# Profit Allocation of Agricultural Machinery Service-Oriented Manufacturing Alliance Based on Modified Shapley Value Method

Authors: Feng Lyu; Yanghang Zhang; Zhuangzhuang Feng; Jianxin Su
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Shapely value is a method of determining the importance of individuals in the collective, avoiding the equal allocation of profit. The profit allocation on SOM (service-oriented manufacturing) alliance between agricultural machinery manufacturing enterprises and suppliers under the SOM mode is a complex problem restricted by many factors, but the Shapely value method does not consider the differences of member enterprises. Therefore, factors that affect the profit allocation are given in this paper, such as input level, effort level, innovation level, risk factor, and value-added factor. Based on these factors, the Euclidean distance is used to modify the traditional TOPSIS method to determine the profit allocation correction coefficient, and the GRA (grey relational analysis) is introduced into the TOPSIS method to calculate the closeness degree, which reflects the position relationship and consistency of data curve. Based on the modified Shapley value method, a profit allocation method of agricultural machinery service-oriented manufacturing alliance is constructed. Finally, an application example is given to verify the effectiveness of the proposed method.


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## Body

## 1. Introduction

Service-oriented manufacturing is a new manufacturing mode by integrating servitization with the traditional manufacturing industry [1], which is based on service and oriented to service and combines manufacturing with both producer and consumer services. In service-oriented manufacturing, each enterprise focuses on core businesses, outsources noncore businesses, and provides producer services for one another to achieve rapid innovation and improve efficiency [2]. In this context, multiple enterprises with different core capabilities will form a community of interests or dynamic alliance [3]. This kind of alliance can enhance the cooperative behavior of enterprises, bring advantages to enterprises, resolve competition conflicts, obtain greater learning benefits, develop innovative products, and respond to the risks of turbulence and market uncertainty. In their respective fields, each cooperative enterprise is committed to its own core competitiveness and realizes complementary advantages, risk sharing, and benefit sharing for alliance member enterprises.In practice, the cooperation between agricultural machinery enterprises and suppliers is not based on altruism, but on the need for self-interest. Cooperation can integrate the self-interest of agricultural machinery enterprises and suppliers into service-oriented manufacturing alliance that achieve their respective goals, whereas competition will push the self-interest of agricultural machinery enterprises and suppliers into the struggle, thereby losing efficiency. Therefore, in the cooperative context, agricultural machinery enterprises and suppliers will regard the activities of other interest groups as their positive external conditions, whereas in the competitive context, agricultural machinery enterprises and suppliers will regard the activities of other interest groups as negative external conditions. [4]. This is one of the main motivations for agricultural machinery enterprises and suppliers to choose to cooperate and form agricultural machinery service-oriented manufacturing alliances.In the process of cooperation in the agricultural machinery service-oriented manufacturing alliance, the agricultural machinery enterprises as the agricultural machinery product service integrator must fully consider the impact of the profit allocation on its cooperative relationship with its suppliers and construct a set of scientific profit allocation methods. Profit allocation is the allocation of the profits obtained through cooperation among the participants. A fair and reasonable profit allocation method will consolidate and develop the cooperative relationship between agricultural machinery enterprises and suppliers, making full use of the complementary resources in cooperation process, so as to achieve common profits [5].Fruitful research studies on profit allocation have been made until now. Nash was the first to study the influence of negotiation on members of supply chain organization. Later, more and more scholars used the bargaining game model to study supply chain coordination [6]. Zhou et al. used an analytic hierarchy process based on the contribution of each supplier to allocate profits reasonably [7]. Du et al. showed that the five key influencing factors on the profit allocation are risk sharing, financing ability, investment, management ability, and effort level [8]. If only consider the profit allocation from the perspective of the value added by the agricultural machinery service-oriented manufacturing alliance, the Shapley value is a scientific and reasonable solution [9].In recent years, scholars have conducted fruitful research on the profit allocation of Shapley value method. Zhu et al. solved the profit allocation plan, by taking advantage of the characteristics of the Shapley value method according to the degree of contribution. After further comprehensively considering the four factors that affect the profit allocation, Zhu et al. established a university water-saving contract profit allocation model based on the modified Shapley value method [10]; Zheng et al. proposed three coordination mechanisms based on Shapley value, nucleolus solution, and equal satisfaction to distribute residual profits. These three mechanisms were evaluated through numerical experiments and further studied the influence of retailers’ fairness concerns on profit allocation [11]; An et al. combined the Shapley value method with the network DEA, discussed the resource sharing and income allocation between the stages in the three-stage system, and established several network DEA models to calculate the optimal system before and after cooperation profit [12]; Zheng et al. proposed an innovative weighted allocation approach, namely, the variable-weighted Shapley value, to coordinate a closed-loop supply chain [13]. Fang et al. proposed an improved Shapley value method that defined the adjusted weight for participant based on the heat-to-power ratio [14]. Song et al. considered the marginal efficiency contribution of each member enterprise to the alliance and applied it to replace the marginal profit contribution in the Shapley value, assumed that each member enterprise’s input and output data are fuzzy numbers, and constructed an efficiency measurement model based on fuzzy DEA [15]. Fahimullah et al. constructed a cooperative game model, taking into account the knowledge of investment, stock, knowledge absorption capacity, coordination cost, and development cost of firms [16]. Xu et al. constructed a theoretical model for the centralized market income distribution mechanism that incorporates three corrective risk factors, ecological investment, and technological level [17]. Ma et al. proposed a method that enables the cloud federation to map the contribution of resources of the participants to the federations into a quality of service metric used to achieve a cloud federation and reveal the possibilities and benefits of different federation compositions using the Shapley value of each resource provider as a way of implementing a fair profit sharing strategy [18]. Zhao and Xiao tried to set up a cooperative distribution mechanism based on a green supply chain and established the model of alliance distribution based on the Shapley value method mainly from contribution levels for the second correction [19]. Zhuang and Zhang proposed a Shapley value method and the ANP improved model to allocate profits [20]. Du et al. proposed four correction factors for modifying the initial allocation, namely, the contribution rate of inputs, the risk-sharing coefficient, the degree of cooperation, and the contribution rate of carbon emissions [21].According to the difference of research problem, the related research on profit allocation can be roughly divided into the profit allocation after cooperation with the goal of collective profits and the profit allocation without cooperation with the goal of individual profits. According to the difference of research method, studies related to profit allocation can be divided into quantitative analysis, qualitative analysis, and case study [22]. However, the research on the profit allocation rarely considers the noneconomic behavior of participants. In fact, the allocation of profit between enterprises is also affected by other noneconomic factors, such as the innovation and risk factors. Therefore, based on the profit allocation of Shapley value method, these factors need to be considered for modification. In view of this, based on the existing research results and the characteristics of service-oriented manufacturing, by combining quantitative and qualitative analysis, this paper aims at maximizing collective profits after cooperation and proposes a profit allocation method for agricultural machinery service-oriented manufacturing alliance based on the modified Shapley value, which provides a feasible way for the problem of profit allocation among enterprises.


## 2. Influential Factors of Profit Allocation

Under the principles of scientificity, comprehensiveness, and operability, this paper combines the characteristics of service-oriented manufacturing and summarizes the factors that affect the profit allocation of the agricultural machinery service-oriented manufacturing alliance as follows: investment level, effort level, risk factor, innovation level, and value-added factor, as shown in Figure1.Figure 1
The main influential factors of the profit allocation on agricultural machinery service-oriented manufacturing alliance.


### 2.1. Investment Level

In economics, investment is the basis for an enterprise to carry out economic activities and an important source of enterprise income. Therefore, the investment level is the basic element for the member enterprises in the agricultural machinery service-oriented manufacturing alliance to participate in the profit allocation, which affects its final profit allocation. Some studies have shown that the investment of member enterprises improves with the increase of their profit allocation ratio and their speculative behaviors decreases with the increase of the profit allocation ratio. Because each member enterprise has different resource and division of labor, the ways of participating in the investment are also different. The allocation of profits should be based on the principle of fair allocation, that is, the additional profits and allocation brought about by the increase in investment should be the same as the increase in investment. Proportion is equal to ensure that member enterprises can receive a reasonable allocation regardless of the form of investment, so as to better mobilize the enthusiasm of member enterprises. Therefore, when distributing the profits of the agricultural machinery service-oriented manufacturing alliance, member enterprises have the right to obtain corresponding allocation shares based on the value of their tangible and intangible investment. That is to say, when determining the profit allocation, it is necessary to follow the allocation principle of consistent investment and profit and fully consider the factor of investment level.


### 2.2. Effort Level

Effort level, that is, the work enthusiasm of the member enterprises, including the degree of effort in their own business and the degree of support to cooperative enterprises, is the embodiment of the quality and ability of the enterprise to participate in market competition. Effort level has a certain of concealment, but it is the key point of profit allocation. The contribution of the effort level of the member enterprises in the agricultural machinery service-oriented manufacturing alliance to the competitiveness of products and services is the core element for realizing the value-added creation of the agricultural machinery service-oriented manufacturing alliance. Through the efforts of the member enterprises, the agricultural machinery service-oriented manufacturing alliance can be promoted to achieve greater profits than the member enterprises’ independent operations and achieve the effect of “1 + 1 > 2.” Therefore, the effort level of the member enterprises is also an important factor affecting the stability of the agricultural machinery service-oriented manufacturing alliance and the profit allocation.It needs to be pointed out that all the efforts of member enterprises require a certain of expenses [23]. Therefore, the enthusiasm shown by member enterprises will vary and some enterprises may harm the profit of other member enterprises in the alliance for their own profit. In addition, conflicts may occur between member enterprises, which means no matter how hard a member enterprise is, other member enterprises hope that it will work harder so that all member enterprises can profit from it. Therefore, in the process of profit allocation, it is necessary to reward member enterprises with high enthusiasm and high level of effort and to punish those member enterprises that lack enthusiasm, be lazy and other “bad behaviors.” Only in this way, the inconsistency between the effort level paid and the return obtained can be avoided, which will damage the enthusiasm of member enterprises and inhibit the “bad behaviors” of member enterprises.


### 2.3. Risk Factor

The agricultural machinery service-oriented manufacturing alliance is a value-added network with multiple participants, multiple links of profit sharing, and risk sharing. It has the characteristics of complexity, dynamic, and interaction, whereas creating huge profits, it will inevitably be accompanied by a variety of uncertain factors due to its exposure to the ever-changing market environment and assume various risks such as market risk, technical risk, cooperation risk, information risk, and dissolution risk. Because of the different tasks and roles undertaken by each member enterprise, the degree of risk faced is also different. Generally speaking, if one party takes more risks, it will obviously require more profits to balance the cost of taking risks. At the same time, risks are transferred and reasonably distributed among member enterprises, which can improve cooperation efficiency and increase profits. Therefore, the primary condition for cooperation among enterprises in the agricultural machinery service-oriented manufacturing alliance is that the member enterprise can get a return that is compatible with the risk.


### 2.4. Innovation Level

Technological innovation is a primary means for many firms to improve the value of their products for customers as well as to increase customers’ willingness to pay, and innovation can be carried out by different parts in the supply chain [24]. In the face of the complex and changeable market competition environment and the increasingly diversified and personalized needs of customers, the excellent innovation level becomes the key to enhancing the core competitiveness and creating profits of the agricultural machinery service-oriented manufacturing alliance. In the agricultural machinery service-oriented manufacturing alliance, the innovation level of each member enterprise is different, and accordingly, the contribution is different. Therefore, innovation level should be taken into account when distributing profits.


### 2.5. Value-Added Factor

The agricultural machinery service-oriented manufacturing alliance is essentially a community of benefit based on the principle of complementary advantages to realize value added. That is, different member enterprises add a part of their own functions or advantage value chain to the overall value of the agricultural machinery service-oriented manufacturing alliance creating. Since member enterprises have different advantages, there are bound to be differences in the value-added activities undertaken and the incremental value created. Therefore, whether the member enterprises in the service-oriented agricultural machinery manufacturing alliance add value in the corresponding value chain and the size of the added value should also be considered as an influencing factor of profit allocation.


## 2.1. Investment Level

In economics, investment is the basis for an enterprise to carry out economic activities and an important source of enterprise income. Therefore, the investment level is the basic element for the member enterprises in the agricultural machinery service-oriented manufacturing alliance to participate in the profit allocation, which affects its final profit allocation. Some studies have shown that the investment of member enterprises improves with the increase of their profit allocation ratio and their speculative behaviors decreases with the increase of the profit allocation ratio. Because each member enterprise has different resource and division of labor, the ways of participating in the investment are also different. The allocation of profits should be based on the principle of fair allocation, that is, the additional profits and allocation brought about by the increase in investment should be the same as the increase in investment. Proportion is equal to ensure that member enterprises can receive a reasonable allocation regardless of the form of investment, so as to better mobilize the enthusiasm of member enterprises. Therefore, when distributing the profits of the agricultural machinery service-oriented manufacturing alliance, member enterprises have the right to obtain corresponding allocation shares based on the value of their tangible and intangible investment. That is to say, when determining the profit allocation, it is necessary to follow the allocation principle of consistent investment and profit and fully consider the factor of investment level.


## 2.2. Effort Level

Effort level, that is, the work enthusiasm of the member enterprises, including the degree of effort in their own business and the degree of support to cooperative enterprises, is the embodiment of the quality and ability of the enterprise to participate in market competition. Effort level has a certain of concealment, but it is the key point of profit allocation. The contribution of the effort level of the member enterprises in the agricultural machinery service-oriented manufacturing alliance to the competitiveness of products and services is the core element for realizing the value-added creation of the agricultural machinery service-oriented manufacturing alliance. Through the efforts of the member enterprises, the agricultural machinery service-oriented manufacturing alliance can be promoted to achieve greater profits than the member enterprises’ independent operations and achieve the effect of “1 + 1 > 2.” Therefore, the effort level of the member enterprises is also an important factor affecting the stability of the agricultural machinery service-oriented manufacturing alliance and the profit allocation.It needs to be pointed out that all the efforts of member enterprises require a certain of expenses [23]. Therefore, the enthusiasm shown by member enterprises will vary and some enterprises may harm the profit of other member enterprises in the alliance for their own profit. In addition, conflicts may occur between member enterprises, which means no matter how hard a member enterprise is, other member enterprises hope that it will work harder so that all member enterprises can profit from it. Therefore, in the process of profit allocation, it is necessary to reward member enterprises with high enthusiasm and high level of effort and to punish those member enterprises that lack enthusiasm, be lazy and other “bad behaviors.” Only in this way, the inconsistency between the effort level paid and the return obtained can be avoided, which will damage the enthusiasm of member enterprises and inhibit the “bad behaviors” of member enterprises.


## 2.3. Risk Factor

The agricultural machinery service-oriented manufacturing alliance is a value-added network with multiple participants, multiple links of profit sharing, and risk sharing. It has the characteristics of complexity, dynamic, and interaction, whereas creating huge profits, it will inevitably be accompanied by a variety of uncertain factors due to its exposure to the ever-changing market environment and assume various risks such as market risk, technical risk, cooperation risk, information risk, and dissolution risk. Because of the different tasks and roles undertaken by each member enterprise, the degree of risk faced is also different. Generally speaking, if one party takes more risks, it will obviously require more profits to balance the cost of taking risks. At the same time, risks are transferred and reasonably distributed among member enterprises, which can improve cooperation efficiency and increase profits. Therefore, the primary condition for cooperation among enterprises in the agricultural machinery service-oriented manufacturing alliance is that the member enterprise can get a return that is compatible with the risk.


## 2.4. Innovation Level

Technological innovation is a primary means for many firms to improve the value of their products for customers as well as to increase customers’ willingness to pay, and innovation can be carried out by different parts in the supply chain [24]. In the face of the complex and changeable market competition environment and the increasingly diversified and personalized needs of customers, the excellent innovation level becomes the key to enhancing the core competitiveness and creating profits of the agricultural machinery service-oriented manufacturing alliance. In the agricultural machinery service-oriented manufacturing alliance, the innovation level of each member enterprise is different, and accordingly, the contribution is different. Therefore, innovation level should be taken into account when distributing profits.


## 2.5. Value-Added Factor

The agricultural machinery service-oriented manufacturing alliance is essentially a community of benefit based on the principle of complementary advantages to realize value added. That is, different member enterprises add a part of their own functions or advantage value chain to the overall value of the agricultural machinery service-oriented manufacturing alliance creating. Since member enterprises have different advantages, there are bound to be differences in the value-added activities undertaken and the incremental value created. Therefore, whether the member enterprises in the service-oriented agricultural machinery manufacturing alliance add value in the corresponding value chain and the size of the added value should also be considered as an influencing factor of profit allocation.


## 3. Shapley Value Method of Profit Allocation

The Shapley value method is a mathematical method for solving cooperativen-person game proposed by Shapley L.S. in 1953 based on the cooperative game theory [25]. When n individuals are engaged in an economic activity, each form of cooperation combined by several of them will get profits. When the profit activities between people are nonantagonistic, the profits brought by their cooperation will not decrease with the increase in the number of people. In this way, the cooperation of all individuals will get the greatest profit [26]. The Shapley value method is an effective method for the allocation of cooperative profits, which is defined as follows.Suppose the participant setN=1,2,…,n, if any subset of N (representing any combination in the set of persons) corresponds to a certain real-valued function vS, and the real-valued function satisfies(1)vϕ=0,(2)vSi∪Sj≥vSi+vSj,Si∩Sj=ϕSi⊆N,Sj⊆N.In the Shapley value method, the profit allocation of each member of the setN is the Shapley value, which is recorded as ϕv=φ1v,φ2v,…,φnv, where φiv represents the allocation of the ith member under the cooperation N, which can be obtained by the following equation:(3)φiv=∑s∈siwSvS−vS\i,(4)wS=n−S!S−1!n!.In equations (3) and (4), Si represents all the subsets of the set N containing member i, S is the number of members included in the subset S, n is the number of members included in the set N, wS represents the weighting factor, and vS is the profit of the subset S, vS\i is the profit that can be obtained after removing member i from subset S.The Shapely value method reflects the importance of individuals in the collective, avoiding the equal allocation of profits; it is a scientific and reasonable method of profit allocation [27]. However, when we use the Shapely value method to solve the problem of profit allocation, the assumption is that the investment of each member enterprise is equal, the degree of effort is the same, and the risk is shared. It does not consider the differences of member enterprises in investment level, effort level, risk factor, innovation level, and value-added factor. In fact, the profit allocation of the agricultural machinery service-oriented manufacturing alliance is a complicated problem, and it is restricted by many factors. Therefore, the Shapely value must be modified on the basis of considering the influence of these factors.


## 4. Determination of the Correction Coefficient of Profit Allocation

This paper uses the integrated and improved TOPSIS method and GRA to determine the profit allocation correction coefficient of the members of the agricultural machinery service-oriented manufacturing alliance. This method can simultaneously reflect the positional relationship between the member enterprises and the positive and negative ideal solutions, as well as the consistency of the data curve. The specific steps are as follows.


### 4.1. Data Standardization

Assuming that there arem member enterprises and n correction factors, we could construct a decision matrix X=xijm×nby m and n, and a standardized decision matrix Y=yijm×n can be obtained after normalization.Since the correction factors in this article are all profit-type indicators, the data normalization can be processed by the following equation:(5)yij=xij−minxijmaxxij−minxij.In equation (5), xij is the jth correction factor value of the ith member enterprise, i=1,2,…,m and j=1,2,…,n.


### 4.2. Determine the Positive Ideal Solution and the Negative Ideal Solution

Define positive ideal solutionY+ and negative ideal solution Y−:(6)Y+=yj+|j=1,2,…,n,(7)Y−=yj−|j=1,2,…,n.The positive ideal solution is(8)yj+=maxiyij,i=1,2,…,m,j=1,2,…,n.The negative ideal solution is(9)yj−=miniyij,i=1,2,…,m,j=1,2,…,n.


### 4.3. Calculate the Weighted Euclidean Distance of Each Member Enterprise to the Positive Ideal Solution and the Negative Ideal Solution

This paper introduces the weighted Euclidean distance to modify the traditional TOPSIS method, which can not only reflect the consistency of the position of the member enterprise and the ideal solution but also eliminate the problem of reverse order caused by weight [28].(10)di+=∑j=1nwjyij−yj+2,(11)di−=∑j=1nwjyij−yj−2.In equations (10) and (11), wj is the weight of the correction factor.


### 4.4. Calculate the Grey Relational Degree between Each Member Enterprise and the Positive Ideal Solutions and Negative Ideal Solutions

In this paper, the grey relational degree is introduced into the equation of the TOPSIS method close degree to reflect the consistency between the member enterprises and the ideal solution in the curve geometry [29].(12)rij+=miniminjΔij++ζmaximaxjΔij+Δij++ζmaximaxjΔij+,(13)rij−=miniminjΔij−+ζmaximaxjΔij−Δij−+ζmaximaxjΔij−,where Δij+=yij−yj+, Δij−=yij−yj−, and ζ is the resolution coefficient, generally take 0.5.Then, the grey relational degree is(14)G+=gj+|i=1,2,…,m,(15)G−=gj−|i=1,2,…,m,where(16)gj+=∑j=1nwjrij+,(17)gj−=∑j=1nwjrij−.


### 4.5. Calculate the Close Degree of Each Member Enterprise to the Ideal Point

Nondimensionalize the distance and grey relational degree:(18)ej+=minidi+di+,(19)ej−=minidi−di−,(20)hi+=gi+minigi+,(21)hi−=gi−minigi−,(22)ci+=αei++1−αhi+,(23)ci−=αei−+1−αhi−.In equations (22) and (23), αis the preference coefficient, which is generally 0.5.Then, the relative closeness of each member enterprise is(24)ci=ci−ci++ci−,i=1,2,…,m.The normalized relative closeness is(25)ci∗=ci∑i=1mci.


### 4.6. Calculate the Correction Coefficient

The classic Shapley value method defaults that the above correction factors are equal among member enterprises, so they are all1/n after normalization. This paper introduces the actual contribution of member enterprises and the equal contribution to compare the difference. Then, the correction coefficient can be obtained:(26)δi=ci−1n,i=1,2,…,m.


## 4.1. Data Standardization

Assuming that there arem member enterprises and n correction factors, we could construct a decision matrix X=xijm×nby m and n, and a standardized decision matrix Y=yijm×n can be obtained after normalization.Since the correction factors in this article are all profit-type indicators, the data normalization can be processed by the following equation:(5)yij=xij−minxijmaxxij−minxij.In equation (5), xij is the jth correction factor value of the ith member enterprise, i=1,2,…,m and j=1,2,…,n.


## 4.2. Determine the Positive Ideal Solution and the Negative Ideal Solution

Define positive ideal solutionY+ and negative ideal solution Y−:(6)Y+=yj+|j=1,2,…,n,(7)Y−=yj−|j=1,2,…,n.The positive ideal solution is(8)yj+=maxiyij,i=1,2,…,m,j=1,2,…,n.The negative ideal solution is(9)yj−=miniyij,i=1,2,…,m,j=1,2,…,n.


## 4.3. Calculate the Weighted Euclidean Distance of Each Member Enterprise to the Positive Ideal Solution and the Negative Ideal Solution

This paper introduces the weighted Euclidean distance to modify the traditional TOPSIS method, which can not only reflect the consistency of the position of the member enterprise and the ideal solution but also eliminate the problem of reverse order caused by weight [28].(10)di+=∑j=1nwjyij−yj+2,(11)di−=∑j=1nwjyij−yj−2.In equations (10) and (11), wj is the weight of the correction factor.


## 4.4. Calculate the Grey Relational Degree between Each Member Enterprise and the Positive Ideal Solutions and Negative Ideal Solutions

In this paper, the grey relational degree is introduced into the equation of the TOPSIS method close degree to reflect the consistency between the member enterprises and the ideal solution in the curve geometry [29].(12)rij+=miniminjΔij++ζmaximaxjΔij+Δij++ζmaximaxjΔij+,(13)rij−=miniminjΔij−+ζmaximaxjΔij−Δij−+ζmaximaxjΔij−,where Δij+=yij−yj+, Δij−=yij−yj−, and ζ is the resolution coefficient, generally take 0.5.Then, the grey relational degree is(14)G+=gj+|i=1,2,…,m,(15)G−=gj−|i=1,2,…,m,where(16)gj+=∑j=1nwjrij+,(17)gj−=∑j=1nwjrij−.


## 4.5. Calculate the Close Degree of Each Member Enterprise to the Ideal Point

Nondimensionalize the distance and grey relational degree:(18)ej+=minidi+di+,(19)ej−=minidi−di−,(20)hi+=gi+minigi+,(21)hi−=gi−minigi−,(22)ci+=αei++1−αhi+,(23)ci−=αei−+1−αhi−.In equations (22) and (23), αis the preference coefficient, which is generally 0.5.Then, the relative closeness of each member enterprise is(24)ci=ci−ci++ci−,i=1,2,…,m.The normalized relative closeness is(25)ci∗=ci∑i=1mci.


## 4.6. Calculate the Correction Coefficient

The classic Shapley value method defaults that the above correction factors are equal among member enterprises, so they are all1/n after normalization. This paper introduces the actual contribution of member enterprises and the equal contribution to compare the difference. Then, the correction coefficient can be obtained:(26)δi=ci−1n,i=1,2,…,m.


## 5. Modification to the Profit Allocation of Members of the Agricultural Machinery Service-Oriented Manufacturing Alliance

According to equation (26), the actual profit allocation modification amount of the member company is(27)Δφiv=vN⋅δi.Then, the actual profit obtained by theith member company is(28)∑i=1nφiv′=∑i=1nφiv+vN⋅δi=vN.Since∑i=1nδi=0, then(29)∑i=1nφiv′=∑i=1nφiv+vN⋅δi=vN.The modified Shapley value method satisfies the validity axiom and additivity axiom [30]. Therefore, improvement is feasible.


## 6. Case Analysis

A certain agricultural machinery service-oriented manufacturing alliance consists of three enterprises, agricultural machinery manufacturing enterprise A, producer service supplier B, and service production suppliers C. The agricultural machinery service-oriented manufacturing alliance maximizes overall profits by optimizing and integrating the core competence of the enterprise.Without forming an agricultural machinery service-oriented manufacturing alliance, agricultural machinery manufacturing enterprise A can obtain a profit of 5 million CNY, producer service supplier B can obtain a profit of 3.5 million CNY, and service production suppliers C can obtain a profit of 2.1 million CNY. Enterprises A and B can obtain a profit of 10.7 million CNY through cooperation, enterprises A and C can obtain a profit of 8.4 million CNY through cooperation, and enterprises B and C can obtain a profit of 7.4 million CNY through cooperation; enterprises A, B, and C form an agricultural machinery service-oriented manufacturing alliance to obtain a profit of 22 million CNY through cooperation.


### 6.1. Shapley Value Method of Profit Allocation

The profit allocation of enterprise A is shown in Table1.Table 1
Calculation table of profit distribution of firm A.
SAAUBAUCAUBUCVS50010708402200VS\A0350210740VS−VS\A5007206301460S1223WS1/31/61/61/3WSVS−VS\A500/3720/6630/61460/3We can obtain(30)φAv=5003+7206+6306+14603=52706=8.78334million CNY.In the same way, we can obtain(31)φBv=3503+5706+5306+13603=45206=7.53333million CNY,(32)φCv=2103+3406+39006+11303=34106=5.68333million CNY.Based on the Shapley value method, the profit allocation results of the member companies of the agricultural machinery service-oriented manufacturing alliance are shown in Table2.Table 2
The profit allocation results of service manufacturing alliance based on the Shapley value method.
Agricultural machinery manufacturing enterprise AProducer service supplier BService production suppliers CProfit allocation (million CNY)8.783347.533335.68333It is easy to verify that after cooperation, each member enterprise of the agricultural machinery service-oriented manufacturing alliance can obtain additional profits, namely,(33)φAv>vA,φBv>vB,φCv>vC.The profits of any member of the setΝfrom cooperation are greater than the sum of the two individual profits, namely,(34)φAv+φBv>10.7million CNY,(35)φAv+φCv>8.4million CNY,(36)φBv+φCv>7.4million CNY.In addition, it also meets(37)φAv+φBv+φCv=φN=22million CNY.


### 6.2. Modified Shapley Value Method of Profit Allocation

In this step, experts are required to evaluate and score the input level, effort level, risk factor, innovation level, and value-added factor of member enterprises A, B, and C. If there are evaluation tables of multiple experts, it is suggested to use Dempster–Shafer evidence theory to integrate the information of experts’ evaluation. Recently, studies of Dempster–Shafer evidence theory have improved the reliability and accuracy of processing highly conflicting data and reduced the problem of information loss in information processing [31, 32], which can be well applied to this step. The original data are shown in Table 3. The normalized matrix can be obtained from equation (5):Table 3
Original data.
Member companiesCorrection factorInvestment levelEffort levelRisk factorInnovation levelValue-added factorA0.860.450.930.580.82B0.780.860.850.820.48C0.570.950.600.550.46(38)Y=1010.11110.7240.8200.75810.05601000.Since the correction factors in this paper are all profit-oriented indicators, it can be seen from equations (6) and (7) that the positive ideal solution Y+ and the negative ideal solution Y− are, respectively,(39)Y+=1,1,1,1,1,Y−=0,0,0,0,0.In order to reduce the fuzziness and subjectivity in the process of evaluation as much as possible, the weight of correction factor is determined by fuzzy analytic hierarchy process; we can obtain(40)wj=0.32,0.14,0.15,0.12,0.27.We can obtaind+ according to Table 4 and equation (10):Table 4
Operator of ideal solution.
Investment levelEffort levelRisk factorInnovation levelValue-added factorTotalA00.14000.09500.235B0.0250.0050.00900.2390.277C0.32000.1500.1200.2700.860(41)d+=0.485,0.526,0.927.We can obtaind− according to Table 5 and equation (11):Table 5
Operator of negative ideal solution.
Investment levelEffort levelRisk factorInnovation levelValue-added factorTotalA0.32000.1500.0010.2700.741B0.1660.0940.0870.1200.0010.468C00.1400000.140(42)d−=0.861,0.684,0.374.From equations (12)–(15), we can get that the grey relational degree of member enterprises, and positive ideal solutions and negative ideal solutions are as follows:(43)G+=0.829,0.625,0.424,(44)G−=0.481,0.524,0.906.From equations (18)–(25), we can obtain the relative closeness between member enterprises and ideal point, and the preference coefficient is 0.5.(45)C+=1,0.838,0.517,(46)C−=0.483,0.563,1,(47)C=0.674,0.598,0.321,(48)C∗=0.423,0.375,0.202.We can obtain the correction coefficient from equation (26):(49)δA=0.089,δB=0.042,δC=−0.131.It is easy to know that the profit allocation of agricultural machinery manufacturing enterprise A is as follows:(50)φAv′=φAv+vN⋅δA=878.334+2200×0.089=10.74134million CNY.Similarly, we can obtain the profit allocation of producer service supplier B and service production suppliers C.


### 6.3. Comparison of Profit Allocation between Shapley Value Method and Modified Shapley Value Method

The results of profit allocation before and after the correction are shown in Table6. It can be seen from Table 6 that, in the improved profit allocation scheme, the profits from cooperation of agricultural machinery manufacturing enterprise, producer service supplier, and service production supplier are greater than those from independent operation. By comparing the revised profit allocation amount with the basic profit allocation, it is easy to know that the profit allocation amount of agricultural machinery manufacturing enterprise A and producer service supplier B increases, and the increase range is larger. Because service supplier C is lower than agricultural machinery manufacturing enterprise A and producer service supplier B in input level, effort level, risk factor, innovation level, and value-added factor in agricultural machinery service-oriented manufacturing alliance, the profit of service supplier C is reduced, but it is still larger than that of single operation.Table 6
The comparison of profit allocation scheme between the improved method and Shapley value method.
Member enterpriseNoncooperation profitShapley value method profitModified Shapley value method profitA500876.3341074.134B350753.333845.733C210568.333280.133Among them, the correction coefficient of agricultural machinery manufacturing enterprise A is 0.089, which indicates that the comprehensive level of the enterprise in investment level, effort level, risk factor, innovation level, and value-added factor is higher than the average level of agricultural machinery service-oriented manufacturing alliance. Therefore, agricultural machinery manufacturing enterprise A has obtained 1.958 million CNY compensation to motivate it. This also clearly shows the status of its core enterprise, which is in line with the actual situation of agricultural machinery service-oriented manufacturing alliance. The correction coefficient of producer service supplier B is 0.042, which indicates that the comprehensive level of the enterprise is slightly higher than the average level of agricultural machinery service manufacturing alliance, so it needs to get 924 thousand CNY compensation. The correction coefficient of service production supplier C is −0.132, which is lower than the average level of agricultural machinery service-oriented manufacturing alliance, so corresponding deduction is made to compensate other enterprises.


## 6.1. Shapley Value Method of Profit Allocation

The profit allocation of enterprise A is shown in Table1.Table 1
Calculation table of profit distribution of firm A.
SAAUBAUCAUBUCVS50010708402200VS\A0350210740VS−VS\A5007206301460S1223WS1/31/61/61/3WSVS−VS\A500/3720/6630/61460/3We can obtain(30)φAv=5003+7206+6306+14603=52706=8.78334million CNY.In the same way, we can obtain(31)φBv=3503+5706+5306+13603=45206=7.53333million CNY,(32)φCv=2103+3406+39006+11303=34106=5.68333million CNY.Based on the Shapley value method, the profit allocation results of the member companies of the agricultural machinery service-oriented manufacturing alliance are shown in Table2.Table 2
The profit allocation results of service manufacturing alliance based on the Shapley value method.
Agricultural machinery manufacturing enterprise AProducer service supplier BService production suppliers CProfit allocation (million CNY)8.783347.533335.68333It is easy to verify that after cooperation, each member enterprise of the agricultural machinery service-oriented manufacturing alliance can obtain additional profits, namely,(33)φAv>vA,φBv>vB,φCv>vC.The profits of any member of the setΝfrom cooperation are greater than the sum of the two individual profits, namely,(34)φAv+φBv>10.7million CNY,(35)φAv+φCv>8.4million CNY,(36)φBv+φCv>7.4million CNY.In addition, it also meets(37)φAv+φBv+φCv=φN=22million CNY.


## 6.2. Modified Shapley Value Method of Profit Allocation

In this step, experts are required to evaluate and score the input level, effort level, risk factor, innovation level, and value-added factor of member enterprises A, B, and C. If there are evaluation tables of multiple experts, it is suggested to use Dempster–Shafer evidence theory to integrate the information of experts’ evaluation. Recently, studies of Dempster–Shafer evidence theory have improved the reliability and accuracy of processing highly conflicting data and reduced the problem of information loss in information processing [31, 32], which can be well applied to this step. The original data are shown in Table 3. The normalized matrix can be obtained from equation (5):Table 3
Original data.
Member companiesCorrection factorInvestment levelEffort levelRisk factorInnovation levelValue-added factorA0.860.450.930.580.82B0.780.860.850.820.48C0.570.950.600.550.46(38)Y=1010.11110.7240.8200.75810.05601000.Since the correction factors in this paper are all profit-oriented indicators, it can be seen from equations (6) and (7) that the positive ideal solution Y+ and the negative ideal solution Y− are, respectively,(39)Y+=1,1,1,1,1,Y−=0,0,0,0,0.In order to reduce the fuzziness and subjectivity in the process of evaluation as much as possible, the weight of correction factor is determined by fuzzy analytic hierarchy process; we can obtain(40)wj=0.32,0.14,0.15,0.12,0.27.We can obtaind+ according to Table 4 and equation (10):Table 4
Operator of ideal solution.
Investment levelEffort levelRisk factorInnovation levelValue-added factorTotalA00.14000.09500.235B0.0250.0050.00900.2390.277C0.32000.1500.1200.2700.860(41)d+=0.485,0.526,0.927.We can obtaind− according to Table 5 and equation (11):Table 5
Operator of negative ideal solution.
Investment levelEffort levelRisk factorInnovation levelValue-added factorTotalA0.32000.1500.0010.2700.741B0.1660.0940.0870.1200.0010.468C00.1400000.140(42)d−=0.861,0.684,0.374.From equations (12)–(15), we can get that the grey relational degree of member enterprises, and positive ideal solutions and negative ideal solutions are as follows:(43)G+=0.829,0.625,0.424,(44)G−=0.481,0.524,0.906.From equations (18)–(25), we can obtain the relative closeness between member enterprises and ideal point, and the preference coefficient is 0.5.(45)C+=1,0.838,0.517,(46)C−=0.483,0.563,1,(47)C=0.674,0.598,0.321,(48)C∗=0.423,0.375,0.202.We can obtain the correction coefficient from equation (26):(49)δA=0.089,δB=0.042,δC=−0.131.It is easy to know that the profit allocation of agricultural machinery manufacturing enterprise A is as follows:(50)φAv′=φAv+vN⋅δA=878.334+2200×0.089=10.74134million CNY.Similarly, we can obtain the profit allocation of producer service supplier B and service production suppliers C.


## 6.3. Comparison of Profit Allocation between Shapley Value Method and Modified Shapley Value Method

The results of profit allocation before and after the correction are shown in Table6. It can be seen from Table 6 that, in the improved profit allocation scheme, the profits from cooperation of agricultural machinery manufacturing enterprise, producer service supplier, and service production supplier are greater than those from independent operation. By comparing the revised profit allocation amount with the basic profit allocation, it is easy to know that the profit allocation amount of agricultural machinery manufacturing enterprise A and producer service supplier B increases, and the increase range is larger. Because service supplier C is lower than agricultural machinery manufacturing enterprise A and producer service supplier B in input level, effort level, risk factor, innovation level, and value-added factor in agricultural machinery service-oriented manufacturing alliance, the profit of service supplier C is reduced, but it is still larger than that of single operation.Table 6
The comparison of profit allocation scheme between the improved method and Shapley value method.
Member enterpriseNoncooperation profitShapley value method profitModified Shapley value method profitA500876.3341074.134B350753.333845.733C210568.333280.133Among them, the correction coefficient of agricultural machinery manufacturing enterprise A is 0.089, which indicates that the comprehensive level of the enterprise in investment level, effort level, risk factor, innovation level, and value-added factor is higher than the average level of agricultural machinery service-oriented manufacturing alliance. Therefore, agricultural machinery manufacturing enterprise A has obtained 1.958 million CNY compensation to motivate it. This also clearly shows the status of its core enterprise, which is in line with the actual situation of agricultural machinery service-oriented manufacturing alliance. The correction coefficient of producer service supplier B is 0.042, which indicates that the comprehensive level of the enterprise is slightly higher than the average level of agricultural machinery service manufacturing alliance, so it needs to get 924 thousand CNY compensation. The correction coefficient of service production supplier C is −0.132, which is lower than the average level of agricultural machinery service-oriented manufacturing alliance, so corresponding deduction is made to compensate other enterprises.


## 7. Conclusions

On the premise that agricultural machinery enterprises and suppliers choose to cooperate and establish an agricultural machinery service-oriented manufacturing alliance, the problem of profit allocation is investigated. The profit allocation of agricultural machinery service-oriented manufacturing alliance based on modified Shapley value was constructed.At present, most of the existing research studies on profit allocation based on the Shapley value method adopted strategies such as adjusting the weight of each participant or using other indicators to replace the marginal profit contribution in Shapley value, but seldom considered the noneconomic behaviors of participants. Therefore, factors that affect the profit allocation are proposed in this paper, such as input level, effort level, innovation level, risk factor, and value-added factor. TOPSIS and GRA are used to determine the correction coefficient of member enterprises in the alliance, and profit allocation based on Shapley value is modified by the correction coefficient. The results show that the modified profit allocation model is consistent with the reality and effectively coordinates the profit allocation between agricultural machinery enterprises and suppliers.The following work may focus on the construction of evaluation index system. In fact, there are many factors that affect the profit allocation. Dempster–Shafer evidence theory is suggested to be a potential method for addressing the main influential factors of the profit allocation for the following research.



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*Source: 7632642-2021-10-11.xml*