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Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns

Data publikacji: 14 Oct 2022
Tom & Zeszyt: AHEAD OF PRINT
Zakres stron: -
Otrzymano: 01 Dec 2020
Przyjęty: 25 Jan 2021
Informacje o czasopiśmie
License
Format
Czasopismo
eISSN
2444-8656
Pierwsze wydanie
01 Jan 2016
Częstotliwość wydawania
2 razy w roku
Języki
Angielski
Introduction

Nowadays, environmental protection and sustainable development issues are being given considerable attention. To protect our environment, a series of policies have been legislated [1]. For example, a greenhouse gases emission reduction target have been set up by International organizations and national governments, it plans a 80% reduction for UK in 2050 [2]. In the meantime, a large number of enterprises are actively adopting advanced and innovative technologies to produce green or environmentally friendly products [3, 4, 5].

According to Ranjan and Jha [6], a green product has comparatively less effect on environment and less harmful on health than a traditional product. On the one hand, with the increase of customers’ environmental concerns, there are many convincing evidences that consumers’ attitudes toward green products have changed significantly [7]. A survey report with 9 developed countries shows that half of the respondents want to purchase green products, and 24% of the respondents are pleased to pay increased prices for buying green product [6]. On the other hand, in order to obtain a higher market share, enterprises would like to carry out appropriate marketing activities for green products in practise. Both of the two aspects mentioned above show that it is critically important to study green supply chain under marketing effort.

In addition, decision makers are usually assumed to be perfectly rational. However, many empirical and experimental studies have shown that decision makers exhibit bounded rationality in their decision process and have different social preferences [8, 9, 10, 11]. Fairness concerns is one of typical social preferences, which illustrates an enterprise’s concern regards to the inequality between supply chain members [12]. Usually, the fairness behavior of enterprises is caused by the uneven distribution of supply chain’ profits. When enterprises involve fairness behavior, they focus on their own income and fair treatment in profit allocation simultaneously [13]. For example, in March 2004, due to the demand for higher-than-normal kickbacks was rejected by Gree, a China’s household appliance retailer Gome decided to terminate its cooperation with Gree. This case reflects that Gome was concerned with distributional fairness and wanted to extract more profit from Gree by its dominating power in the retailing industry [14]. This reveals that we should pay more attention to the fairness behavior of enterprises when making decisions such as investment, pricing and designing contract.

Motivated by the above observations and discussions, in this paper, we study a green supply chain with a socially responsible manufacturer and a fair-mined retailer, where the manufacturer adopts advanced and innovative technologies to produce green products, and the retailer carries out marketing activities to obtain higher market share. We mainly focus on the optimal decisions about green quality level, marketing effort level, and pricing, as well as how to improve the supply chain’s economic and environmental performances. Meanwhile, we analyze the effect of the fairness behavior on the optimal decisions.

The main contribution of our study is threefold as follows. Firstly, we develop decentralized decision-making models with WP contract, and derive the optimal decisions for each member with a manufacturer Stackelberg game. Also, we use the centralized case to establish a performance benchmark. Secondly, we discuss the effect of the fairness behavior on the optimal strategies and profits. Thirdly, we propose a RCS contract to coordinate the supply chain and improve the supply chain’s performance.

The remainder of this paper is organized as follows. We review the relevant literature in next section. Section 3 presents the model setting, notations and assumptions. In Section 4, we use the centralized case to establish a performance benchmark. In Section 5, we develop decentralized supply chain models with WP contract under the scenarios whether the retailer involves fairness concerns or not. Several numerical investigations are given in Section 6. We conclude in Section 7.

Literature Review

This paper is closely related to the literature on green supply chain with marketing effort. Ranjan and Jha [6] investigated the pricing strategies and coordination mechanism in a dual-channel supply chain, where the market demand is a linear function consists of selling price, green quality level, and sales effort level. They proposed a surplus profit-sharing mechanism to achieve channel coordination. Basiri and Heydari [2] investigated the channel coordination issue in a two-stage green supply chain, in which the manufacturer produces green and traditional two substitutable products, and market demand for both products also be a function consists of retail price, green quality level and sales effort level. Li et al. [15] examined a low-carbon closed-loop supply chain (CLSC) under four different game structures and determined manufacturers’ carbon emission reduction level and retailers’ low-carbon promotion effort level. Gao et al. [16] considered a CLSC with price, collection effort and sales effort dependent demand and proposed coordination strategy for the decentralized supply chain. De Giovanni [17] investigated environmental collaboration via a reverse revenue sharing contract in a CLSC under the setting that the retailer invest in green advertising to build up the goodwill dynamic.

Some previous studies in conventional non-green environments which consider the product quality and marketing effort dependent demand are technically related to our paper. Nouri et al. [18] studied channel coordination of a manufacturer-retailer chain under a stochastic demand, in which the demand is dependent on the retailer’s promotional and the manufacturer’s innovation efforts. Huang et al. [19] addressed the coordination and profit allocation issues in a vendor-managed inventory supply chain via a combined contract composed of option and cost-sharing, where random demand is dependent on product quality level and marketing effort level. Ma et al. [20] investigated the issue of channel coordination for a two-stage supply chain under the demand is influenced by the retailer’s sales effort and manufacturer’s quality improvement efforts. Considering that both innovation and advertising contribute to the product demand, Song et al. [21] found that the optimal equilibriums under two different game structures, and proposed a new two-way subsidy policy to coordinate channel. Gurnani et al. [22] considered a two-echelon supply chain where the product supplier invests in quality improvement and the purchasing firm invests in the product market development via selling effort, and explored the impact of product pricing and timing of efforts investment. Liu et al. [23] also considered a supply chain with manufacturers’ product quality improvement effort and retailers’ sales effort improvement. They investigated the timing effect of retailer’s commitment of sales effort on the firms’ equilibrium investment and pricing decisions.

Another closely related literatures to our study is supply chain management (SCM) with fairness concerns. Cui et al. [12] was among the first to incorporate fairness concerns into SCM research using an analytical model, and investigated the role of WP contract in channel coordination under linear demand function. Then, the problem about SCM with fairness concerns is subsequently extended in different scenarios. Caliskan-Demirag et al. [24] extended Cui et al. [12] to allow nonlinear demand functions, and showed that compares with the linear demand function under the setting that the retailer is fair-minded, an exponential demand function is easier to achieve coordination. Zheng et al. [14] considered a three-echelon CLSC consisting of one manufacturer, one distributor, and one retailer, where the retailer exhibits fairness concerns. They investigated supply chain coordination by cooperative game approaches. Zhang et al. [25] examined the effects of consumer environmental awareness and retailer’s fairness concerns on the green product’s environmental quality, wholesale price and retail price in a manufacturer-retailer supply chain. Ma et al. [26] considered CLSC with retailer’s marketing-dependency demand under four reverse channel structures. They investigated how retailer’s fairness concerns affect optimal decisions and supply chain performance. Liu et al. [27] studied the effects of distributional fairness concerns and peer-induced fairness concerns on the order allocation’s decision-making in logistics service supply chain. Sharma [28] explored the impact of channel members’ fairness concerns on optimal decisions under the manufacturer-led Stackelberg game and vertical Nash game. Qian et al. [29] investigated a channel coordination problem in a two-echelon sustainable supply chain with a socially responsible manufacturer and a fair-minded retailer under cap-and-trade regulation.

As far as we know, no researches that address the optimal decisions and channel coordination problems in a green supply chain considering marketing effort and fairness concerns simultaneously. This paper deals with the gap in the literature. Most related works are found in Ma et al. [20] and Song et al. [21]. They investigated the optimal decisions and channel coordination issues of for a two-stage supply chain with one manufacturer and one retailer, where market demand is influenced by retail price and investment in product quality and marketing effort. But they assumed that both the manufacturer and the retailer are perfectly rational. Different from them, this paper considers a two-stage supply chain consisting of a socially responsible manufacturer and a fair-minded retailer, where market demand depends on green quality level, marketing effort level, and retail price. We focus mainly on the impact of the fairness behaviour on the optimal decisions and corresponding profits. Moreover, we examine how to coordinate the supply chain via a RCS contract combining revenue sharing and cost sharing, since revenue sharing contract is widely used to resolve channel conflict [30] and cost sharing contract is often used to coordinate the investments or efforts in both production and retail [19].

Model Description

We consider a two-stage green supply chain consisting of one socially responsible manufacturer and one fair-minded retailer in a single period, in which the manufacturer produces green products and sells them to end consumers through the retailer. In order to satisfy the requirements of consumers, the manufacturer invests in green quality improvement, which lead the market demand increasing. In the meantime, in order to expand market and enhance demand, the retailer exerts marketing activities such as advertisement and promotional displays to publish the green information of products. In this case, the market demand of products depends on the retail price, green quality level and market effort level. Notations are listed in Table 1.

Notations.

Notation Implication
c production cost per unit of product
w wholesale price per unit of product
p retail price per unit of product
a primary intrinsic demand
g green quality level
e marketing effort level
b consumer’s sensitivity parameter in retail price
α consumer’s sensitivity parameter in green quality level
β consumer’s sensitivity parameter in marketing effort level
m cost coefficient of greening investment
n cost coefficient of marketing investment
λ fairness concerns coefficient of the retailer
ϕ revenue-sharing coefficient
γ cost-sharing coefficient
π profit function
U utility function

Following the literature [16, 20, 31], the demand d is a linear function of the retail price p, green quality level g and market effort level e, which can be expressed by d=abp+αg+βe d = a - bp + \alpha g + \beta e where a is the primary intrinsic demand of products. b(b > 0), α(α > 0) and β(β > 0) are consumer’s sensitivity parameters in retail price, green quality level and market effort level, respectively. Generally, the higher green quality level the manufacturer provides, the more investment cost the greening innovation takes. We assume that the green quality improvement cost at level g is mg2/2 as the existing literature [32] did, in which m(m > 0) is the cost coefficient of greening investment. Similarly, the better the marketing effort level, the higher the investment cost. According to the existing literature [2], the retailer’s marketing effort cost is assumed to be ne2/2, where n(n > 0) is the cost coefficient of marketing investment. In order to avoid the unreasonable cases, we assume p > w > c. Thus we have a > bc. We know that the cost of investment in green quality and marketing effort is high in practical application. According to the finds of [20-21], the cost coefficients of investment in green quality and marketing effort have to be large enough to avoid trivial analysis, that is, 2bnb2 > 0 and 2bnna2mb2 > 0.

Following the literature [20-21], we assume that the manufacturer acts as the leader in the supply chain, and first determine the green quality level and sets the wholesale price. Then, taking into consideration the green quality level and the wholesale price, the retailer decides its marketing effort level and the retail price. Customer demand takes place over the period and are satisfies without stockout during this time. The manufacturer is perfectly rational and aims to maximize its profit, while the retailer aims to maximize the utility since it involves fairness concerns.

In addition, subscripts m, r, sc and λ denote manufacturer, retailer and supply chain, respectively. Superscripts I, D and R denote centralized supply chain model, decentralized supply chain model with WP contract, and decentralized supply chain model with RCS contract, respectively.

Centralized Supply Chain Model

In this section, we investigate the centralized supply chain, the manufacturer and retailer joint operate as one decision-maker. Then the centralized supply chain’s profit is πscI=(pIc)(abpI+αgI+βeI)12m(gI)212n(eI)2 \pi_{sc}^I = ({p^I} - c)(a - b{p^I} + \alpha {g^I} + \beta {e^I}) - {1 \over 2}m{({g^I})^2} - {1 \over 2}n{({e^I})^2}

Differentiating with respect to gI, eI and pI gives πscIgI=α(pIc)mgI {{\partial \pi_{sc}^I} \over {\partial {g^I}}} = \alpha ({p^I} - c) - m{g^I} πscIeI=β(pIc)neI {{\partial \pi_{sc}^I} \over {\partial {e^I}}} = \beta ({p^I} - c) - n{e^I} πscIpI=a2bpI+bc+αgI+βeI {{\partial \pi_{sc}^I} \over {\partial {p^I}}} = a - 2b{p^I} + bc + \alpha {g^I} + \beta {e^I}

The Hessian matrix of πscI \pi_{sc}^I with respect to gI, eI and pI satisfy that 2πSCI(gI)2=m<0 {{{\partial^2}\pi_{SC}^I} \over {\partial {{({g^I})}^2}}} = - m < 0 H(gI,eI)=|2πSCI(gI)22πSCIgIeI2πSCIgIeI2πSCI(eI)2|=mn>0 H({g^I},{e^I}) = \left| {\matrix{{{{{\partial^2}\pi_{SC}^I} \over {\partial {{({g^I})}^2}}}{{{\partial^2}\pi_{SC}^I} \over {\partial {g^I}\partial {e^I}}}} \cr {{{{\partial^2}\pi_{SC}^I} \over {\partial {g^I}\partial {e^I}}}{{{\partial^2}\pi_{SC}^I} \over {\partial {{({e^I})}^2}}}} \cr}} \right| = mn > 0 H(gI,eI,pI)=|2πscI(gI)22πscIgIeI2πscIgIpI2πscIeIgI2πscI(eI)22πscIeIpI2πscIpIgI2πscIpIeI2πscI(pI)2|=2bmn+nα2+mβ2<0 H({g^I},{e^I},{p^I}) = \left| {\matrix{{{{{\partial^2}\pi_{sc}^I} \over {\partial {{({g^I})}^2}}}{{{\partial^2}\pi_{sc}^I} \over {\partial {g^I}\partial {e^I}}}{{{\partial^2}\pi_{sc}^I} \over {\partial {g^I}\partial {p^I}}}} \hfill \cr {{{{\partial^2}\pi_{sc}^I} \over {\partial {e^I}\partial {g^I}}}{{{\partial^2}\pi_{sc}^I} \over {\partial {{({e^I})}^2}}}{{{\partial^2}\pi_{sc}^I} \over {\partial {e^I}\partial {p^I}}}} \hfill \cr {{{{\partial^2}\pi_{sc}^I} \over {\partial {p^I}\partial {g^I}}}{{{\partial^2}\pi_{sc}^I} \over {\partial {p^I}\partial {e^I}}}{{{\partial^2}\pi_{sc}^I} \over {\partial {{({p^I})}^2}}}} \hfill \cr}} \right| = - 2bmn + n{\alpha^2} + m{\beta^2} < 0

The Hessian matrix is negative definite. This implies there exist unique optimal strategies (gI*, eI*, pI*) and the optimal solutions determined by πscI/gI=0 \partial \pi_{sc}^I/\partial {g^I} = 0 , πscI/eI=0 \partial \pi_{sc}^I/\partial {e^I} = 0 and πscI/pI=0 \partial \pi_{sc}^I/\partial {p^I} = 0 . Thus, we obtain the following proposition.

Proposition 1

In the centralized supply chain, the optimal green quality level, market effort level and retail price are gI*=(abc)nα2bmnnα2mβ2 {g^{I*}} = {{(a - bc)n\alpha} \over {2bmn - n{\alpha^2} - m{\beta^2}}} eI*=(abc)mβ2bmnnα2mβ2 {e^{I*}} = {{(a - bc)m\beta} \over {2bmn - n{\alpha^2} - m{\beta^2}}} pI*=amn+bcmncnα2cmβ22bmnnα2mβ2 {p^{I*}} = {{amn + bcmn - cn{\alpha^2} - cm{\beta^2}} \over {2bmn - n{\alpha^2} - m{\beta^2}}}

According to Proposition 1, we can obtain the channel maximum profit at gI*, eI* and pI* and the channel maximum profit is πscI*=(abc)2mn2(2bmnnα2mβ2) \pi_{sc}^{I*} = {{{{(a - bc)}^2}mn} \over {2(2bmn - n{\alpha^2} - m{\beta^2})}}

In the following sections, the decentralized system is investigated. We will discuss the effects of the retailer’s fairness concerns and propose a RCS contract model to coordinate the supply chain.

Decentralized Supply Chain Model

In the decentralized supply chain, a manufacturer-led Stackelberg game is considered. In this mode, the manufacturer acts as the leader and the retailer acts as the follower. We first explore the market effort level and retail price of retailer’s decision and then investigate the green quality level and wholesale price of the manufacturer’s strategy.

Wholesale Price Contract Model without Fairness Concerns

In this subsection, we assume that the retailer does not involve fairness concerns. Then in the WP contract model, the expected profits of the manufacturer and the retailer are πmD=(wDc)(abpD+αgD+βeD)12m(gD)2 \pi_m^D = ({w^D} - c)(a - b{p^D} + \alpha {g^D} + \beta {e^D}) - {1 \over 2}m{({g^D})^2} πrD=(pDwD)(abpD+αgD+βeD)12n(eD)2 \pi_r^D = ({p^D} - {w^D})(a - b{p^D} + \alpha {g^D} + \beta {e^D}) - {1 \over 2}n{({e^D})^2}

Given any fixed green quality level and wholesale price, the first order derivatives of πrD \pi_r^D with respect to eD and pD are πrDeD=β(pDc)neD {{\partial \pi_r^D} \over {\partial {e^D}}} = \beta ({p^D} - c) - n{e^D} πrDpD=a2bpD+bw+αgD+βeD {{\partial \pi_r^D} \over {\partial {p^D}}} = a - 2b{p^D} + bw + \alpha {g^D} + \beta {e^D}

The Hessian matrix of πrD \pi_r^D with respect to eD and pD satisfy that 2πrD(eD)2=n<0 {{{\partial^2}\pi_r^D} \over {\partial {{({e^D})}^2}}} = - n < 0 H(eD,pD)=|2πrD(eD)22πrDeDpD2πrDpDeD2πrD(pD)2|=2bnβ2>0 H({e^D},{p^D}) = \left| {\matrix{{{{{\partial^2}\pi_r^D} \over {\partial {{({e^D})}^2}}}{{{\partial^2}\pi_r^D} \over {\partial {e^D}\partial {p^D}}}} \cr {{{{\partial^2}\pi_r^D} \over {\partial {p^D}\partial {e^D}}}{{{\partial^2}\pi_r^D} \over {\partial {{({p^D})}^2}}}} \cr}} \right| = 2bn - {\beta^2} > 0

This implies that πrD \pi_r^D is jointly concave in eD and pD. Solving πrD/eD=0 \partial \pi_r^D/\partial {e^D} = 0 and πrD/pD=0 \partial \pi_r^D/\partial {p^D} = 0 simultaneously, we get eD=(abwD+αgD)β2bnβ2 {e^D} = {{(a - b{w^D} + \alpha {g^D})\beta} \over {2bn - {\beta^2}}} pD=an+bnwD+nαgDwDβ22bnβ2 {p^D} = {{an + bn{w^D} + n\alpha {g^D} - {w^D}{\beta^2}} \over {2bn - {\beta^2}}}

Substituting Eqs. (16) and (17) into Eq. (11) and differentiating with respect to gD and wD gives πmDgD=bn(αwDcα2mgD)+mgDβ22bnβ2 {{\partial \pi_m^D} \over {\partial {g^D}}} = {{bn(\alpha {w^D} - c\alpha - 2m{g^D}) + m{g^D}{\beta^2}} \over {2bn - {\beta^2}}} πmDwD=bn(a+bc2bwD+αgD)2bnβ2 {{\partial \pi_m^D} \over {\partial {w^D}}} = {{bn(a + bc - 2b{w^D} + \alpha {g^D})} \over {2bn - {\beta^2}}}

The Hessian matrix of πmD \pi_m^D with respect to gD and wD satisfy that 2πmD(gD)2=m<0 {{{\partial^2}\pi_m^D} \over {\partial {{({g^D})}^2}}} = - m < 0 H(gD,wD)=|2πmD(gD)22πmDgDwD2πmDwDgD2πmD(wD)2|=b2n(4bmnnα22mβ2)(2bnβ2)2>0 H({g^D},{w^D}) = \left| {\matrix{{{{{\partial^2}\pi_m^D} \over {\partial {{({g^D})}^2}}}{{{\partial^2}\pi_m^D} \over {\partial {g^D}\partial {w^D}}}} \cr {{{{\partial^2}\pi_m^D} \over {\partial {w^D}\partial {g^D}}}{{{\partial^2}\pi_m^D} \over {\partial {{({w^D})}^2}}}} \cr}} \right| = {{{b^2}n(4bmn - n{\alpha^2} - 2m{\beta^2})} \over {{{(2bn - {\beta^2})}^2}}} > 0

This implies that there exist unique optimal solutions (gD*, wD*) determined by πmD/gD=0 \partial \pi_m^D/\partial {g^D} = 0 and πmD/wD=0 \partial \pi_m^D/\partial {w^D} = 0 . Then, we substitute the optimal decisions of the manufacturer into Eq. (16) and Eq. (17). In this case, we have the following result.

Proposition 2

When there is no fairness concerns involved in WP contract model, the optimal green quality level and wholesale price of the manufacturer are gD*=(abc)nα4bmnnα22mβ2 {g^{D*}} = {{(a - bc)n\alpha} \over {4bmn - n{\alpha^2} - 2m{\beta^2}}} wD*=am(2bnβ2)+bc(2bmnnα2mβ2)b(4bmnnα22mβ2) {w^{D*}} = {{am(2bn - {\beta^2}) + bc(2bmn - n{\alpha^2} - m{\beta^2})} \over {b(4bmn - n{\alpha^2} - 2m{\beta^2})}}

and the optimal market effort level and retail price of the retailer are eD*=(abc)mβ4bmnnα22mβ2 {e^{D*}} = {{(a - bc)m\beta} \over {4bmn - n{\alpha^2} - 2m{\beta^2}}} pD*=am(3bnβ2)+bc(bmnnα2mβ2)b(4bmnnα22mβ2) {p^{D*}} = {{am(3bn - {\beta^2}) + bc(bmn - n{\alpha^2} - m{\beta^2})} \over {b(4bmn - n{\alpha^2} - 2m{\beta^2})}}

Proposition 2 shows that the manufacturer’s profit can be maximized at gD* and wD*, and the retailer’s profit can be maximized at eD* and pD*. Further, the optimal profits of the manufacturer and the retailer can be characterized respectively as πmD*=(abc)2mn2(4bmnnα22mβ2) \pi_m^{D*} = {{{{(a - bc)}^2}mn} \over {2(4bmn - n{\alpha^2} - 2m{\beta^2})}} πrD*=(abc)2m2n(2bnβ2)2(4bmnnα22mβ2)2 \pi_r^{D*} = {{{{(a - bc)}^2}{m^2}n(2bn - {\beta^2})} \over {2{{(4bmn - n{\alpha^2} - 2m{\beta^2})}^2}}}

Thus, the total channel profit of the supply chain in the decentralized system is πscD*=(abc)2mn(6bmnnα23mβ2)2(4bmnnα22mβ2)2 \pi_{sc}^{D*} = {{{{(a - bc)}^2}mn(6bmn - n{\alpha^2} - 3m{\beta^2})} \over {2{{(4bmn - n{\alpha^2} - 2m{\beta^2})}^2}}}

Moreover, conducting the comparison analysis, we can obtain that gI*gD*=(abc)mnα(2bnβ2)(4bmnnα22mβ2)(2bmnnα2mβ2)>0 {g^{I*}} - {g^{D*}} = {{(a - bc)mn\alpha (2bn - {\beta^2})} \over {(4bmn - n{\alpha^2} - 2m{\beta^2})(2bmn - n{\alpha^2} - m{\beta^2})}} > 0 eI*eD*=(abc)m2β(2bnβ2)(4bmnnα22mβ2)(2bmnnα2mβ2)>0 {e^{I*}} - {e^{D*}} = {{(a - bc){m^2}\beta (2bn - {\beta^2})} \over {(4bmn - n{\alpha^2} - 2m{\beta^2})(2bmn - n{\alpha^2} - m{\beta^2})}} > 0 πscI*πscD*=(abc)2m3n(2bnβ2)22(4bmnnα22mβ2)2(2bmnnα2mβ2)>0 \pi_{sc}^{I*} - \pi_{sc}^{D*} = {{{{(a - bc)}^2}{m^3}n{{(2bn - {\beta^2})}^2}} \over {2{{(4bmn - n{\alpha^2} - 2m{\beta^2})}^2}(2bmn - n{\alpha^2} - m{\beta^2})}} > 0

In summary, we get the following Corollary.

Corollary 3

When the retailer does not involve fairness concerns, we have gD* < gI*, eD* < eI* and πscD*<πscI* \pi_{sc}^{D*} < \pi_{sc}^{I*} .

Corollary 3 shows that all the optimal green quality level, market effort level and total profit of the supply chain in the decentralized supply chain with WP contract are less than that in the centralized system due to double marginalization. This implies that it is necessary to propose more effective contracts to mitigate the adverse impact of double marginalization, so as to improve the supply chain’s economic and environmental performances.

Wholesale Price Contract Model with Fairness Concerns

In this subsection, we discuss the scenario of a fair-minded retailer in the decentralized system with WP contract. Usually, we introduce the profit difference into the utility function to characterize the fairness concerns of decision-makers, and use the coefficient of fairness concerns to depict the impact of the fairness concerns caused by the profit difference between the manufacturer and the retailer. Following the literature [12], we assume that the equitable reference point of the retailer is the manufacturer’s profit. Thus, the retailer’s utility function with fairness concerns is UrD=πrDλ˜(πmDπrD) U_r^D = \pi_r^D - \tilde \lambda (\pi_m^D - \pi_r^D) where λ˜(0,) \tilde \lambda \in (0,\infty) is the coefficient of retailer’s fairness concerns. For simplicity, we let λ=λ˜/(1+λ˜) \lambda = \tilde \lambda /(1 + \tilde \lambda) , Eq. (35) can be rewritten as UrλD=πrDλπmD U_{r\lambda}^D = \pi_r^D - \lambda \pi_m^D , where λ satisfies 0 < λ < 1. Specifically, λ = 0 corresponds to the completely rational scenario, namely, the retailer is fairness-neutral. We can now see that the retailer’s utility will be increased when its profit is greater than the profit of the manufacturer, otherwise, the retailer’s utility will be reduced.

Thus, the utility function of the retailer, denoted as UrD U_r^D , is given as UrD=[pλDwλD(1+λ)+λc](abpλD+αgλD+βeλD)+12λm(gλD)212n(eλD)2 U_r^D = \left[ {p_\lambda^D - w_\lambda^D(1 + \lambda) + \lambda c} \right](a - bp_\lambda^D + \alpha g_\lambda^D + \beta e_\lambda^D) + {1 \over 2}\lambda m{(g_\lambda^D)^2} - {1 \over 2}n{(e_\lambda^D)^2}

Given any fixed green quality level and wholesale price, now we need to derive the retailer’s optimal market effort level and retail price by maximizing Eq. (36). Then, substituting the retailer’s optimal decisions into Eq. (13), we can solve the optimal green quality level and wholesale price of the manufacturer by profit maximizing. Thus, we get Proposition 3.

Proposition 4

In WP contract model with a fair-mind retailer, the optimal green quality level and wholesale price satisfy that gλD*=(abc)nα4bmn(1+λ)nα22mβ2(1+λ) g_\lambda^{D*} = {{(a - bc)n\alpha} \over {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)}} wλD*=am(2bnβ2)+bc[2bmn(1+2λ)nα2mβ2(1+2λ)]b[4bmn(1+λ)nα22mβ2(1+λ)] w_\lambda^{D*} = {{am(2bn - {\beta^2}) + bc\left[ {2bmn(1 + 2\lambda) - n{\alpha^2} - m{\beta^2}(1 + 2\lambda)} \right]} \over {b\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}} and the optimal market effort level and retail price of the retailer are eλD*=(abc)mβ(1+λ)4bmn(1+λ)nα22mβ2(1+λ) e_\lambda^{D*} = {{(a - bc)m\beta (1 + \lambda)} \over {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)}} pλD*=am(3bnβ2)(1+λ)+bc[bmn(1+λ)nα2mβ2(1+λ)]b[4bmn(1+λ)nα22mβ2(1+λ)] p_\lambda^{D*} = {{am(3bn - {\beta^2})(1 + \lambda) + bc\left[ {bmn(1 + \lambda) - n{\alpha^2} - m{\beta^2}(1 + \lambda)} \right]} \over {b\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}}

Proposition 4 shows that the manufacturer’s profit is maximized at grD* g_r^{D*} and wrD* w_r^{D*} , and the retailer’s utility is maximized at erD* e_r^{D*} and prD* p_r^{D*} . Base on Proposition 4, the retailer’s optimal utility is UrλD*=(abc)2mn[2bmn(1+λ)2+λnα2mβ2(1+λ)2]2[4bmn(1+λ)nα22mβ2(1+λ)]2 U_{r\lambda}^{D*} = {{{{(a - bc)}^2}mn\left[ {2bmn{{(1 + \lambda)}^2} + \lambda n{\alpha^2} - m{\beta^2}{{(1 + \lambda)}^2}} \right]} \over {2{{\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}^2}}}

Further, we can get the optimal profits of the manufacturer and retailer, which can be characterized respectively as πmλD*=(abc)2mn2[4bmn(1+λ)nα22mβ2(1+λ)] \pi_{m\lambda}^{D*} = {{{{(a - bc)}^2}mn} \over {2\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}} πrλD*=(abc)2m2n(2bnβ2)(1+4λ+3λ2)2[4bmn(1+λ)nα22mβ2(1+λ)]2 \pi_{r\lambda}^{D*} = {{{{(a - bc)}^2}{m^2}n(2bn - {\beta^2})(1 + 4\lambda + 3{\lambda^2})} \over {2{{\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}^2}}}

Thus, the total channel profit of the supply chain in the decentralized system is πscλD*=(abc)2mn[6bmn(1+λ)2nα23mβ2(1+λ)2]2[4bmn(1+λ)nα22mβ2(1+λ)]2 \pi_{sc\lambda}^{D*} = {{{{(a - bc)}^2}mn\left[ {6bmn{{(1 + \lambda)}^2} - n{\alpha^2} - 3m{\beta^2}{{(1 + \lambda)}^2}} \right]} \over {2{{\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}^2}}}

Let λ = 0, all the optimal strategies and profits in fair-minded scenario are consistent with that in the fair-neutral scenario. It implies that Proposition 2 is a special case of Proposition 4. This also indicates that the formulations in characterizing the fairness concerns are effective.

Taking the first-order derivative of gλD* g_\lambda^{D*} with respect to λ, we have gλD*λ=2(abc)mnα(2bnβ2)[nα24bmn(1+λ)+2mβ2(1+λ)]2<0 {{\partial g_\lambda^{D*}} \over {\partial \lambda}} = - {{2(a - bc)mn\alpha (2bn - {\beta^2})} \over {{{\left[ {n{\alpha^2} - 4bmn(1 + \lambda) + 2m{\beta^2}(1 + \lambda)} \right]}^2}}} < 0

Similarly, we have wλD*λ=2(abc)m2(2bnβ2)2b[nα24bmn(1+λ)+2mβ2(1+λ)]2<0 {{\partial w_\lambda^{D*}} \over {\partial \lambda}} = - {{2(a - bc){m^2}{{(2bn - {\beta^2})}^2}} \over {b{{\left[ {n{\alpha^2} - 4bmn(1 + \lambda) + 2m{\beta^2}(1 + \lambda)} \right]}^2}}} < 0 eλD*λ=(abc)mnα2β[nα24bmn(1+λ)+2mβ2(1+λ)]2<0 {{\partial e_\lambda^{D*}} \over {\partial \lambda}} = - {{(a - bc)mn{\alpha^2}\beta} \over {{{\left[ {n{\alpha^2} - 4bmn(1 + \lambda) + 2m{\beta^2}(1 + \lambda)} \right]}^2}}} < 0 pλD*λ=(abc)mnα2(3bnβ2)b[nα24bmn(1+λ)+2mβ2(1+λ)]2<0 {{\partial p_\lambda^{D*}} \over {\partial \lambda}} = - {{(a - bc)mn{\alpha^2}(3bn - {\beta^2})} \over {b{{\left[ {n{\alpha^2} - 4bmn(1 + \lambda) + 2m{\beta^2}(1 + \lambda)} \right]}^2}}} < 0

In summary, we get Corollary 5.

Corollary 5

When the retailer involves fairness concerns, in the decentralized supply chain with WP contract, we have gλD*/λ<0 \partial g_\lambda^{D*}/\partial \lambda < 0 , wλD*/λ<0 \partial w_\lambda^{D*}/\partial \lambda < 0 , eλD*/λ<0 \partial e_\lambda^{D*}/\partial \lambda < 0 and pλD*/λ<0 \partial p_\lambda^{D*}/\partial \lambda < 0 .

Corollary 5 shows that with the fairness concerns coefficient increase, the optimal strategies, including green quality level, wholesale price, market effort level and retail price, decrease. All of the optimal solutions in fair-minded case are lower than that in the fair-neutral case. This reveals that the retailer’s fairness behavior will reduce not only its own investment in marketing effort but also the manufacturer’s investment in green quality. As a result, the impact of the retailer’s fairness behavior is expand and has a negative effect on the environmental performance of the supply chain.

Taking the first-order derivative of πmλD* \pi_{m\lambda}^{D*} with respect to λ, we have πmλD*λ=(abc)2m2n(2bnβ2)[nα24bmn(1+λ)+2mβ2(1+λ)]2<0 {{\partial \pi_{m\lambda}^{D*}} \over {\partial \lambda}} = - {{{{(a - bc)}^2}{m^2}n(2bn - {\beta^2})} \over {{{\left[ {n{\alpha^2} - 4bmn(1 + \lambda) + 2m{\beta^2}(1 + \lambda)} \right]}^2}}} < 0

Similarly, we have πrλD*λ=(abc)2m2n(2bnβ2)[4bmn(1+λ)2mβ2(1+λ)nα2(2+3λ)][4bmn(1+λ)nα22mβ2(1+λ)]3 {{\partial \pi_{r\lambda}^{D*}} \over {\partial \lambda}} = - {{{{(a - bc)}^2}{m^2}n(2bn - {\beta^2})\left[ {4bmn(1 + \lambda) - 2m{\beta^2}(1 + \lambda) - n{\alpha^2}(2 + 3\lambda)} \right]} \over {{{\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}^3}}} UrλD*λ=(abc)2mn2α2(8bmnλ+nα24mβ2λ)2[4bmn(1+λ)nα22mβ2(1+λ)]3<0 {{\partial U_{r\lambda}^{D*}} \over {\partial \lambda}} = - {{{{(a - bc)}^2}m{n^2}{\alpha^2}(8bmn\lambda + n{\alpha^2} - 4m{\beta^2}\lambda)} \over {2{{\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}^3}}} < 0 πscλD*λ=(abc)2m2n2α2(2bnβ2)(1+3λ)[4bmn(1+λ)nα22mβ2(1+λ)]3<0 {{\partial \pi_{sc\lambda}^{D*}} \over {\partial \lambda}} = - {{{{(a - bc)}^2}{m^2}{n^2}{\alpha^2}(2bn - {\beta^2})(1 + 3\lambda)} \over {{{\left[ {4bmn(1 + \lambda) - n{\alpha^2} - 2m{\beta^2}(1 + \lambda)} \right]}^3}}} < 0

In summary, we obtain the following corollary.

Corollary 6

When the retailer involves fairness concerns, in the decentralized supply chain with WP contract, we have (i) πmλD*/λ<0 \partial \pi_{m\lambda}^{D*}/\partial \lambda < 0 , UrD*/λ<0 \partial U_r^{D*}/\partial \lambda < 0 , and πscλD*/λ<0 \partial \pi_{sc\lambda}^{D*}/\partial \lambda < 0 ; (ii) if4bmn(1 + λ) − na2(2 + 3λ) − 2mb2(1 + λ) > 0, then πrλD*/λ<0 \partial \pi_{r\lambda}^{D*}/\partial \lambda < 0 , otherwise πrλD*/λ>0 \partial \pi_{r\lambda}^{D*}/\partial \lambda > 0 .

Corollary 6 shows the impact of the retailer’s fairness behavior on the profits of the manufacturer, retailer and supply chain, as well as the impact of the retailer’s fairness behavior on its utility. It indicates that the manufacturer’s profit, supply chain’s profit and retailer’s utility are decreasing in the fairness concerns coefficient. Namely, the retailer’s fairness behavior always makes the manufacturer and total supply chain suffer in terms of profits. In addition, Corollary 6 reveals that the retailer’s optimal profit may be increasing or decreasing in the fairness concern coefficient. That is, the retailer can benefit from the fairness behavior as long as the retailer keeps the fairness concern at a proper level. However, the retailer’s utility is always decreased.

Revenue-Cost-Sharing Contract Model with Fairness Concerns

As we have proved, WP contract can not make the channel’s profit get the decentralized system. Then we introduce a RCS contract to improve the supply chain’s performance. Under the RCS contract, the retailer earns the revenue of per unit product in (1 − ϕ) portion and the manufacturer earns the other ϕ portion. In the meantime, the retailer share the cost the manufacturer incurs in greening investment, and the manufacturer share the cost the retailer incurs in marketing investment. Namely, the retailer pays a fraction (1 − γ) of greening investment cost to the manufacturer and assumes the same portion (1 − γ) of marketing investment, the manufacturer assumes the remaining γ fraction of greening investment cost and pays the same portion γ of marketing investment to the retailer.

Under the RCS contract, the expected profits of the manufacturer and the retailer are πmλR=(ϕpλR+wc)(abpλR+αgλR+βeλR)12mγ(gλR)212nγ(eλR)2 \pi_{m\lambda}^R = (\phi p_\lambda^R + w - c)(a - bp_\lambda^R + \alpha g_\lambda^R + \beta e_\lambda^R) - {1 \over 2}m\gamma {(g_\lambda^R)^2} - {1 \over 2}n\gamma {(e_\lambda^R)^2} πrλR=[(1ϕ)pλRw](abpλR+αgλR+βeλR)12m(1γ)(gλR)212n(1γ)(eλR)2 \pi_{r\lambda}^R = \left[ {(1 - \phi)p_\lambda^R - w} \right](a - bp_\lambda^R + \alpha g_\lambda^R + \beta e_\lambda^R) - {1 \over 2}m(1 - \gamma){(g_\lambda^R)^2} - {1 \over 2}n(1 - \gamma){(e_\lambda^R)^2}

When the retailer involves fairness concerns, given any fixed gλR g_\lambda^R , the utility of the retailer is UrR=[(1ϕ)pλRλ(ϕpλR+wc)](abpλR+αgλR+βeλR)12m(1γγλ)(gλR)212n(1γγλ)(eλR)2 \matrix{{U_r^R = \left[ {(1 - \phi)p_\lambda^R - \lambda (\phi p_\lambda^R + w - c)} \right](a - bp_\lambda^R + \alpha g_\lambda^R + \beta e_\lambda^R)} \hfill \cr {- {1 \over 2}m(1 - \gamma - \gamma \lambda){{(g_\lambda^R)}^2} - {1 \over 2}n(1 - \gamma - \gamma \lambda){{(e_\lambda^R)}^2}} \hfill \cr}

Given any fixed green quality level gλR g_\lambda^R , we get the fair-minded retailer’s optimal market effort level and retail price by maximizing Eq. (51). Then, we substitute the optimal decisions of the fair-minded retailer into Eq. (49) and derive the optimal green quality level by profit maximizing. Thus, we have the following proposition.

Proposition 7

In the RCS contract model with fair-minded retailer, the optimal green quality level of the manufacturer is gλR*=BC g_\lambda^{R*} = {B \over C} where B=bcnαβ2[1ϕ+γ(λ2ϕ+ϕ+2λϕ2λ1)]+2abn2αϕ(γλ+γ1)2 anαβ2γ(λϕ+ϕ1)2bnwαβ2[1+γ(1+λ)(λϕ+ϕ2)]2b2n2α(cw)(γλ+γ1)2 \matrix{{B = bcn\alpha {\beta^2}\left[ {1 - \phi + \gamma ({\lambda^2}\phi + \phi + 2\lambda \phi - 2\lambda - 1)} \right] + 2ab{n^2}\alpha \phi {{(\gamma \lambda + \gamma - 1)}^2}} \hfill \cr {- an\alpha {\beta^2}\gamma {{(\lambda \phi + \phi - 1)}^2} - bnw\alpha {\beta^2}\left[ {1 + \gamma (1 + \lambda)(\lambda \phi + \phi - 2)} \right] - 2{b^2}{n^2}\alpha (c - w){{(\gamma \lambda + \gamma - 1)}^2}} \hfill \cr} C=4b2mn2γ(γλ+γ1)2β2(nα2+mβ2)γ(λϕ+ϕ1)2 2bn2α2ϕ(γλ+γ1)24bmnβ2γ(γλ+γ1)(λϕ+ϕ1) \matrix{{C = 4{b^2}m{n^2}\gamma {{(\gamma \lambda + \gamma - 1)}^2} - {\beta^2}(n{\alpha^2} + m{\beta^2})\gamma {{(\lambda \phi + \phi - 1)}^2}} \hfill \cr {- 2b{n^2}{\alpha^2}\phi {{(\gamma \lambda + \gamma - 1)}^2} - 4bmn{\beta^2}\gamma (\gamma \lambda + \gamma - 1)(\lambda \phi + \phi - 1)} \hfill \cr} and the optimal market effort level and retail price of the retailer are eλR*=β[b(wcλ+wλ)+a(λϕ+ϕ1)+gλR*α(λϕ+ϕ1)]2bn(γλ+γ1)β2(λϕ+ϕ1) e_\lambda^{R*} = {{\beta \left[ {b(w - c\lambda + w\lambda) + a(\lambda \phi + \phi - 1) + g_\lambda^{R*}\alpha (\lambda \phi + \phi - 1)} \right]} \over {2bn(\gamma \lambda + \gamma - 1) - {\beta^2}(\lambda \phi + \phi - 1)}} pλR*=β2(wcλ+wλ)(λϕ+ϕ1)n(1+γ+γλ)[b(wcλ+wλ)(a+gλR*α)(λϕ+ϕ1)](λϕ+ϕ1)[2bn(γλ+γ1)β2(λϕ+ϕ1)] p_\lambda^{R*} = {{{\beta^2}\left({w - c\lambda + w\lambda} \right)\left({\lambda \phi + \phi - 1} \right) - n\left({- 1 + \gamma + \gamma \lambda} \right)\left[ {b\left({w - c\lambda + w\lambda} \right) - (a + g_\lambda^{R*}\alpha)\left({\lambda \phi + \phi - 1} \right)} \right]} \over {\left({\lambda \phi + \phi - 1} \right)\left[ {2bn\left({\gamma \lambda + \gamma - 1} \right) - {\beta^2}\left({\lambda \phi + \phi - 1} \right)} \right]}}

Proposition 7 shows that, under the RCS contract, the manufacturer’s profit is maximized at gλR* g_\lambda^{R*} , and the retailer’s utility is maximized at eλR* e_\lambda^{R*} and pλR* p_\lambda^{R*} . According to the classical literature [30], let gλR*=gI* g_\lambda^{R*} = {g^{I*}} , eλR*=eI* e_\lambda^{R*} = {e^{I*}} and pλR*=pI* p_\lambda^{R*} = {p^{I*}} , we get Proposition 8.

Proposition 8

In the RCS contract model with fair-mind retailer, the supply chain can be coordinated by setting ϕ = γ = w/c.

Proposition 8 implies that the supply chain’s system-wide optimal performances are achieved under the RCS contract. Base on Proposition 7 and Proposition 8, the optimal profits of the manufacturer and retailer are πmλR*=(abc)2mn(cw)2c(2bmnnα2mβ2) \pi_{m\lambda}^{R*} = {{{{(a - bc)}^2}mn(c - w)} \over {2c(2bmn - n{\alpha^2} - m{\beta^2})}} πrλR*=(abc)2mnw2c(2bmnnα2mβ2) \pi_{r\lambda}^{R*} = {{{{(a - bc)}^2}mnw} \over {2c(2bmn - n{\alpha^2} - m{\beta^2})}}

Obviously, we have πmλR*=(1w/c)πscI* \pi_{m\lambda}^{R*} = (1 - w/c)\pi_{sc}^{I*} and πrλR*=(w/c)πscI* \pi_{r\lambda}^{R*} = (w/c)\pi_{sc}^{I*} . Under coordinated RCS contract, the manufacturer’s profit is decreasing in the wholesale price while the retailer’s profit increase. That is, the RCS contract can allocate the channel profit arbitrarily between the manufacturer and the retailer. It also implies that both the manufacturer and the retailer are willing to accept the RCS contract so long as they jointly confirm an appropriate wholesale price.

Numerical Analysis

In this section, using several numerical investigations, we illustrate how the retailer’s fairness behavior affects the optimal decisions and profits, as well as how to share profit to achieve a win-win outcome under the RCS contract. We set the parameters as a = 100, b = 1, c = 10, α = 2, β = 1, m = 3 and n = 2.

We see from Figure 1 that all the optimal green quality level, wholesale price, market effort level and retail price are decreasing in the retailer’s fairness concerns coefficient. That is, the fairness behavior makes the retailer exert less marketing effort, and the manufacturer accordingly reduces the investment in green quality of products. This reveals that the fairness behavior has a negative effect on the supply chain performance, however, the consumer could benefit from the retailer’s fairness behavior due to the retailer would charge less when fairness concerns coefficient increase.

Fig. 1

Impact of the fairness concerns coefficient on the optimal decisions.

In the decentralized system with the WP contract, Figure 2 shows the effect of the fairness concerns coefficient on the optimal profits of the manufacturer, retailer and supply chain, as well as the effect of the fairness concerns coefficient on the retailer’ optimal utility. The optimal profit of the manufacturer is always decreasing in the fairness concerns coefficient, whereas the retailer’s optimal profit first increases and then decreases with the fairness concerns coefficient increase. In this numerical analysis, when 0 < λ < 1/3, the retailer’s optimal profit increases, while the retailer’s optimal profit decreases when λ ≥ 1/3. This analysis indicates that the retailer could benefit from the fairness behavior under certain conditions. In addition, when 0 < λ < 1/3, the manufacturer is more sensitive to the fairness concerns coefficient than the retailer, namely, the increase in retailers’ profit is less than the decrease in manufacturers’ profit. As a result, the supply chain’s optimal profit is always decreasing in the fairness concerns coefficient. Moreover, the retailer’s utility is always decreasing in the fairness concerns coefficient although the retailer’s optimal profit may be increasing in the fairness concerns coefficient.

Fig. 2

Impact of the fairness concern coefficient on the optimal profits and utility.

In the premise of supply chain coordination with the RCS contract, Figure 3 illustrates each party’s share on the channel profit of the supply chain. As we have proved previously, the manufacturer’s profit is decreasing in the wholesale price while the profit of the retailer is increasing in the wholesale price. We let λ = 0.1, and when w = 0.92, the retailer just earns as much as that it under the WP contract. When w = 9.15, the manufacturer is just as well off as it is under the WP contract. Thus in the region w ∈ (0.92,9.15), both the manufacturer and the retailer obtain a win-win outcome, and are willing to accept the RCS contract.

Fig. 3

Profit sharing between the manufacturer and the retailer under coordination with the RCS contract.

Conclusions

In this paper, a single period green supply chain consisting of a manufacturer and a retailer is studied. In this system, the manufacturer produces green products and sells them to end consumers through the retailer. Market demand depends not only on the retail price but also on the manufacturer’s green quality level and the retailer’s marketing effort level. The manufacturer is perfectly rational and aims to maximize its profit, while the retailer aims to maximize the utility since it involves fairness concerns. We mainly focus on the optimal decisions of each member and supply chain coordination problems.

First, we use the centralized case to establish a performance benchmark. Then, we develop decentralized supply chain models under the scenarios whether the retailer involves fairness concerns or not. We find that both the supply chain’s economic and environmental performances under WP contract are less than that under the centralized system. All the optimal green quality level, wholesale price, marketing effort level and retail price are decreasing in the retailer’s fairness concerns coefficient. Accordingly, the profits of both the manufacturer and the total supply chain are decreasing in the retailer’s fairness concerns coefficient. However, the retailer’s profit first increases and then decreases with the increase of the fairness concerns coefficient. Last, we introduce a RCS contract to coordinate supply chain. Under supply chain coordination, the manufacturer’s profit is decreasing in the wholesale price while the profit of the retailer is increasing in the wholesale price. It is proved that a win-win outcome is reachable by the RCS contract.

As a natural extension of our work, future research could be done by considering more complex supply chains with multiple manufacturers/retailers competing for more consumers with respect to green quality and marketing effort.

Fig. 1

Impact of the fairness concerns coefficient on the optimal decisions.
Impact of the fairness concerns coefficient on the optimal decisions.

Fig. 2

Impact of the fairness concern coefficient on the optimal profits and utility.
Impact of the fairness concern coefficient on the optimal profits and utility.

Fig. 3

Profit sharing between the manufacturer and the retailer under coordination with the RCS contract.
Profit sharing between the manufacturer and the retailer under coordination with the RCS contract.

Notations.

Notation Implication
c production cost per unit of product
w wholesale price per unit of product
p retail price per unit of product
a primary intrinsic demand
g green quality level
e marketing effort level
b consumer’s sensitivity parameter in retail price
α consumer’s sensitivity parameter in green quality level
β consumer’s sensitivity parameter in marketing effort level
m cost coefficient of greening investment
n cost coefficient of marketing investment
λ fairness concerns coefficient of the retailer
ϕ revenue-sharing coefficient
γ cost-sharing coefficient
π profit function
U utility function

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