1. Introduction
With the rapid development of the global economy, there is an increasing awareness of the problems of global warming, environmental deterioration and resource depletion [
1,
2]. Governments have actively worked to develop a green economy and to improve the eco-environment [
3]. According to a statement released after the 2020 annual Central Economic Work Conference, China will formulate an action plan to tackle increasing carbon dioxide emissions before 2030. Environmental crises and the increasing pressure from governments are responsible for the appearance of various green approaches to be considered in supply chain management [
4].
An increasing number of enterprises are staring to practice green supply chain management, for example, the utilization of electric cars made by the Japanese car-maker Nissan and fluorine-free air conditioners produced by the Chinese major appliance manufacturer Gree Electric [
5,
6], As early as 2015, Wal-Mart required all of its packaging materials to be recyclable or to meet environmental standards. As of 2020, Wal-Mart has consecutively topped the list of the global 500 for seven years.
A large number of enterprises, such as Huawei, Haier, Basic Motor, Shanghai Zhenhua Heavy, Joyoung, and Tianneng Battery in China, have been practicing green supply chain management, and they have already achieved good results [
7]. Therefore, the implementation of green supply chain management is an irreversible trend that governments, manufacturers, retailers, and consumers can benefit from, and not only can it improve the environment but also it can help enterprises to obtain a competitive advantage [
8].
In different supply chain sectors, logistics and transportation are recognized as among the major contributors to environmental threats, such as air pollution, global warming and resource depletion [
4]. The logistics industry plays a comprehensive role in the service industry [
9]. With continuous improvement, logistics service provision has attained supply chain characteristics. The logistics service supply chain (
LSSC) is a special type of supply chain within the service supply chain in which logistics service integrators (
LSIs) serve as the core players in general.
Flexible services are provided by
LSSCs to ensure effective logistics operations [
10]. Modern logistics services operations play a significant role in reducing the environmental burden of a supply chain [
11]. This requires all production, distribution, and other associated enterprises in the
LSSC to cooperate in order to minimize the adverse impact on the environment. For example, the
LSI and functional logistics service suppliers (
LSPs) fund the development of green storage facilities and technologies and buy new green energy vehicles, thus, providing greater energy conservation and environmental protection of green logistics services in transportation and storage [
12].
However, the logistics service market is volatile and uncertain. As a more innovative service, due to the lack of historical data, green logistics services have a large demand fluctuation. Therefore, decision-makers only can have a vague understanding of the market demand environment of such emerging services. Furthermore, the risk preference of logistics enterprises leads to more outstanding uncertainties in the green management of the LSSC. Therefore, it is vitally important to solve how enterprises can provide cost-effective green services to consumers.
Fuzzy theory is an important tool to solve the uncertain phenomenon in management decision making and game problems. Li [
13] established a new method for decision making and game research via the application of intuitionistic fuzzy sets. Yu et al. [
14] introduced a model and method for an interval cooperative game in economic management with preference deviation. Much research has been limited to the case study in green
LSSC, and the different combinations of risk preferences among a
LSSC participants have generally been ignored.
Therefore, it is of great practical significance to use fuzzy demand theory and behavioral game theory to study the green operation efficiency of an LSSC. The demand function is a linear continuous function in this paper, and thus the game model can be solved by the method of ranking fuzzy numbers in order to obtain the optimal expected value. However, rough sets or neutrosophic sets are primarily used to solve the uncertainty and discontinuous information problems. Consequently, we cannot use rough sets or neutrosophic sets in this model.
With these issues in mind, this research used game theory to investigate the following questions:
(1) How do risk preferences of logistics enterprises affect the sustainable decision of the LSSC?
(2) What is the impact of the risk preferences on the demand function and the sustainability indicators (greening level and greening innovation cost)?
(3) Given various combination of participants’ risk preferences, what are the profits and equilibrium variables of the LSSC participants?
To answer the above question and address these emerging concerns, in this paper, we explore decision making in a two-stage LSSC under fuzzy environments, with consideration of the influence of environment and risk preferences, in which the LSI is the leader and the LSP is the follower. There are different risk preference behaviors of LSSC participants that can be proposed by the fuzzy expected value model and the chance-constrained programming model.
Then, we present seven theoretical game models with different risk preferences and obtain their optimal solutions by solving the maximum profits function of the participants in the LSSC under various scenarios. In short, given the whole LSSC perspective, this paper explore the effects of green low-carbon activities on logistics, and comprehensively examines the impact of the combination of participants’ risk preferences.
Our goal is to characterize the impact of risk preferences on the optimal decision making of the LSSC under fuzzy environments, with consideration of the environment. The main novelty of this article is the investigation of how the participants’ risk preference affects the greening level, price, and profits of the LSSC. Indeed, the environment and risk preference behavior have rarely been considered in studies related to LSSC decision making.
In addition, this paper simultaneously discusses seven kinds of decision models to comprehensively analyze the combinations of risk preferences. We note that total involvement and cooperation among participants are vital factors for the improvement in green management in the LSSC, and risk preference plays a key role in how LSSC participants make decisions under fuzzy environments. Additionally, a dominant position in the LSSC plays a crucial role in generating profit.
The structure of this paper is as follows:
Section 2 describes the background literature regarding the
LSSC and the role of behavioral factors in supply chain decision making. In
Section 3, descriptions of the problem and assumptions for the models are outlined and discussed.
Section 4 investigates the seven game models with different risk preferences under three scenarios in the
LSSC.
Section 5 presents the numerical analysis.
Section 6 summarizes the main conclusions and discusses the discovered management insights. The limitations and future work are shown in
Section 7.
4. The Model Building
In this section, we assumed that the
LSI and
LSP present a Stackelberg game in the
LSSC. The
LSI is the leader, and it determines the profit margin of the green logistics service by using the respond function of the
LSP. Then, the
LSP acts as the follower, and it decides the greening level and outsourcing price of the logistics service. In similar studies [
40,
41], different risk preference behaviors of
LSSC members were proposed by the fuzzy expected value model and the chance-constrained programming model. The decision making process of the
LSP and
LSI was simulated with the following three scenarios, as shown in
Figure 2.
Scenario 1: A game between the risk-neutral LSI and LSP with different risk preferences. In this case, there are two-echelon LSSC models composed of a risk-neutral LSI and a risk averse or risk appetite LSP, namely, a pessimistic or optimistic LSP under a fuzzy decision environment, indexed by the subscripts NP and NO, respectively.
Scenarios 2: A game between the LSI with different risk preferences and a risk-neutral LSP. In this case, there are LSSC models composed of a risk averse or risk appetite LSI and a risk-neutral LSP under a fuzzy decision environment, indexed by the subscripts PN and ON, respectively.
Scenarios 3: A game between the LSI and LSP with the same risk preferences. In this case, both the LSI and LSP with risk-neutral, risk-averse, or risk appetite attitudes are explored in the LSSC models, indexed by the subscripts NN, PP, and OO, respectively.
For the different scenarios, we built different models. The optimal decisions of the LSP and the LSI were first investigated; the corresponding optimal outsourcing price and the optimal price of a green logistics service could then be estimated; and finally, the optimal greening level was determined. Taking all of these results into consideration, a comparison was conducted among the three scenarios.
4.1. A Risk-Neutral LSI and an LSP with Different Risk Preferencesl
In this scenario, there were two LSSC models composed of a risk-neutral LSI acting as the leader and a risk averse or risk appetite LSP acting as the follower under a fuzzy decision environment, and these can be called the pessimistic LSP decision model and the optimistic LSP decision model, respectively.
The risk-neutral
LSI determines the profit margin of the green logistics service by using the respond function of the different risk preferences
LSP. After this, the
LSP decides the greening level and outsourcing price of the green logistics service. Based on the fuzzy chance-constrained programming model proposed by Liu et al. [
40], the benefits of decision-makers can be maximized at a certain confidence level. Then, we can obtain the minimax and maximax chance-constrained programming for the
LSSC.
4.1.1. The Pessimistic LSP Decision Model
In this section, the fuzzy
LSSC used a risk-neutral
LSI as the leader and a risk-averse pessimistic
LSP as the follower, indexed by the subscript
NP. The risk-neutral
LSI determines the profit margin
(m), and the risk-averse
LSP decides the greening level (
) and outsourcing price
(w) to maximize their profit. Hence, we can obtain the minimax chance-constrained programming for the
LSSC.
where
is a predetermined confidence level for the profit of the
LSP and
LSI. For each fixed feasible solution
,
is the minimum value that the
LSP’s profit function
obtains with the least possible
, and
is the expected profit of the risk-neutral
LSI. We formulated the following minimax chance-constrained programming model in which the risk-neutral
LSI and the risk-averse
LSP attempt to maximize their optimal expected and
-pessimistic profit by selecting the best
and
strategies, respectively [
40,
41].
It is clear that model (5) can be recast as model (6):
Theorem 1. Let , be the expected profit of the risk-neutral LSI and α-pessimistic value of the risk-averse LSP’s profit, respectively. The profit margin textitm chosen by the LSI is given. If , and , then the optimal solutions (, , , ) of the fuzzy LSSC are: Proof. According to Equations (2) and (3), we can obtain the expected profit of the risk-neutral
LSI and the
-pessimistic value of the risk-averse
LSP’s profit, respectively.
From Equation (
10), the first-order derivatives of
with respect to
w and
can be obtained:
Therefore, the Hesse matrix of the
with respect to
w and
is
. In fact, the Hesse matrix of the
is negative definite, as
,
and
,
,
are positive fuzzy variables. Consequently,
is jointly concave in
and
. Therefore, we can obtain the optimal response functions
and
of
LSP by solving
and
, which provides (15) and (16).
Substituting
and
in Equations (15) and (16) into Equation (
3), we can obtain:
Thus, the first and second-order derivatives of
with respect to
m can be obtained:
is a concave function in m, as , , , and all of the fuzzy variables are positive. The optimal margin profit of the risk-neutral LSI can be attained by solving , which are shown in (7).
Then, substituting into Equations (15) and (16), we can obtain the optimal and , which are shown in (8) and (9) for the LSCC under the NP scenario. Combining Equations (7) and (9) into easily yields the optimal price of the LSI.
Thus, the proof of Theorem 1 is complete. □
4.1.2. The Optimistic LSP Decision Model
In this section, a risk-neutral
LSI acts as the leader, and an optimistic risk appetite
LSP acts as the follower under a fuzzy decision environment, indexed by the subscript
NO. The risk-neutral
LSI determines the profit margin (
m), and the optimistic
LSP decides the greening level
and outsourcing price (
w) to maximize their profit. The decision making model is as follows:
where
is a predetermined confidence level for the profit of the
LSP and
LSI. For each given feasible solution
,
is the maximum value that the optimistic
LSP’s profit function
obtains with least possible
, and
is the expected profit of the risk-neutral
LSI. We formulated the following maximax chance-constrained programming model in which a risk-neutral
LSI and a risk appetite
LSP atempt to maximize their optimal expected and
-optimistic profit by selecting the best
m and
strategies, respectively.
It is clear that model (20) can be reformulated as model (21):
Theorem 2. Let and be the expected profit of the risk-neutral LSI and the α-optimistic value of the risk appetite LSP’s profit, respectively. The profit margin m chosen by LSI is given. If , and , then the optimal solutions of the fuzzy LSSC are: Proof. We can obtain the
-optimistic value of the risk appetite
LSP’s profit by:
From Equation (
26), the first-order derivatives of
with respect to
and
can be obtained. Then, similar to the Theorem 1
is jointly concave in
and
. Therefore, we can obtain the optimal response functions
and
of the risk appetite
LSP by solving
and
, which provides (27) and (28).
Then, substituting
and
into Equation (
3), we can obtain the expected profit of the risk-neutral
LSI.
Thus, the first and second order derivatives of with respect to m can be obtained, Similar to the Theorem 1, is a concave function in m, as , , , and all of the fuzzy variables are positive. The optimal margin profit of the risk-neutral LSI can be attained by solving , which is shown in (22).
Then, substituting into Equations (27) and (28), we can obtain the optimal and which are shown in (23) and (24). Combining Equations (22) and (24) into easily yields the optimal price of the LSI.
Thus, the proof of Theorem 2 is complete. □
4.2. An LSI with Different Risk Preference and a Risk-Neutral LSP
This section includes two LSSC models composed of a risk appetite or risk-averse LSI acting as the leader and a risk-neutral LSP acting as the follower under a fuzzy decision environment, called the pessimistic LSI decision model, respectively. The LSI with different risk preferences determines the profit margin of the green logistics service using the respond function of the risk-neutral LSP. After this, the risk-neutral LSP decides the greening level and outsourcing price of the logistics service.
4.2.1. The Pessimistic LSI Decision Model
This section refers to an LSSC where a pessimistic risk-averse LSI acts as the leader and a risk-neutral LSP is the follower under a fuzzy decision environment, indexed by the subscript PN. The pessimistic LSI determines the profit margin , and the risk-neutral LSP decides the greening level and outsourcing price to maximize their profit.
Hence, we can obtain the minimax chance-constrained programming for the
LSSC.
. where is a predetermined confidence level for the profit of the LSP and LSI. For each given feasible solution , is the minimum value that the LSI’s profit function obtains with the least possible , and is the expected profit of the risk-neutral LSP. We formulated the following minimax chance-constrained programming model in which the risk-averse LSI and the risk-neutral LSP attempt to maximize their optimal -pessimistic and expected profit by selecting the best and strategies, respectively.
It is clear that model (29) can be reformulated as model (30)
Theorem 3. Let , be the α-pessimistic value of the risk-averse LSI’s profit and expected profit of the risk-neutral LSP. The profit margin m chosen by the LSI is given. If , and , then the optimal solutions (, , , ) of the fuzzy LSSC are:where , . Proof. The
-pessimistic value of the risk-averse
LSI’s profit
and the expected profit of the risk-neutral
LSP can be formulated as follows, respectively:
From Equation (
36), the first-order derivatives of
with respect to
w and
can be obtained:
Therefore, the Hesse matrix of
with respect to
w and
is:
. Only when
, H > 0, is the Hesse matrix of
negative definite; thus,
is jointly concave in
w and
. Therefore, we can obtain the optimal response functions
and
of the risk-neutral
LSP by solving
and
, which provides (39) and (40).
Substituting
and
into Equation (
35), we can obtain the
-pessimistic value of the risk-averse
LSI’s profit:
Thus, we can obtain the first and second order derivatives of . Since , and all of the fuzzy variables are positive, ; therefore, is a concave function in m. The optimal marge profit of the risk-averse LSI can be attained by solving , which is shown in (31).
Then, substituting into (39) and (40), we can obtain the optimal and for the LSCC under the PN scenario, which is shown in Equations (32) and (33).
Combining Equations (31) and (33) into m+w=p easily yields the optimal price of the risk-averse LSI. The proof of Theorem 3 is complete. □
4.2.2. The Optimistic LSI Decision Model
In this section, the risk appetite LSI acts as the leader and the risk-neutral LSP acts as the follower under a fuzzy decision environment, indexed by the subscript ON. The risk appetite optimistic LSI determines the profit margin (m), and the LSP decides the greening level and outsourcing price (w) to maximize their profit.
Hence, we can obtain the maximax chance-constrained programming for the
LSSC.
where
is a predetermined confidence level for the profit of the
LSP and
LSI. For each given feasible solution
(m),
is the maximum value that the optimistic
LSI’s profit function
obtains with the least possible
, and
is the expected profit of the risk-neutral
LSP. We formulate the following Maximax chance-constrained programming model in which the risk appetite
LSI and the risk-neutral
LSP attempt to maximize their
-optimistic and optimal expected profit by selecting the best
m and
strategies, respectively.
It is clear that model (42) can be formulated as model (43):
Theorem 4. Let , be the α-pessimistic value of the risk appetite LSI’s profit and expected profit of the risk-neutral LSP, respectively. The profit margin m chosen by the LSI is given. If , and , then the optimal solutions (, , , ) of the fuzzy LSSC are:where , . Proof. The
-optimistic value of the risk appetite
LSI’s profit
can be formulated as follows:
From Equations (39) and (40), we can obtain the optimal response functions
and
of the risk-neutral
LSP. Then, substituting
and
into Equation (
48), we can obtain the
-pessimistic value of the risk-averse
LSI’s profit. This is similar to the proof of Theorem 3. The optimal marge profit
of the risk-averse
LSI can be attained by solving
, which is shown in (44).
Then, substituting into (39) and (40), we can obtain the optimal and for the LSCC under the ON scenario, which is shown in Equations (45) and (46).
Combining Equations (44) and (46) into m+w=p easily yields the optimal price of the risk appetite LSI.
The proof of Theorem 4 is complete. □
4.3. The LSI and LSP with the Same Risk Preference
In this scenario, there were three green LSSC models under a fuzzy decision environment. We addressed a risk-neutral, risk-averse, and risk appetite LSI acting as the leader and an LSP with the same risk preference behaviors as the follower.
4.3.1. The Expected Decision Model
In this section, the fuzzy LSSC comprised a risk-neutral LSI acting as the leader and a risk-neutral LSP acting as the follower under a fuzzy decision environment, indexed by the subscript NN. The risk-neutral LSI determines the profit margin(m), and the risk-neutral LSP decides the greening level and outsourcing price(w) to maximize their profit.
Hence, the expected chance-constrained programming for the fuzzy
LSSC can be formulated as follows:
Theorem 5. Let and be the fuzzy expected value of the profit for the LSI and LSP, respectively. If , and , then the optimal solutions of the fuzzy LSSC are:where , . Proof. From Equations (39) and (40), we can obtain the optimal response functions
and
of the risk-neutral
LSP. Then, substituting them into Equation (
9), we can obtain Equation (
54):
Thus, we can obtain the first and second order derivatives of
. Since
, and all of the fuzzy variables are positive,
; therefore,
is a concave function in
m. The optimal margin profit
of the risk-neutral
LSI can be obtained by solving
, which is shown in Equation (
50).
Then, substituting into Equations (39) and (40), we can obtain the optimal and for the LSCC under the scenario, which is shown in Equations (51) and (52).
Combining Equations (50) and (51) into easily yields the optimal price of the risk-averse LSI.
Thus, the proof of Theorem 5 is complete. □
4.3.2. The Pessimistic Decision Model
In this section, the risk-averse LSI acts as the leader, and the risk-averse LSP acts as the follower under a fuzzy decision environment, indexed by the subscript PP. The pessimistic LSI determines the profit margin (m), and the pessimistic LSP decides the greening level and outsourcing price (w) to maximize their profit.
Hence, we can obtain the minimax chance-constrained programming for the
LSSC.
where
is a predetermined confidence level for the profit of the
LSP and
LSI. For each given feasible solution
(m),
is the minimum value that the pessimistic
LSI’s profit function
obtains with the least possible
, and
is the minimum value that the pessimistic
LSP’s profit function
obtains with the least possible
. We formulated the following minimax chance-constrained programming model in which the risk-averse
LSI and
LSP attempt to maximize their
- pessimistic profit by selecting the best
m and
strategies, respectively.
It is clear that model (55) can be formulated as model (56):
Theorem 6. Let and be the α-pessimistic value of the profit of the risk-averse LSI and LSP, respectively. If , and , then the optimal solutions of the fuzzy LSSC are: Proof. From Equations (15) and (16), we can obtain the optimal response functions
and
of the risk-averse
LSP. Then, substituting them into Equation (
35), which is the
-pessimistic value of the risk-averse
LSI’s profit, we can obtain Equation (
61):
Thus, we can obtain the first and second-order derivatives of
. Since
and all of the fuzzy variables are positive,
; therefore,
is a concave function in
m. The optimal margin profit
of the risk-neutral
LSI can be obtained by solving
, which are shown in Equation (
57).
Then, substituting into Equations (7) and (8), we can obtain the optimal and for the LSCC under the PP scenario, which is shown in Equations (58) and (59).
Combing Equations (57) and (59) into
m+w=p easily yields the optimal price
of the risk-averse
LSI, which is shown in Equation (
60).
Thus, the proof of Theorem 6 is complete. □
4.3.3. The Optimistic Decision Model
In this section, the risk appetite LSI acts as the leader, and the risk appetite LSP acts as follower under a fuzzy decision environment, indexed by the subscript OO. The optimistic LSI determines the profit margin (m), and the optimistic LSP decides the greening level and outsourcing price (w) to maximize their profit.
Hence, we can obtain the maximum chance-constrained programming for the
LSSC.
where
is a predetermined confidence level for the profit of the
LSP and
LSI. For each given feasible solution
,
is the maximum value that the optimistic
LSI’s profit function
obtains with the least possible
, and
is the maximum value that the optimistic
LSP’s profit function
obtains with the least possible
. We formulated the following maximax chance-constrained programming model in which the optimistic
LSI and
LSP attempt to maximize their
-optimistic profit by selecting the best
m and
strategies, respectively.
It is clear that model (62) can be reformulated as model (63):
Theorem 7. Let and be the α-optimistic value of the profit for risk- appetite LSI and LSP, respectively. If , , and , then the optimal solutions of the fuzzy LSSC are: Proof. From Equations (27) and (28), we can obtain the optimal response functions
and
of the risk appetite
LSP. Then, substituting them into Equation (
48), which is the
-optimistic value of the risk appetite
LSI’s profit, we can obtain (68):
We can obtain the optimal margin profit
of the risk appetite
LSI by solving
, which is shown in Equation (
64). Then, substituting
into Equations (27) and (28), we can obtain the optimal
and
under the
OO scenario, which is shown in Equations (65) and (66).
Combing Equations (64) and (66) into
m+w=p easily yields the optimal price
of the risk-averse
LSI, which is shown in Equation (
67).
Thus, the proof of Theorem 7 is complete. □
Remark 1. If the fuzzy parameters in each model are crisp real numbers, the models (5), (20), (29), (42), (49), (55), and (62) can degenerate into the following model (69), which was introduced by Lau et al. [42]: Remark 2. When the total market potential , the price sensitivity of consumer demand , the LSP’s green innovation parameter ξ, the LSP’s unit cost of logistics service capacity , and the green sensitivity of consumer demand all degenerate into crisp real numbers, then the optimal results in Theorems 1–7 can degenerate into the following: if and , the optimal solutions are:which are the conventional results in crisp cases [42]. In this section, the environment and risk preference behavior are considered in LSSC decision making. We simultaneously discuss seven kinds of decision models to comprehensively analyze the combinations of risk preferences between the LSI and LSP under three scenarios. The games between the LSI and LSP with different risk preference behaviors are comprehensively proposed by the fuzzy expected value model and chance-constrained programming model. Then, the optimal decisions of the greening level and outsourcing price for the LSP, price and profit margin for LSI are drawn. This provides a solid foundation for numerical analysis.
5. Case and Numerical Analysis
With regard to there being many fuzzy variables in models, the established fuzzy decision models are more complex, and the optimal solutions are also complicated. Consequently, the properties of the formulae are not obvious. Furthermore, it is not easy to obtain a more accurate explanation. For this purpose, we use case study and numerical examples to show the equilibrium strategy decisions under different parameter setting, as well as to verify the seven game models and propositions above in this subsection.
5.1. A Case Study
In recent years, many well-known logistics service enterprises have gained higher economic and social benefits by carrying out green supply chain management. Cainiao Network (hereafter Cainiao) is one of the typical demonstration enterprises of green LSSC management in China. In May 2013, Alibaba established Cainiao Alliance with logistics enterprises, such as SF Express (hereafter SF), YTO Express (hereafter YTO), ZTO Express (hereafter ZTO), STO Express (hereafter STO), and Yunda Express (hereafter Yunda).
Through the effective integration of logistics resources, this alliance provides high-quality socialized storage facilities and equipment and network services for all kinds of manufacturing, retail, and e-commerce enterprises; supports the transformation and upgrading of the logistics industry; establishes an efficient coordination mechanism of socialized resources; and improves the quality of China’s socialized logistics services.
At present, for Cainiao and SF, scientific and technological research and development represent the core driving force, and the companies are making efforts, from green packaging, distribution, storage and other aspects to carrying out green logistics, with the goal of achieving low pollution, low consumption, low emission, high efficiency, and high benefits.
Cainiao is a very successful LSI in China. Cainiao and its logistics partners are using smart technologies and innovative models to make logistics greener. A green LSSC is formed from packaging and dispatch, transfer and sorting, and transportation and delivery. Specifically, Cainiao’s electronic bill will help the whole industry to reduce more than 5 billion pieces of paper, and an intelligent packing algorithm can reduce the use of packaging materials by 15% on average.
In the “last kilometer of express delivery”, 40,000 Cainiao courier stations and 35,000 express delivery outlets across the country have sorted and recycled express packages to realize a “small cycle of environmental protection”. In addition, Cainiao are also cooperating with YTO, ZTO, STO, Yunda, and Best Express to launch the “National Carton Recycling Day” to spread awareness regarding environmental protection.
We now take the Cainiao Alliance
LSSC as our research object and select the most representative Cainiao and SF partners to conduct simulation research in order to verify the effectiveness of the model. This has been widely used by Chen et al. [
1] and Wang et al. [
7]. In the two-stage
LSSC operation process composed of Cainiao and SF, where Cainiao serves as the
LSI and SF as the
LSP, we analyzed the impact of the participants’ risk preference behaviors on the
LSSC performance and decision making through different confidence level setting under fuzzy environments. The confidence level was given beginning with
and the step length was 0.05 to ensure that our analysis would fall within a feasible region.
5.2. Numerical Analysis
Numerical analysis was conducted to verify the seven game models and propositions above. Considering the case where the overall logistics service market scale
and SF’s green innovation
are moderate, the logistics serviceprice sensitivity
is very sensitive, and both the green sensitivity
and the logistics service cost are low. The relationship between an expert’s fuzzy language and a triangular fuzzy number is determined by fuzzy theory [
41,
43]. The triangular fuzzy number of the parameters are as follow:
,
,
,
, and
. The parameter values assumed in the numerical analysis are listed in
Table 1. The pessimistic and optimistic values of
,
,
,
, and
are presented below.
The expected values of the parameters are as follows:
Consequently, we can obtain:
Based on the above analysis, we can obtain the optimal solutions and profit of the expected, -pessimistic, and –optimistic values of the fuzzy green LSSC system.Then, we discuss the impacts of the risk preference on them.
5.2.1. Impact of on , , , and
In this subsection, we discuss the impacts of the risk preference on the optimal greening level , outsourcing price w, marginal profit m, and price p through different confidence level settings.
Figure 3 shows that the optimal greening level is the highest in the
OO model, and the lowest in the NP model. Considering the increseaing change in the confidence level
, the values of
show an upward trend in the
ON,
PP, and
NP models but a decline in the
PN,
OO, and
NO models. Moreover, there are
,
, and
at all confidence levels.
The relationships among the optimal greening levels under different risk preferences in
Figure 3 are as follows:
Observing
Figure 4, it is obvious that the optimal outsourcing price is the highest in the
NO model and the lowest in the
NN model. With the confidence level
increasing, the values of
generate an increase in the
ON,
PP, and
NP models and a decrease in the
PN,
OO, and
NO models. Moreover, there are
,
, and
at all confidence levels.
The relationships among the optimal outsourcing prices under different risk preferences in
Figure 4 are as follows:
Figure 5 demonstrates that the optimal price is the highset in the
OO model and the lowest in the
NP model. Considering the increseaing change in the confidence level
, the values of
display an upward trend in the PN, PP, and NP models but a decline in the
ON,
OO, and
NO models. Moreover, there are
,
and
at all confidence levels.
The relationships among the optimal price under different risk preferences in
Figure 5 are as follows:
As shown in
Figure 6, the optimal marginal profit is the highset in the
ON model and the lowest in
NO model. With the increasing change in the confidence level
, the values of
show an upward trend in the
PN,
PP, and
NO models but a decline in the
NP,
OO, and
NO models. Moreover, there are
,
, and
at all confidence levels.
The relationships among the optimal marginal profit of the
LSI under different risk preferences in
Figure 6 are as follows:
5.2.2. Impact of on , , , and
In this section, we discuss the impacts of the risk preference on the optimal green innovation cost and profit through different confidence level
setting.
Figure 7 shows that the optimal green innovation cost is the highset in the
OO model and the lowest in the
NP model. As the confidence level
increasingly changes, the values of
display an upward trend in the
ON,
PP, and
NP models but a decline in the
PN,
OO, and
NO models. Furthermore, there are
,
, and
at all confidence levels.
The relationships among the optimal green innovation cost under different risk preferences in
Figure 7 are as follows:
As shown in
Figure 8, it is obvious that when the confidence level
becomes close to 1, the optimal total profit of the
LSSC in the
NN model is the highest and is the lowest in the
OO model. Moreover, as
increasingly changes, the optimal total profit of the
LSSC show an upward trend in the
NP,
PN,
PP,
OO, and
ON models. Howerver, it is only in the
NO model that the optimal total profit of the
LSSC declines. Moreover, there are
,
, and
at all confidence levels.
The relationships among the optimal total profits of the
LSSC under different risk preferences in
Figure 8 are as follows:
In
Figure 9, we can see that the optimal profit for the
LSP is the highset in the
NO model, and it is initially the lowest in the
ON model first and then in the
NN model. Considering the increasing change in the confidence level
, the values of
display an upward trend in the
NP,
PP, and
ON models but decline in model the
PN,
OO, and
NO models. Still, there are
,
, and
at all confidence levels.
It can be seen in
Figure 9 that the relationships among the optimal profits of the
LSP under different risk preferences are as follows:
As shown in
Figure 10, we can determine that the profit for the
LSI is the highset in
NN model and lowest in
OO model. With the increasing changes in the confidence level
, the values of
display an upward trend in the
PP,
OO,
ON,
PN, and
NO models but only decline in the
NP model. In addition, there are
and
at all confidence levels.
Figure 10 demonstrates that the relationships among the optimal profit of the
LSI under different risk preferences are as follows:
Figure 3,
Figure 4,
Figure 7 and
Figure 9 display a definite trend in that the
,
,
, and
demonstrate the same change with different confidence levels
in different scenarios. Specifically, they all decline in the
NO,
OO, and
PN models and increase in the
NP,
ON, and
PP models. Meanwhile, both
and
obtain the highest value in the
OO model and lowest value in the
NP model. Overall, all of the optimal solutions show a gradual upward trend in the
PP model. When
becomes close to 1, both
and
obtian the highest value in the
NN model and lowest value in the
OO model.
Extreme risk preference is ascribed to the value curves for , and all being steeply downward sloping in the OO model and upward sloping in the PP model. With regard to the influence of variable determiners, the value curves for slope steeply upward in the NP model and decline in the NO model, while the curves for steeply decline in the ON model and increase in the PN model, and the curves for steeply decline in the NO model and increase in the NP model. Due to the extreme risk preference and the influence of the variable determiners, the value curves for all steeply rise in the OO and ON models. Taking into account the impact of the leading rights on the LSSC and participants’ risk preferences, the value curves for all slope sharply upward in the ON, OO, and PP models, but steeply decline in the NO model.
6. Conclusions and Management Insights
6.1. The Main Conclusions
A win–win situation for the LSI and LSP can be achieved by forming an LSSC through which they can cooperate with one another. Additionally, logistics service operations play a significant role in reducing the environmental burden of the supply chain. Thus, green research on the LSSC is imperative. However, decision-makers have a vague understanding of the market environment of such green services due to the lack of reference historical data.
In order to explore the decision making problem in a two-stage LSSC with consideration of the influence of the environment, game theoretical models led by the LSI were developed in this paper to determine strategies for risk preference behavior selection and green service supply under a fuzzy environment. Subsequently, the optimal solutions of the LSP and the LSI were drawn. Then, numerical examples were presented to explore the impact of LSSC participants’ risk preference on the optimal solutions under the fuzzy environment. Based on the analysis and discussion above, we summarize and provide four conclusions as follows.
First, optimistic risk attitude can appropriately improve the greening level, price, and green innovation cost of logistics services. Of the various risk preference strategies, they all take maximum value when an optimistic LSP cooperates with a risk appetite LSI, and obtain minimum optimal solution in the NP model, in which a risk-neutral LSI works in cooperation with a risk-adverse LSP. In general, the greening level and green innovation cost in optimistic models are higher than those in pessimistic models.
Next, in terms of risk preference behavior, beyond a certain confidence level, both risk appetite and risk averse attitudes can also lead to a rise in the outsourcing price. When the confidence level is greater than 0.56, both the optimistic and pessimistic values of the outsourcing price are higher than the expected value. Specifically, it is clear that the risk preferences are ascribed to a higher outsourcing price.
Moreover, when the decision maker is risk neutral, the partner’s risk attitude has a significant effect on the value of the decision variables and cost. Taking into account that the greening level, outsourcing price, and green innovation cost are all determined by the LSP, the LSI determines the marginal profit. This is essential, because when one participant is risk-neutral, the partner’s risk preference plays a major role in the optimal solution. Moreover, the results were somewhat different from these of other models.
Finally, the optimal profits of the different risk preference behaviors between the LSI and LSP differ among various game models under fuzzy environments. Of the various risk preference strategies, to gain maximum profit, the best decision for the LSI is to remain neutral when the LSP is risk neutral; however, the LSP’s best decision is to adopt an optimistic attitude when the LSI is risk neutral, the LSP adopts an optimistic attitude. Furthermore, the total LSSC gains maximum profit in the NN model, which means that both the LSI and LSP remain risk-neutral, helping the supply chain to make a large profit.
6.2. Insights for Managers
A better understanding of the green logistics service supply chain game considering the impact of risk preference can offer better insight for logistics policymakers as to how to best make decisions under fuzzy environments. There are three important managerial implications of this study for LSSC games considering risk preference under fuzzy environments.
First, total involvement and cooperation among participants are vital factors for improving green management in the LSSC. The highest greening level is in the OO model, which means that only with a risk appetite LSI and LSP can the green and environmental level of the logistics service be significantly improved. This also shows that it is not only the LSP that can effectively affect the greening level; the LSI is also capable of this. Overall, to reduce the negative impact of logistics services on the environment, optimistic, full participation and effective cooperation of supply chain members are needed.
Secondly, risk preference plays a key role in how LSSC participants make decisions under fuzzy environments. The risk preference behavior of the LSI and LSP differs among the various game models under fuzzy environments. Of the various risk preference strategies, the best decision for the LSI is to be risk neutral when the LSP is risk neutral to obtain maximum profit. However, the LSP’s best decision for the greening level is to adopt an optimistic attitude to cooperate with the LSI.
Thirdly, the dominant position in a LSSC plays a crucial role in making profit. In our research, the LSI is the leader, and the profits of the LSI are always higher than those of the LSP in any risk preference model. Hence, the dominant leader in the LSSC, such as the LSI in this paper, obtains the higher profit, while the follower obtains the lower profit. Under these circumstances, it should be noted that in order to produce greater profit in the LSSC, participants must strive to improve their competitiveness to gain more control power.
7. Limitations and Future Work
This study focused on the decision making for the green LSSC composed of an LSI and an LSP with risk preference under fuzzy environments. Although our investigation provides useful management recommendations, there are still some limitations in this research. First, the theoretical model adopted in this study may be limited by certain technical assumptions used.
The assumptions of deterministic settings produced several limitations. For instance, we assumed that there was only one LSI and one LSP in the LSSC. This is a huge simplification of the real problem. Second, we only investigated the power structure led by LSI. There are other power structures in the real world. For instance, the LSSC may be dominated by the LSP or by both the LSP and LSI.
In the future, the proposed method can be applicable to other real-life problems, such as product pricing, supply chain contract design, and supplier selection. In addition, the demand function in this way was linear, and we can explore other forms of demand functions, such as stochastic demand functions. Finally, the inclusion of multiple competitive LSSC participants and other game power structures are also important directions for future research.