𝑐𝑜
𝑑
∗
∗
(
)
𝑑
(
∗
∗
𝛱 𝑟 = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑝 ‒ 𝑤) ≥ 𝛱 𝑟 𝑝 ,𝑑 𝑠 + 𝜃 𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐 𝑝 ,𝑑 𝑠 𝑐𝑜
𝑑
(
∗
∗
)
(
𝑑
(
)) ∗
(24) ∗
𝛱 𝑚 = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑤 ‒ 𝑐 ‒ 𝑑𝑠) ≥ 𝛱𝑚 𝑝 ,𝑑 𝑠 + 𝛽 𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐 𝑝 ,𝑑 𝑠 0<𝜃+𝛽≤1 𝐴 0 ≤ 𝑑𝑠 & 0 ≤ 𝑝 ≤ ( 𝑏)
))
(25) (26) (27)
Where, Eq. (23), as the objective function of collaborative decision-making, aims to maximize the channel profit. Constraints (24) and (25) ensure that the retailer and the manufacturer profits through collaboration strategy are at least equal to the decentralized 𝑑
∗
∗
decision-making profit, respectively. In other words, terms ‘𝜃(𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐(𝑝 ,𝑑 𝑠 ))’ and 𝑑
∗
∗
‘𝛽(𝛱𝑠𝑐(𝑝,𝑑𝑠) ‒ 𝛱𝑠𝑐(𝑝 ,𝑑 𝑠 ))’ in the right-hand of the inequalities (24-25) guarantee enough motivations for the retailer and the manufacturer to participate in collaborative decisionmaking, respectively. Constraint (27) ensures that the solution is rational and finite. 5.3.
Numerical Experiments in Case II
To show the outcome of the proposed collaborative model numerically, a set of experiments are examined. Three numerical examples are tested to evaluate the proposed collaborative model numerically. The parameters and the decentralized decision results
16
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are presented in Table 2. All datasets satisfy the requirements and assumptions of the proposed models and are consistent with literature in this area.
Table 2: Three numerical examples datasets and decentralized decision results Parameters
Decentralized Decision ∗
∗ 𝑑𝑠
𝐷2
𝛱𝑚
𝛱𝑟
𝛱𝑆𝐶
𝐴
𝑏
𝛾
𝑐
𝑤
Ex. 1
50
2.0
1.0
10
21
23.38
1.50
4.75
45.13
11.28
56.41
Ex. 2
100
0.8
0.7
28
80
102.64
0.29
18.10
936.03
409.51
1345.54
Ex. 3
150
1.5
0.5
40
85
92.50
0.00
11.25
506.25
84.38
590.63
𝑝
The results of running the proposed collaborative model for various amount of 𝜃 on the three investigated examples are presented in Table 3. In all experiments it is assumed that 𝜃 = 1 ‒ 𝛽. According to Table 3, the retail price and donation size will increase simultaneously by increasing 𝜃 which result in a fixed demand for all combinations of 𝜃 and 𝛽. Furthermore, as expected, by increasing 𝜃, profit of the retailer increases while the profit of the manufacturer decreases. For all combinations of 𝜃 and 𝛽 both the retailer and the manufacturer have a better position than the decentralized decision model. Test problems show that when 𝜃 decreases, the model creates higher profit for the whole channel and manufacturer while the retailer’s share decreases. By comparing Tables 2 and 3, one can conclude that in all test problems the collaboration model is more profitable for the SC and both SC members and therefore participating in the collaborative decision making is guaranteed. We expected this result according to the previous proposed collaborative models (e.g. Basiri & Heydari, 2017). The results also
17
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approve the conceptual researches in cause-related marketing (Müller et al., 2014) that participation in a CM campaign can help business economics by increasing sales volume. Comparing Tables 2 and 3 shows that, in all test problems, the proposed collaboration model results in a greater demand amount than the decentralized model. While the realized demands for three investigated examples are 4.75, 18.1, and 11.25 in decentralized model, demands increase to 9.5, 36.2, and 22.5 in collaborative model, respectively. In addition, in all experiments, the collaboration model results in a higher donation size (than the decentralized model) from one side and lower prices (than the decentralized model) from the other side. This means the proposed collaboration model causes a more socially concerned SC with lower price offered to the customers. Table 3: Collaboration model results under various 𝜃 𝒄𝒐 ∗
𝜽 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
𝒑 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3
22.19 91.31 88.75 22.40 92.59 89.69 22.58 93.83 90.36 22.74 95.03 90.86 22.87 96.20 91.25 22.98 97.35 91.56 23.08 98.46 91.82 23.17 99.54 92.03 23.24 100.59 92.21
𝒄𝒐 ∗
𝒅𝒔
3.88 13.21 11.25 4.31 14.67 14.06 4.67 16.09 16.07 4.97 17.46 17.58 5.23 18.81 18.75 5.46 20.11 19.69 5.66 21.38 20.45 5.83 22.62 21.09 5.99 23.82 21.63
𝒄𝒐
𝒄𝒐
𝒄𝒐
𝑫𝟐
𝜫𝒎
𝜫𝒓
𝜫𝒔𝒄
9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50 9.50 36.20 22.50
67.69 1404.04 759.38 63.59 1351.31 696.09 60.17 1300.04 650.89 57.27 1250.18 616.99 54.79 1201.66 590.63 52.46 1154.44 569.53 50.77 1108.46 552.27 49.11 1063.67 537.89 47.63 1020.03 525.72
11.28 409.51 84.38 13.33 455.65 105.47 15.04 500.52 120.54 16.49 544.15 131.84 17.72 586.60 140.63 18.80 627.92 147.66 19.74 668.15 153.41 20.57 707.34 158.20 21.31 745.52 162.26
78.97 1813.55 843.76 76.92 1806.96 801.56 75.21 1800.56 771.43 73.76 1794.33 748.83 72.51 1788.26 731.26 71.26 1782.36 717.19 70.51 1776.61 705.68 69.68 1771.01 696.09 68.94 1765.55 687.98
18
Total paid Donation 36.81 478.36 253.12 40.92 531.09 316.41 44.33 582.36 361.61 47.23 632.23 395.51 49.71 680.74 421.88 51.85 727.97 442.97 53.73 773.95 460.23 55.39 818.73 474.61 56.87 862.37 486.78
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0.9 1.0
Ex. 1 Ex. 2 Ex. 3 Ex. 1 Ex. 2 Ex. 3
23.31 101.62 92.37 23.38 102.63 92.50
6.13 25.00 22.10 6.25 26.14 22.50
9.50 36.20 22.50 9.50 36.20 22.50
46.31 977.50 515.29 45.13 936.03 506.25
21.97 782.74 165.74 22.56 819.03 168.75
68.28 1760.24 681.03 67.69 1755.06 675.00
58.19 904.90 497.21 59.38 946.37 506.25
6. Conclusions This paper considers a social channel coordination in a two-echelon SC consist of a manufacturer, who contributes in a cause-related marketing campaign by donating a portion of sales revenue to support a social cause, and a retailer. Based on previous researches in the effect of donation size on consumer's demand and willingness to pay, demand is considered as a linear function of donation size. The channel is analyzed in two cases. In Case I the manufacturer decides on donation size in presence of a given retail price, while in Case II the manufacturer decides on donation size and at the same time the retailer determines the retail price. In Case I, a cost sharing contract is proposed to improve channel performance and depicts a win-win outcome for both players. In Case II a collaborative model is developed to improve decision making process. The numerical examples show that the suggested collaborative mechanism is capable of improving whole channel performance. Indeed, the solution experiences a Pareto-improvement in which the whole channel profit better off without making no player worse off than the decentralized decision making. In addition, numerical study reveals that the proposed collaborative model increases donation size and decrease the retail price at the same time which means a more socially concerned SC and more satisfied customers. Though the academic researches on CM grew in recent years, they only studied this strategy conceptually. Moreover, the previous researches on social supply chains evaluated the effect of social activities by 19
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considering CSR investment or CSR level in quantitative models. However, in this study we formulated social activities through donation size as a key success factor in a CM campaign. Indeed, the main contribution of this paper is considering the concept of cause-related marketing in the quantitative models. In addition, unlike the previous studies in modeling of social supply chains, we introduce and apply the concept of consumer social awareness (CSA) and its impact on stimulating market demand. The managerial implication of our proposed coordination contract and collaboration model is helping the SC mangers to design an optimal CM strategy in alignment with the whole supply chain profitability where the SC not only earns more profit, but also enhances its social reputation. Although this paper provides interesting ideas about how a social supply chain with causerelated marketing strategy can be managed to achieve maximum profit, as a first research in this area, it has some limitations which we leave them for future researches. For example, for the sake of simplicity, the demand is assumed as a deterministic linear function in both the investigated cases which can be further investigated by considering a stochastic donation size dependent demand. Moreover, two-echelon supply chain considered in this paper can be expanded and a competitive environment can be investigated in future studies instead of the considered dyadic SC.
Acknowledgements We would like to appreciate the two anonymous reviewers for their valuable comments which have helped us to enhance the quality of paper. The financial support of University of Tehran for this research under grant number 29917-01-01 is also appreciated.
20
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Appendix: proofs Proof of Theorem 1: Differentiating 𝛱𝑚 with respect to 𝛼, as the only decision variable of 𝑑∗
the manufacturer and equating it to zero, results in 𝛼
=
𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 2𝑝
given that 𝛱𝑚is a
2
concave function of 𝛼 as
𝑑 𝛱𝑚 2
𝑑𝛼
2
2
2
=‒ 𝛾𝑝 ‒ 𝛾𝑝 =‒ 2𝛾𝑝 < 0. 𝑑∗
Proof of lemma 1: The manufacturer participates in CM campaign if 𝛼 results in 𝑤 ‒ 𝑐 >
> 0, which
𝐴 ‒ 𝑏𝑝 . 𝛾 2
Proof of lemma 2: As
𝑑 𝛱𝑠𝑐 2
𝑑𝛼
2
=‒ 2𝛾𝑝 < 0 ensures that 𝛱𝑠𝑐 is a concave function in 𝛼, 𝑐∗
results in optimal value for 𝛼 as 𝛼
=
𝑑𝛼
=0
𝑝 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 . 2𝑝
Proof of lemma 3: The rational decision on retailer price (𝑝 > 𝑤) results in 𝑤 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 2𝑝
𝑑𝛱𝑠𝑐
𝑝 ‒ 𝑐 𝐴 ‒ 𝑏𝑝 ‒ 2𝛾𝑝 > 2𝑝
which results in a greater donation size under the centralized decision making
than the decentralized decision making.
(
𝑐∗
Proof of lemma 4: Substituting Eq. (8) in Eq. (1) results in 𝛱𝑚 𝛼
) = 𝛾(𝐴 2𝛾‒ 𝑏𝑝 + 𝑝 2‒ 𝑐)
(𝐴 2𝛾‒ 𝑏𝑝 + 2𝑤 ‒2𝑝 ‒ 𝑐). Replacing (𝑝 ‒ 𝑐) by (𝑝 ‒ 𝑤) + (𝑤 ‒ 𝑐) in the first parentheses of (𝛼𝑐 ∗ )
(𝑝 ‒2 𝑤)
𝑐∗
and some simplifications we have 𝛱𝑚(𝛼 2
> 0, therefore, 𝛾
((
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 𝑝‒𝑤 2 ‒ + ( ) 2𝛾 2 2
)=𝛾
) < 𝛾(
)
((
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 𝑝‒𝑤 2 ‒ + ( ) 2𝛾 2 2
)
𝐴 ‒ 𝑏𝑝 𝑝‒𝑐 2 + ) . 2𝛾 2
). Since
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 . + 2𝛾 2
)
Proof of lemma 5: Substituting Eq. (8) in the SC profit function leads to
(
𝛱𝑚
𝑐∗
𝛱𝑠𝑐(𝛼
)=𝛾
Moreover, if we replace (𝑤 ‒ 𝑐) in the first parenthesis of Eq.(7) with (𝑝 ‒ 𝑐)
21
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𝑑∗
‒ (𝑝 ‒ 𝑤), then 𝛱𝑠𝑐(𝛼
)=𝛾
((
𝐴 ‒ 𝑏𝑝 𝑝‒𝑐 2 𝑝‒𝑤 2 ‒ + 2𝛾 2 2
) ( ))
. Since
𝑝‒𝑤 2 > 0, 2
( )
therefore, 𝛱𝑠𝑐
(𝛼𝑑 ∗ ) < 𝛱𝑠𝑐(𝛼𝑐 ∗ ). Proof of lemma 6: The manufacturer and the retailer both accept CS contract when CS contract results in a greater or at least equal profit for them than respective decentralized 𝑐𝑠
𝑐𝑠
profits, i.e., 𝛱𝑚 ≥ 𝛱𝑚 and 𝛱𝑟 ≥ 𝛱𝑟. In other words, (
𝐴 ‒ 𝑏𝑝 𝑤‒𝑐 2 + ) 2𝛾 2
and
𝜑 𝐴 ‒ 𝑏𝑝 𝐴 ‒ 𝑏𝑝 𝛾(𝑤 ‒ 𝑐) 𝛾(𝑝 ‒ 𝑐) 2 ≥ 2 + 2 + 𝛾 2 2
) (
(
(1 ‒ 𝜑) 𝐴 ‒ 𝑏𝑝 𝛾(𝑝 ‒ 𝑐) 2 ( + ) ≥𝛾 𝛾 2 2
)(𝑝 ‒ 𝑤).
Simplifying
these
inequalities, a range of CS fraction 𝜑 for achieving a win-win situation can be extracted as Eq. (13). Proof of lemma 7: We must prove that the interval [𝜑,𝜑] is non-empty interval. In other words, we must show that: 2𝛾(𝑝 ‒ 𝑤)
2
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐)
(𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
2
≤1‒
‒ 𝑐) . We use proof (𝐴𝐴 ‒‒ 𝑏𝑝𝑏𝑝 ++ 𝛾(𝑤 𝛾(𝑝 ‒ 𝑐) )
by contradiction and suppose that the above interval is empty. Hence, we have: 2𝛾(𝑝 ‒ 𝑤)
𝐴 ‒ 𝑏𝑝 + 𝛾(𝑤 ‒ 𝑐) (𝐴 ‒ 𝑏𝑝 + 𝛾(𝑝 ‒ 𝑐))
2
2>1‒
‒ 𝑐) . Simplifying this inequality results in 𝑤 > 𝑝 (𝐴𝐴 ‒‒ 𝑏𝑝𝑏𝑝 ++ 𝛾(𝑤 𝛾(𝑝 ‒ 𝑐) )
that is not true. Therefore, the proof by contradiction is invalid and the interval [𝜑,𝜑]is a non-empty interval. Proof of lemma 8: Substituting 𝜑 and 𝜑 from Eq. (13) into Eq. (12) results in 𝑤 and 𝑤, respectively. Proof of lemma 9: Differentiating 𝛱𝑟(𝑝,𝑑𝑠) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑝 ‒ 𝑤) with respect to 𝑝 and ∗
equating it to zero results in 𝑝 =
𝐴 + 𝑏𝑤 + 𝛾𝑑𝑠 2𝑏
2
given that
function in 𝑝.
22
𝑑 𝛱𝑟 2
𝑑𝑝
= ‒ 2𝑏 < 0 and 𝛱𝑟 is a concave
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∗
Proof of lemma 10: Substituting the value of 𝑝 into the manufacturer profit function 𝛱𝑚 (𝑝,𝑑𝑠) = (𝐴 ‒ 𝑏𝑝 + 𝛾𝑑𝑠)(𝑤 ‒ 𝑐 ‒ 𝑑𝑠), necessary conditions ∗
𝑑𝑠 =
𝑑𝛱𝑚 𝑑𝑑𝑠
= 0 yields:
𝑤 ‒ 𝑐 2(𝐴 ‒ 𝑏𝑝) ‒ 3 3𝛾 2
Note that 𝛱𝑚 is a concave function in 𝑑𝑠 as
𝑑 𝛱𝑚 2
𝑑𝑑𝑠
=‒ 𝛾 ≤ 0.
Proof of lemma 11: According to Eq. (18), if 𝑤 ‒ 𝑐 >
𝐴 ‒ 𝑏𝑤 𝛾
∗
then 𝑑 𝑠 > 0 that means
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Varadarajan, P. R., & Menon, A. (1988). Cause-related marketing: A coalignment of marketing strategy and corporate philanthropy. The Journal of Marketing, 58-74.
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Highlights:
Contributing a SC in a Cause-related Marketing campaign is optimized Donation size and price decisions in a SC contributing in a CM campaign are coordinated A cost sharing mechanism is developed to create a win-win solution A collaborative decision model is proposed to coordinate donation size and retail price The proposed models result in less prices and higher donation sizes