A Determination Method of Optimal Customization Degree of Logistics Service Supply Chain with Mass Customization Service

Abstract

Customization degree is a very important field of mass customization. Its improvement could enhance customer satisfaction and further increase customer demand while correspondingly it will increase service price and decrease customer satisfaction and demand. Therefore this paper discusses how to deal with such issues in logistics service supply chain (LSSC) with a logistics service integrator (LSI) and a customer. With the establishment of customer demand function for logistics services and profit functions of the LSI and the customer, three different decision modes are proposed (i.e., customization degree dominated by LSI, customization degree dominated by customer, and customization degree decided by concentrated supply chain); many interesting findings are achieved. Firstly, to achieve customization cooperation between LSI and customer, measures should be taken to make the unit increase cost of the customized logistics services lower than a certain value. Secondly, there are differences between the optimal customization degree dominated by LSI and that dominated by customer. And in both cases, the dominator could realize more profit than the follower. Thirdly, with the profit secondary distribution strategy, the modified decentralized decision mode could accomplish the maximum profit achieved in centralized decision mode and meanwhile get the optimal customization degree.

1. Introduction

Currently, customer requirements for specialized and customized logistics services have increased. So, many logistics enterprises begin to explore the way that can meet the specialized service [1], change the logistics service mode, and even attempt to provide mass customization logistics service (MCLS) instead of only mass logistics service. In the MCLS environment, many logistics enterprises spontaneously form a logistics service supply chain (LSSC) through unions and integrations to meet customized demand and offer large-scale services [2, 3]. In a logistics service supply chain (LSSC) [3], a logistics service integrator (LSI) provides customized logistics services by integrating the service capacities of multiple functional logistics service providers (FLSPs); the LSI and the FLSPs constitute a logistics service supply chain (LSSC). For instance, Baogong Logistics Company, one of the largest LSI in China, integrates more than 500 storage companies, more than 1,200 highway transportation companies, and over 500 manual loading and unloading companies as its FLSPs and then accomplishes the integrated logistics services for its customers such as Procter & Gamble and Philips.

In mass customization service, the customization degree is a very important parameter which will directly affect the cooperation between the LSI and the customer. From the customer’s perspective, the improvement of customization degree can enhance customer satisfaction and then increase the customer demand. However, the customization degree also will lead to service price rising, which can result in the reduction of customer satisfaction and demand. And from the LSI’s perspective [4], although higher customization degree can get more customers demand, it also increases the cost of enterprise services and does not necessarily get higher profits. Obviously, from the practical level, coordinating the customization degree of service between the LSI and the customer reasonably is a significant precondition for them to cooperate. This is also the practical motivation for the research.

This paper is also motivated by the existing literature shortages. From the literature research, on the one hand, most of the research on mass customization degree is for qualitative analysis (e.g., da Silveira et al. [5]; Bardakci and Whitelock [6]; Cavusoglu et al. [7]). Though some scholars have turned to quantitative research (e.g., Lian and Ji [8]; Sami Spahi [9]; Xu et al. [10]), generally the conclusion is about the relationship between customization degree and a certain influence factor which does not give the exact customization degree. On the other hand, most of the study on mass customization degree is about manufacturing supply chain, and studying on LSSC in mass customization is still very few. Moreover, the existing decision research about LSSC in mass customization [11–14] does not consider the problem of optimal customization degree. Therefore, this paper will focus on the issue of customization degree in mass customization service. From the perspective of maximizing profit of the LSI and the customer, the optimal service customization degree could be determined.

The organizational structure of this paper is shown as follows. Section 2 reviews the related contents about mass customization production mode, customization degree, and mass customization service mode. In Section 3, with customer demand function for logistics services established, the LSI and the customer’s profit function are proposed. Section 4 illustrates three different decision models about customization degree. And how the profit of the LSI or customer as well as the overall supply chain change is discussed along with the customization degree in different decision models. Then the decision model of the optimal customization degree based on the profits secondary distribution strategy is proposed. In Section 5, the numerical analysis is carried out within Matlab 8.0, and it verifies these conclusions made in this paper. Section 6 summarizes main conclusions and points out future research prospects.

2. Literature Review

At present, the research on mass customization degree mainly focuses on manufacturing supply chain, while the research on service supply chain, especially logistics service supply chain, is still relatively lacking. Hence, according to the research contents of this paper, the literature review section mainly includes two aspects. (1) Summarize the related research results about Mass customization production mode and customization degree; (2) Review the literatures of mass customization service mode.

2.1. Mass Customization Production Mode and Customization Degree

Since the concept of mass customization production mode was proposed, many enterprises have implemented this advanced mode of production. Mass customization has become a key competitive advantage for many companies, and many enterprises have benefited from the production mode [15, 16], such as automobile enterprises, clothing enterprises, and computer manufacturing enterprises. Many scholars have done much exploration about the theory of mass customization in different areas. Currently, the research field of mass customization mainly concentrated in the food industry [17], electronic industry [18], large-scale engineering products [19], mobile phones [20], and other production areas. Although the study of mass customization has obtained many achievements, according to the research of Fogliatto et al. [21] who has reviewed the related literatures of MC over the past decade, there are many problems about MC still not solved, such as supply chain coordination, quality control, and rapid manufacturing are still the research field of MC for the future.

In mass customization, the coordination of customization degree is very important. The implementation of mass customization will cause the price of customized products increased [6]. They find that customization is not optimal when the cost of soliciting customer preference information is sufficiently high [7]. Therefore, it is particularly important to determine an appropriate customization degree. To determine an appropriate customization degree, customer demand and enterprise’s production capacity should be analyzed scientifically [5]. As the research of mass customization degree gets more attention, the research of customization degree is gradually changing from qualitative research to quantitative research. Liang and Zhou [22] from the perspective of customer satisfaction and enterprise cost, discussed how enterprise determines the customization degree reasonably, when the enterprise’s ability of MC is certain. Li and Cheng [23] analyzed the optimization problem of customization degree from two aspects, which are product family functional of MC and customer satisfaction. Lian and Ji [8] and Zhou et al. [4] analyzed the customization degree of mass customized products and discussed the relationship between the customization degree and the market demand and the manufacturer’s profits. Sami Spahi [9] defined a customization degree of products from the perspective of product structure and established an optimization model to determine the optimal customization degree that can meet organizational goals. Using the combination analysis method, Xu et al. [10] established a measurement model of product customization degree which is based on the attribute significance. At the point of view of dynamic customization degree, Wang [24] analyzed the demand and supplied uncertain problems. He also did a further research [25] on different industry implementing VMI strategy cost model and a quantitative model for the customization degree.

While the existing researches on customization degree are reviewed, it is found that most of them are about qualitative analysis. Though some scholars have turned to quantitative research, generally the conclusion is about a relationship between customization degree and a certain influence factor which does not give the exact expression of customization degree.

2.2. Mass Customization Service Mode

In the service industry, especially logistics services industry, with large-scale logistics service turned to mass customization logistics service, some scholars have begun to research mass customization service problems. But the literatures still lack research on the optimal customization degree of service. For example, van Hoek [26] analyzed the challenges to the third party logistics service providers (LSP) which is put forward by MC and proposed a logistics services framework for the delay of MC. Chandra and Kamrani [11] discussed the impact of the MC demand on the MC strategy and logistics service in supply chain. On the basis of Koste and Malhotra’s research [27], Lummus et al. [28] established a supply chain service model which can meet the demand of customers personalized, from the perspective of MC. Liu et al. [12] studied the issue of time schedule in mass customization logistics service mode. Liu et al. [13] also studied the issue of order allocation of logistics service supply chain with mass customization logistics service. In addition, the decision problem of customer order decoupling point (CODP) with mass customization service is also beginning to be studied [14].

The literature review indicates that now the study of the optimal customization degree is relatively lack in mass customization service. Although scholars have focused on the optimal customization degree of production, these studies have focused on the relationship between customization degree and a certain influence factor which does not give the exact customization degree.

Therefore, for the deficiency of previous literatures, this paper will focus on the coordinated issue of customization degree in mass customization service. And from the perspective of maximizing profit of the LSI and the customer, the optimal service customization degree would be determined.

3. Model Building

This part mainly studies model building. In Section 3.1, the problem description is presented and the model assumptions and variables are given. Then, in Section 3.2, the demand function of the customer for logistics services is built, and on this basis, the LSI and the customer’s profit function are provided.

3.1. Problem Description

In a LSSC with mass customization service, the coordination issue of customization degree between a LSI and a customer (e.g., a certain manufacturing enterprise) would be discussed. The LSI can provide large-scale service and customized service to customer, and the customer’s demand consists of a certain customization degree. When the LSI receives the order of customer, he will analyze the customization degree and then provide the corresponding logistics services to the customer.

The customer who has chosen mass customization service improved the market reaction speed, compared with the merchants that did not choose mass customization service. Therefore, it will increase product customers and sales volume of product and greatly improve the customer satisfaction. Figure 1 shows the model of LSSC with mass customization service.

Figure 1 

Logistics service supply chain (LSSC) model.

Table 1 shows the notations of the model. Other assumptions of the model are as follows.(1)In fact, when the LSI 𝐼 received the customer’s orders, he will deliver them to the FLSP 𝑆 who can provide Large-scale service and customized service. It is assumed that the capacity of the FLSP 𝑆 could always meet the demand of customer, and its capacity could never be insufficient. To simplify the analysis, we regard the FLSP 𝑆 as a branch of the LSI 𝐼, and the LSI can provide mass customization to customer directly, when he received the customer’s orders.(2)It is assumed that the customization degree is 𝛾=𝑛/𝑚 (𝑚 represents the total link number of service that customer demand, 𝑛 represents the link number of customized service that the LSI provides to the customer, 𝑚≥𝑛) [4], so 𝛾∈[0,1]. When 𝛾=0, it represents the LSI provides complete large-scale service to customer; when 0<𝛾<1, it represents the LSI provides mass customization service to customer; when 𝛾=1, it represents the LSI provides complete customization service to customer.(3)The LSI’s cost includes the cost of large-scale service and the cost of customization service. When the customer accepts the mass customization service, the production cost of the customer’s product 𝑃₀ and the unit price of the product 𝑃₁ are all constant.(4)Generally, the unit cost of customization service is higher than that of large scale service. Therefore, if the cost of the customization service of the LSI is too high, it will result in an excessive price to customer, which will also decrease customer demand. The profit of the LSI may be decreased. So it is assumed that the increased cost, compared with complete large-scale logistics service, should be shared with the customer and the LSI together; the proportion, respectively, is 𝛽 and 1−𝛽.

Table 1 

Model notations.

3.2. Model Building

3.2.1. The Demand of Customer for Logistics Service

In the MCLS, the demand of customer will increase with the increase of customization degree, but with the increase of customized price, it will reduce. The demand function of economics 𝑄=𝑎−𝑏𝑃 just defines the relationship between the demand and the price. Considering that with the increase of customization degree, the demand of customer also will increase, so the customization degree factor 𝑡 is introduced and set as 𝑡=𝛾/(1−𝛾). Therefore, referring to the above demand function, the total logistics service demand function of customer could be shown as: 𝑄=𝑎−𝑏𝑃+𝑡𝑄₀𝛾=𝑎−𝑏𝑃+𝑄1−𝛾⁰. (1)

In (1), 𝑎, 𝑏 are constants greater than 0, 𝑏𝑃 represents the decreased demand that is just caused by the price, and (𝛾/(1−𝛾))𝑄₀ represents the decreased demand that is just caused by customization degree. When the LSI provides complete large-scale logistics service to the customer, the demand of customer 𝑄₁ should not be less than 0, namely, when 𝛾=0, the equation of customer’s demand is shown in the following: 𝑄₁=𝑎−𝑏𝑃≥0. (2)

When providing MCLS to customer, the LSI’s total cost mainly includes the cost of large-scale logistics 𝐶₁ and the cost of customization logistics service 𝑡𝐶₂, as shown in the following: 𝐶=𝐶₁+𝑡𝐶₂=𝐶₁+𝛾𝐶1−𝛾². (3)

And in this equation, 𝐶₂ is the unit increased cost that compared with complete large-scale logistics service that the LSI provides to customer. 𝑡=𝛾/(1−𝛾) is the customization degree factor.

According to the assumption (4), the increased cost, compared with complete large-scale logistics service, should be borne by the customer and the LSI corporately, and the proportion, respectively, is 𝛽 and 1−𝛽. Therefore, the unit price of MCLS that the LSI provides to customer 𝑃 includes two parts, one is large-scale logistics service’s cost 𝐶₁(1+𝜔) which considers the LSI’s marginal profit, and the other is Customized logistics service costs 𝛽𝑡𝐶₂, which considers the compensation of customized service. So 𝑃 can be expressed as follows: 𝑃=𝐶₁(1+𝜔)+𝛽𝑡𝐶₂=𝐶₁()𝛾1+𝜔+𝛽𝐶1−𝛾². (4)

With (4) substituted into (1), the total demand of customer for logistics service with MCLS is presented as follows: 𝑄=𝑎−𝑏𝐶₁(1+𝜔)+𝛽𝑡𝐶₂+𝑡𝑄₀=𝑎−𝑏𝐶₁()𝛾1+𝜔+𝛽𝐶1−𝛾²+𝛾𝑄1−𝛾⁰. (5)

To further study the impact of customized services on the demand of customer, take the first-order derivative of 𝑄 versus 𝑡𝜕𝑄𝜕𝑡=𝑄₀−𝑏𝐶₂𝛽. (6)

Equation (6) represents the change degree of customer’s demand with the change of customization degree factor, which could be defined as 𝜇, that is, the change rate of demand caused by customization, which is seen in the following: 𝜇=𝑄₀−𝑏𝐶₂𝛽. (7)

Theorem 1. The total demand of customer for logistics service is influenced by both the price and the customization degree. And it will increase with the increase of customization degree, but with the increase of price, it will decrease.

The state of Theorem 1 is obvious. It can be obtained from the former analysis, and in the article of Zhou et al. [4], the similar state can be found.

Corollary 2. When the increased demand caused by the increasing customization degree is higher than the decreased demand caused by the increasing price, the change rate of demand will be positive; namely, 𝜇>0; and when the increased demand caused by the increasing customization degree is lower than the decreased demand caused by the increasing price, the change rate of demand will be negative; namely, 𝜇<0. But only when 𝜇>0, it will be a feasible solution for the MCLS.

Proof. When 𝜇<0, the increased demand caused by the increasing customization degree is lower than the decreased demand caused by the increasing price. According to the assumption (3), it is assumed that the unit price of the product 𝑃₁ is constant; hence, in this condition, if choosing the MCLS, the profit of the LSI and the customer will be lower than choosing the complete large-scale logistics service (see Appendix A for a detailed proof).
Hence, considering the LSI and the customer pursuing the maximum profit, when 𝜇<0, both of them will not choose the MCLS. Therefore, 𝜇<0 would not be taken into consideration and later studies would focus on the condition where 𝜇≥0.

3.2.2. The Profit Function of the LSI

The profit of the LSI is the difference between its total income and total cost, it can be expressed as follows: 𝜋₁=𝑃𝑄−𝐶𝑄. (8)

Substituting (1), (3), and (4) into (8), the profit function of the LSI will turn to 𝜋₁=−𝐶₁𝜔+𝐶₂𝑡×−1+𝛽−𝑎−𝑄₀𝑡+𝑏𝐶₁+𝐶₁𝜔+𝐶₂𝑡𝛽. (9)

In order to determine the optimal customization degree that can maximize the profit of the LSI, the first-order and the second-order derivative of 𝜋₁ on 𝑡 are calculated as follows. Consider 𝜕𝜋₁𝜕𝑡=𝑄₀𝐶₁𝜔+2𝐶₂𝑡−1+𝛽+𝑎𝐶₂−1+𝛽+𝑏𝐶₂−2𝐶₂𝑡−1+𝛽𝛽+𝐶₁,𝜕1+𝜔−𝛽−2𝜔𝛽₂𝜋₁𝜕𝑡²=2𝐶₂−1+𝛽𝑄₀−𝑏𝐶₂𝛽. (10)

As 𝜇=𝑄₀−𝑏𝐶₂𝛽≥0 (seen in Theorem 1) and 𝜕²𝜋₁/𝜕𝑡²<0, hence the function 𝜋₁ is strictly convex function on 𝑡(−∞,+∞).

Therefore, to optimize profit of the LSI, 𝜕𝜋₁/𝜕𝑡=0 should be required in first-order condition, resulting in 𝑡₁=(𝐶₁𝜔[𝑄₀−𝑏𝐶₂𝛽]−𝐶₂(1−𝛽)[𝑎−𝑏𝐶₁(1+𝜔)])/(2𝐶₂(1−𝛽)(𝑄₀−𝑏𝐶₂𝛽)).

In the mathematical calculation, 𝑡₁ can be all the real numbers. It is the point which can make (9) maximum. But in this paper it is the customization degree factor, so it should be positive.

As 𝑡₁∈(−∞,+∞) in this situation, it should be carefully discussed to limit 𝑡∈(0,+∞).(1)When 𝑡₁>0, on [0,+∞), at first the function of 𝜋₁ monotonically increases, then it monotonically decreases. When 𝑡=𝑡₁, the LSI gets the maximum profit, and the maximum profit is 𝜋^′₁=𝐶₁−𝑄₀𝜔+𝑏𝐶₂(1+𝜔−𝛽)+𝑎𝐶₂(−1+𝛽)²4𝐶₂−1+𝛽−𝑄₀+𝑏𝐶₂𝛽. (11)(2)When 𝑡₁≤0, on [0,+∞), the function of 𝜋₁ monotonically decreases. When 𝑡₁=0; namely, the SLI provides complete large-scale service to customer; the LSI will get the maximum profit. Hence, in this condition the SLI will refuse to provide MCLS to customer.

Therefore, in order to ensure the LSI provides MCLS to customer, it should be ensured that 𝑡₁>0. And obviously 𝐶₂ is a function of 𝑡₁, so it can be assumed that 𝑡₁=𝑓₁𝐶₂=𝐶₁𝜔𝑄₀−𝑏𝐶₂𝛽−𝐶₂1−𝛽𝑎−𝑏𝐶₁(1+𝜔)2𝐶₂1−𝛽𝑄₀−𝑏𝐶₂𝛽. (12)

Then it only needs to ensure 𝑓₁(𝐶₂)>0.

3.2.3. The Profit Function of the LSI

According to the description of the model, when the customer received the products which uses the MCLS, he will sell these products to the product customers to gain the profits. Hence, the profit of the customer is the difference between his total income and total cost as follows: 𝜋₂=𝑃₁𝑄−𝑃+𝑃₀𝑄. (13)

Substituting (1) and (4) into (13), the profit function of the customer will become 𝜋₂=𝑃₀−𝑃₁+𝐶₁(1+𝜔)+𝐶₂×𝑡𝛽−𝑎−𝑄₀𝑡+𝑏𝐶₁(1+𝜔)+𝐶₂𝑡𝛽. (14)

To further study the impact of the customization degree on customer service profit and determine the optimal customization degree that can maximize the profit of the customer, the first-order and the second-order derivative of 𝜋₂ on 𝑡 are presented as follows: 𝜕𝜋₂=𝜕𝑡−𝑄₀+𝑏𝐶₂𝛽𝑃₀−𝑃₁+𝐶₁(1+𝜔)+𝐶₂𝑡𝛽+𝐶₂𝛽−𝑎−𝑄₀𝑡+𝑏𝐶₁(1+𝜔)+𝐶₂;𝜕𝑡𝛽₂𝜋₂𝜕𝑡²=2𝐶₂𝛽−𝑄₀+𝑏𝐶₂𝛽. (15)

From Theorem 1, 𝜇=𝑄₀−𝑏𝐶₂𝛽≥0 and 0<𝛽<1, so 𝜕²𝜋₂/𝜕𝑡²<0 can be obtained; hence the function 𝜋₂ is strictly convex function on 𝑡(−∞,+∞).

Therefore, finding the optimal profit of the customer only requires first-order condition 𝜕𝜋₂/𝜕𝑡=0. After some calculation, 𝑡₂ could be obtained as follows: 𝑡₂=𝑃₀−𝑃₁+𝐶₁(1+𝜔)𝑄₀−𝑏𝐶₂𝛽+𝐶₂𝛽𝑎−𝑏𝐶₁(×1+𝜔)2𝐶₂𝛽−𝑄₀+𝑏𝐶₂𝛽⁻¹. (16)

Similar to the LSI, in the mathematical calculation, 𝑡₂ can be all the real numbers. It is the point which can make (14) maximum. But in this paper it is the customization degree factor, so it should be positive, and thus it should be limited as 𝑡∈(0,+∞).(1)When 𝑡₂>0, on [0,+∞), at first the function of 𝜋₂ monotonically increases, then it monotonically decreases. When 𝑡=𝑡₂, the customer gets the maximum profit, and the maximum profit is 𝜋^′₂=−−𝑃₁𝑄₀+𝐶₁𝑄₀(1+𝜔)−𝑎𝐶₂𝛽+𝑏𝐶₂𝑃₁𝛽+𝑃₀𝑄₀−𝑏𝐶₂𝛽²×4𝐶₂𝛽−𝑄₀+𝑏𝐶₂𝛽⁻¹. (17)(2)When 𝑡₂≤0, on [0,+∞), the function of 𝜋₂ monotonically decreases; that is, with the increase of the customization degree, customer profit will gradually decrease. When 𝑡₂=0, namely, when the customer receives complete large-scale service, the customer will get the maximum profit. Hence, in this condition the customer will refuse to choose MCLS.

Therefore, to ensure that the customer chooses MCLS, 𝑡₂>0 should be guaranteed. And obviously 𝐶₂ is a function of 𝑡₂, so it could be assumed that 𝑡₂=𝑓₂𝐶₂=𝐶₁𝜔𝑄₀−𝑏𝐶₂𝛽−𝐶₂1−𝛽𝑎−𝑏𝐶₁(1+𝜔)2𝐶₂1−𝛽𝑄₀−𝑏𝐶₂𝛽. (18)

Then it only needs to ensure 𝑓₂(𝐶₂)>0.

Considering the conditions that the LSI provides the MCLS and the customer chooses the MCLS, Theorem 3 could be obtained.

Theorem 3. Only when 𝐶₂<min{𝐶₁𝜔𝜇/(1−𝛽)𝑄₁,[𝑃₁−𝑃₀−𝐶₁(1+𝜔)]𝜇/𝛽𝑄₁}, the LSI and the customer will cooperate with MCLS.

Proof. In order to ensure that both LSI and the customer choose the MCLS, 𝑓₁(𝐶₂)>0 and 𝑓₂(𝐶₂)>0 must be guaranteed. As 𝑓₁(𝐶₂)>0, 𝐶₂<𝐶₁𝜔𝜇/(1−𝛽)𝑄₁. And 𝑓₂(𝐶₂)>0, 𝐶₂<[𝑃₁−𝑃₀−𝐶₁(1+𝜔)]𝜇/𝛽𝑄₁. Therefore when 𝐶₂<min{𝐶₁𝜔𝜇/(1−𝛽)𝑄₁,[𝑃₁−𝑃₀−𝐶₁(1+𝜔)]𝜇/𝛽𝑄₁}, that is, the unit increased cost compared with complete large-scale logistics service is less than a certain value, the LSI and the customer would likely cooperate with MCLS.

4. The Analysis of the Customization Degree in Three Different Decision Modes

From Section 3, it has been found that the customization degree factors which can maximize the profit of LSI and customer are different. Therefore, in order to determine the customization degree that can satisfy the LSI and the customer coordination could be taken into consideration. In this section, three different decision modes are considered: customization degree dominated by LSI (Case A), customization degree dominated by customer (Case B), and customization degree decided by concentrated supply chain (Case C). And we will explore the effect of different decision modes on optimal customization degree factor and put forward the optimal customization degree decision model based on the profit secondary distribution strategy.

4.1. The Customization Degree Dominated by LSI

As a leader in the coordination of the supply chain, the LSI will provide logistics service to customer with the customization degree factor 𝑡₁, which can maximize his profit. And the customer has to cooperate with the LSI at 𝑡=𝑡₁. In this case, the customization degree factor is 𝑡^caseA=𝑡₁=𝐶₁𝜔𝑄₀−𝑏𝐶₂𝛽−𝐶₂1−𝛽𝑎−𝑏𝐶₁(1+𝜔)2𝐶₂1−𝛽𝑄₀−𝑏𝐶₂𝛽. (19)

The profit of the LSI is 𝜋^caseA₁=𝐶₁−𝑄₀𝜔+𝑏𝐶₂(1+𝜔−𝛽)+𝑎𝐶₂(−1+𝛽)²4𝐶₂−1+𝛽−𝑄₀+𝑏𝐶₂𝛽. (20)

The profit of the customer is 𝜋^caseA₂=𝐶₁𝑄₀𝜔−𝑏𝐶₂1+𝜔−𝛽+𝑎𝐶₂∗2𝑄1−𝛽−1+𝛽₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀+𝑎𝐶₂𝛽−𝐶₁𝑏𝛽𝐶₂1+𝜔−𝛽−2(1+𝜔)𝑄₀+𝛽(2+𝜔)𝑄₀×4𝐶₂(−1+𝛽)²(−𝑄₀+𝑏𝐶₂𝛽)⁻¹. (21)

The profit of whole supply chain is 𝜋^caseA_𝑇=𝜋^caseA₁+𝜋^caseA₂.

4.2. The Customization Degree Dominated by Customer

When the customization degree is dominated by customer, the customer will choose logistics service with the customization degree factor 𝑡₂, which can maximize his profit. And the LSI has to cooperate with the customer at 𝑡=𝑡₂. In this case, the customization degree factor is 𝑡^caseB=𝑡₂=𝑃₀−𝑃₁+𝐶₁(1+𝜔)𝑄₀−𝑏𝐶₂𝛽+𝐶₂𝛽𝑎−𝑏𝐶₁(×1+𝜔)2𝐶₂𝛽−𝑄₀+𝑏𝐶₂𝛽⁻¹. (22)

The profit of the LSI is 𝜋^caseB₁=−𝑃₁𝑄₀+𝐶₁𝑄₀(1+𝜔)−𝑎𝐶₂𝛽+𝑏𝐶₂𝑃₁𝛽+𝑃₀𝑄₀−𝑏𝐶₂𝛽∗−1+𝛽𝑄₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝑎𝐶₂𝛽+𝐶₁2𝑏𝐶₂𝛽−1−𝜔+𝛽+𝑄₀×1+𝜔−𝛽+𝜔𝛽4𝐶₂𝛽²−𝑄₀+𝑏𝐶₂𝛽⁻¹. (23)

The profit of the customer is 𝜋^caseB₂=−−𝑃₁𝑄₀+𝐶₁𝑄₀(1+𝜔)−𝑎𝐶₂𝛽+𝑏𝐶₂𝑃₁𝛽+𝑃₀𝑄₀−𝑏𝐶₂𝛽²×4𝐶₂𝛽−𝑄₀+𝑏𝐶₂𝛽⁻¹. (24)

The profit of whole supply chain is 𝜋^caseB_𝑇=𝜋^caseB₁+𝜋^caseB₂.

4.3. The Customization Degree Decided by Concentrated Supply Chain

In this case, the LSI and the customer form a joint venture to achieve the goal of optimizing the supply chain as a whole. The total profit of the whole supply chain is the difference between the LSI and the customer’s total income and total cost. That is 𝜋_𝑇=𝑃₁𝑄−𝑃₀+𝐶𝑄. (25)

Substituting (1) and (3) into (25), the profit function of the supply chain will become 𝜋_𝑇=𝑃₁−𝐶₁−𝑃₀−𝐶₂𝑡×𝑎+𝑄₀𝑡−𝑏𝐶₁(1+𝜔)+𝐶₂𝑡𝛽. (26)

To further study the impact of the customization degree on the profit of the whole supply chain, take the first-order and the second-order derivative of 𝜋_𝑇 versus 𝑡; then 𝜕𝜋_𝑇𝜕𝑡=−𝑎𝐶₂−𝑄₀𝐶₁+𝑃₀−𝑃₁+2𝐶₂𝑡+𝑏𝐶₂𝑃₀−𝑃₁+2𝐶₂𝑡𝛽+𝐶₁,𝜕1+𝜔+𝛽₂𝜋_𝑇𝜕𝑡²=2𝐶₂−𝑄₀+𝑏𝐶₂𝛽=−2𝐶₂𝜇. (27)

Let 𝜕𝜋_𝑇/𝜕𝑡=0; then 𝑡₃=(𝐶₂[𝑎−𝑏𝐶₁(1+𝜔)]+(𝑃₀−𝑃₁+𝐶₁)[𝑄₀−𝑏𝐶₂𝛽])/(−2𝐶₂(𝑄₀−𝑏𝐶₂𝛽)).

Similar to the above, in the mathematical calculation, 𝑡₃ can be all the real numbers. It is the point which can make (26) maximum. But in this paper it is the customization degree factor, so it should be positive.

From Theorem 1, it could be known that 𝜇=𝑄₀−𝑏𝐶₂𝛽≥0, so 𝜕²𝜋_𝑇/𝜕𝑡²<0. According to Theorem 3, if the LSI and the customer cooperate together, it should be ensured that 𝑓₁(𝐶₂)>0, 𝑓₂(𝐶₂)>0. According to these conclusions, it can be proved that 𝑡₃>0 (seen in the Appendix B). Hence the function 𝜋_𝑇 is strictly convex function on 𝑡(0,+∞). At last, the whole supply chain will get its maximal profit when 𝑡=𝑡₃, and the maximal profit is 𝜋^′_𝑇=−𝑎𝐶₂+𝐶₁+𝑃₀−𝑃₁𝑄₀+𝑏𝐶₂𝐶₁(1+𝜔)+𝛽𝑃₁−𝐶₁−𝑃₀²×4𝐶₂𝑄₀−𝑏𝐶₂𝛽⁻¹. (28)

In the LSSC with centralized decision mode, the target is to get the maximal profit of the whole supply chain. So in this case, the customization degree factor is 𝑡^caseC=𝑡₃=𝐶₂𝑎−𝑏𝐶₁(+𝑃1+𝜔)₀−𝑃₁+𝐶₁𝑄₀−𝑏𝐶₂𝛽×−2𝐶₂𝑄₀−𝑏𝐶₂𝛽⁻¹. (29)

The profit of the LSI is 𝜋^caseC₁=𝑎𝐶₂−𝑏𝐶₁𝐶₂(1+𝜔)+𝑄₀+𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝐶₁∗𝑎𝐶₂−1+𝛽−𝑄₀2𝐶₁𝜔+−1+𝛽𝑃₁−𝐶₁−𝑃₀+𝑏𝐶₂𝑃₁−𝑃₀−1+𝛽𝛽+𝐶₁×1+𝜔−𝛽1+𝛽4𝐶₂−𝑄₀+𝑏𝐶₂𝛽⁻¹. (30)

The profit of the customer is 𝜋^caseC₂=−𝑎𝐶₂−𝑏𝐶₁𝐶₂(1+𝜔)+𝑄₀+𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝐶₁∗2𝑃₁𝑄₀−𝑏𝐶₂𝛽−𝑃₁𝛽𝑄₀−𝑏𝐶₂𝛽+𝑃₀−2+𝛽𝑄₀−𝑏𝐶₂𝛽+𝑎𝐶₂𝛽+𝐶₁𝑏𝐶₂1+𝜔−𝛽𝛽+𝑄₀×−2−2𝜔+𝛽4𝐶₂−𝑄₀+𝑏𝐶₂𝛽⁻¹. (31)

The profit of the whole supply chain (i.e., the centralized supply chain) is 𝜋^caseC_𝑇=−𝑎𝐶₂+𝐶₁+𝑃₀−𝑃₁𝑄₀+𝑏𝐶₂𝐶₁(1+𝜔)+𝛽𝑃₁−𝐶₁−𝑃₀²×4𝐶₂𝑄₀−𝑏𝐶₂𝛽⁻¹. (32)

Table 2 shows three optimal decision values in different decision modes. Through comparing the profit of different decision modes, Theorems 4 and 5 could be obtained as follows.

Table 2 

Profits comparing in different LSSC decision mode.

Theorem 4. The profit of the centralized supply chain is greater than that of LSSC dominated by LSI or customer.

Theorem 5. Whether LSSC is dominated by LSI or customer, the dominator will obtain more profit than he is a partner: That is to say 𝜋₁^{𝑐𝑎𝑠𝑒𝐴}≥𝜋₁^{𝑐𝑎𝑠𝑒𝐶}≥𝜋₁^{𝑐𝑎𝑠𝑒𝐵} and 𝜋₂^{𝑐𝑎𝑠𝑒𝐵}≥𝜋₂^{𝑐𝑎𝑠𝑒𝐶}≥𝜋₂^{𝑐𝑎𝑠𝑒𝐴}.

For more detailed proof of Theorems 4 and 5, please see the Appendices C and D.

4.4. The Decision Model of Optimal Customization Degree Based on the Profit Secondary Distribution Strategy

Through calculation of Table 2, it has been known that 𝜋^caseA₁≥𝜋^caseC₁≥𝜋^caseB₁ and 𝜋^caseB₂≥𝜋^caseC₂≥𝜋^caseA₂. Obviously, the profits of the LSI or the customer are less than the profits generated in their own leading, when they carry out the cooperation mode of Case C. Neither of them have the motives to carry out the cooperation model of Case C. Therefore, it is particularly important to design a reasonable profit coordinate mechanism, which can make the LSI and the customer implement the centralized decision of mass customization LSSC. So a profit secondary distribution strategy is introduced in this section.

At first, the profit losses of the LSI and the customer is calculated when the centralized decision mode is chosen. And the profit losses of the LSI are Δ𝜋₁=𝜋^caseC₁−𝜋^caseA₁𝑄=−⁰−𝑏𝐶₂𝛽𝐶₁𝜔+1−𝛽𝑃₀+𝐶₁−𝑃₁²4𝐶₂.1−𝛽 (33)

The profit losses of the customer are Δ𝜋₂=𝜋^caseC₂−𝜋^caseB₂𝑄=−⁰−𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝐶₁1−𝛽−𝐶₁𝜔²4𝐶₂𝛽. (34)

Obviously, Δ𝜋₁<0, Δ𝜋₂<0.

A good profit coordinate mechanism is to decrease the loss as little as possible. It is necessary for us to make profit secondary distribution in order to make both of them choose a common customization degree which can maximize the profit of the whole supply chain. Assumption in the cooperative enterprise is composed of the LSI and the customer, the profit given to the LSI is 𝑀₁, the profit given to the customer is 𝑀₂, and 𝑀₁+𝑀₂=0. Then according to NASH Bargaining Model, the optimization model is shown as follows: Max𝑍=Δ𝜋₁+𝑀₁Δ𝜋₂+𝑀₂s.t.𝑀₁+𝑀₂=0. (35)

With (33) and (34) substituted into (35), it could be presented as 𝑍=𝑀₁+𝑄₀−𝑏𝐶₂𝛽𝐶₁𝜔+(1−𝛽)(𝐶₁+𝑃₀−𝑃₁)²4𝐶₂×1−𝛽−𝑀₁+𝑄₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝐶₁1−𝛽−𝐶₁𝜔²4𝐶₂𝛽. (36)

In order to determine the optimal 𝑀₁that can maximize 𝑍, take the first-order and the second-order derivative of 𝑍 as follows: 𝜕𝑍𝜕𝑀₁=14−8𝑀+−1+2𝛽𝑄₀−𝑏𝐶₂𝛽×𝐶₁𝜔−𝑃₁−𝐶₁−𝑃₀1−𝛽²×𝐶₂1−𝛽𝛽⁻¹;𝜕²𝑍𝜕𝑀²₁=−2. (37)

Let 𝜕𝑍/𝜕𝑀₁=0; then 𝑀₁=−1+2𝛽𝑄₀−𝑏𝐶₂𝛽×𝐶₁𝜔−𝑃₁−𝐶₁−𝑃₀1−𝛽²×8𝐶₂1−𝛽𝛽⁻¹. (38)

Obviously, 𝑀₁=(−1+2𝛽)(𝑄₀−𝑏𝐶₂𝛽)[𝐶₁𝜔−(𝑃₁−𝐶₁−𝑃₀)(1−𝛽)]²/8𝐶₂(1−𝛽)𝛽 is the optimal 𝑀₁ which can maximize 𝑍.

Therefore, 𝑀₁=(−1+2𝛽)(𝑄₀−𝑏𝐶₂𝛽)[𝐶₁𝜔−(𝑃₁−𝐶₁−𝑃₀)(1−𝛽)]²/8𝐶₂(1−𝛽)𝛽; 𝑀₂=−(−1+2𝛽)(𝑄₀−𝑏𝐶₂𝛽)[𝐶₁𝜔−(𝑃₁−𝐶₁−𝑃₀)(1−𝛽)]²/8𝐶₂(1−𝛽)𝛽.

Hence, the customization degree factor is 𝑡^caseC which eventually both of them agreed. And finally, the profit of the LSI is 𝜋^caseC₁+𝑀₁ and the profit of the customer is 𝜋^caseC₂+𝑀₂. Then, substituting 𝑡^caseC into 𝑡=𝛾/(1−𝛾), the optimal customization degree is found where 𝛾=𝑡^caseC/(1+𝑡^caseC).

5. Numerical Analysis

In Section 5, in order to verify some of the theorems put forward above, numerical analysis is conducted by the software of Matlab 8.0 for numerical calculation. In Section 5.1, how the profits of the LSI and the customer change with the customization degree factor t is discussed. In Section 5.2, in different decision modes, how the optimal customized degree factor and the profits (such as the LSI’s profit, the customer’s profit and the total profit of LSI and customer) change would be discussed. The parameters in numerical analysis are as follows: 𝐶₁=50, 𝜔=0.3, 𝛽=0.8, 𝑎=1000, 𝑏=10, 𝑄₀=20, 𝑃₀=1000, 𝑃₁=1200.

5.1. The Change of LSI’s Profit and Customer’s Profit with the Changing of 𝑡

First of all, the range of the unit increased cost 𝐶₂ is figured out. As the case that the change rate of demand is greater than zero is considered, 𝜇=𝑄₀−𝑏𝐶₂𝛽>0 should be ensured. From Theorem 3, if the LSI and the customer both choose MCLS, it need f₁(C₂)>0 and f₂(C₂)>0. Substituting them into (12) and (18), 𝐶₂<1.58 is easily obtained.

When the unit increased cost 𝐶₂ is set as a certain value, the change of LSI’s profit and customer’s profit with 𝑡 is shown in Figures 2 and 3.

Figure 2 

The change of the LSI’s profit with 𝑡, when 𝐶2=1.5.

Figure 3 

The change of the customer’s profit with 𝑡, when 𝐶2=1.5.

From Figures 2 and 3, it can be seen that point 𝐴₁, 𝐴₂ is the highest point of the curve, respectively. Obviously, at first, the profit of LSI and customer increases and then it will decrease with the increase of customization degree factor 𝑡. Thus the customization degree should not be too high, and a reasonable customization degree can ensure that the LSI and the customer achieve maximum profit. In addition, when 𝑡=𝑡₁, the LSI achieves the maximum profit, but when 𝑡=𝑡₂, the customer achieves the maximum profit, and 𝑡₁<𝑡₂. So the LSI and the customer can not realize optimal synchronously. Therefore, it is necessary to coordinate the customization degree of service between the LSI and the customer.

5.2. The Change of the Profit of the LSI and the Customer in Three Different Decision Modes

In order to further explore the impact of the customization degree on the profit and the best way to coordinate, the unit increased cost 𝐶₂ is chosen as 1.57, 1.5, 1.3, 1.1, …, 0.5, 0.3, 0.1, 0.01, respectively; then study how the LSI’s profit, the customer’s profit, and the total profit of LSI and customer change in different decision modes. Detailed results are shown in Tables 3, 4, and 5.

Table 3 

The optimal customization degree factor and the optimal profit when the customization degree is dominated by LSI.

Table 4 

The optimal customization degree factor and the optimal profit when the customization degree is dominated by customer.

Table 5 

The optimal customization degree factor and profit when the customization degree decided by concentrated supply chain, after applying secondary distribution strategy.

From Table 3, when customization degree is dominated by LSI, along with the decrease of the unit increased cost, the customization degree factor of the LSI is gradually increasing, and the profit of the LSI and the customer will also increase. But when 𝐶₂ takes the same value, comparing 𝜋^caseA_𝑇 in Table 3 with 𝜋^caseC_𝑇 in Table 5, the total profit of the LSI and the customer is still lower than the LSSC with centralized decision mode. Therefore this decision mode is not the optimal.

From Table 4, when customization degree is dominated by customer, along with the decrease of the unit increased cost, the customization degree factor expected by the customer will increase and the profit of the customer also will increase; however, the profit of the LSI will decrease, even to be negative. Comparing 𝜋^caseB_𝑇 in Table 4 with 𝜋^caseC_𝑇 in Table 5, it can be found that the total profit of the LSI and the customer is still lower than that in the LSSC with centralized decision mode. Therefore the decision mode dominated by the customer is not the optimal.

From Table 5, when the customization degree is decided by concentrated supply chain, if secondary distribution strategy is applied, along with the decreasing of the unit increased cost, the customization degree factor will increase gradually, and the profit of the LSI 𝜋_last1 and the profit of the customer 𝜋_last2 will increase. In addition, comparing Tables 3, 4, and 5, some other conclusions have been found.(1)When the customization degree is decided by concentrated supply chain, the total profit of the LSI and the customer (𝜋^caseC_𝑇 in Table 5) is higher than that dominated by the LSI (𝜋^caseA_𝑇 in Table 3) or the customer (𝜋^caseB_𝑇 in Table 4). So Theorem 4 is proved. At the same time it shows that the LSSC with centralized decision mode is the best coordination strategy. And the customization degree factor is optimal in this case.(2)When the customization degree is dominated by LSI, the profit of the LSI (𝜋^caseA₁ in Table 3) is greater than that dominated by customer (𝜋^caseB₁ in Table 4), and it is also greater than that decided by concentrated supply chain (𝜋^caseC₁ in Table 5). And when the customer is dominating the decision mode, the profit of the customer is greater than that in the LSI dominating (𝜋^caseA₂ in Table 3), and it is also greater than that in the LSSC with centralized decision mode (𝜋^caseC₂ in Table 5). Hence, the Theorem 5 is proved.(3)In addition, it is found that 𝑡^caseC is between 𝑡^caseA and 𝑡^caseB. And after applying secondary distribution strategy, the profit of the LSI 𝜋^′₁ and the profit of customer 𝜋^′₂ are lower than the profit generated in the modes dominated by themselves, respectively, but higher than the profit generated in the mode dominated by the partner. And the loss of profit is minimum, compared with those dominated by themselves.

6. Conclusions and Future Works

6.1. Main Conclusions

While a LSSC with mass customization service is considered, this paper discussed the coordination issue of customization degree between the LSI and the customer. First, demand function of the customer for logistics services is built, and on this basis, the LSI and the customer’s profit function is provided. And then three different decision modes about customization degree are presented. After that, in different decision modes, how the profit of the LSI, custome, and the overall supply chain changes with the customization degree is analyzed in detail. The main conclusions are listed as follows.(1)The total demand of customer for logistics service is influenced by both the price and the customization degree. And it will increase with the increase of customization degree, but with the increase of price, it will decrease.(2)When the increased demand caused by the increasing customization degree is higher than the decreased demand caused by the increasing price, the change rate of demand will be positive; and when the increased demand caused by the increasing customization degree is lower than the decreased demand caused by the increasing price, the change rate of demand will be negative.(3)To achieve MCLS cooperation between the LSI and the customer, the LSI should make the unit increase cost of the customized logistics services lower than a certain value; that is, 𝐶₂<min{𝐶₁𝜔𝜇/(1−𝛽)𝑄₁,[𝑃₁−𝑃₀−𝐶₁(1+𝜔)]𝜇/𝛽𝑄₁}.(4)Whoever dominates the customization degree realizes more profit than as a participator in decentralized LSSC or as partner in centralized LSSC.(5)In the LSSC with centralized decision mode, the profit of the whole supply chain is greater than decentralized decision mode. And a profits secondary distribution strategy could be used to obtain maximum profit which is the same as the profit of LSSC with centralized decision mode.

6.2. Research Limitations and Future Work

There are some limitations in the profit model of the LSI and the customer. For example, it is assumed that the unit price of the product 𝑃₁ is determined by market as a constant value. However, when the product is sensitive to time, the greater the customization degree of logistics service is (e.g., the product delivery time is shorter), the higher the price of the product will be. Therefore, the decision model of variable 𝑃₁ could be considered in future research. In addition, to simplify the model, LSI’s cost is divided into two parts, that is, the large-scale service cost and the customization service cost in this paper. However, with the varying of customization degree, the peculiar monitoring cost of customized logistics service may be changed. These problems need to be explored in detail in future research.

Appendices

A. Proof That When 𝜇<0, Choosing the MCLS, the Profit of the LSI and the Customer Will Be Lower Than Choosing the Complete Large-Scale Logistics Service

Proof. when the customer chooses complete large-scale logistics service, the customization degree factor is 0; that is, 𝑡=0. In this case, with 𝑡=0 substituted into (9), the profit of the LSI can be obtained as 𝜋₁^𝑡=0=𝐶₁𝜔[𝑎−𝑏𝐶₁(1+𝜔)] and with 𝑡=0 substituted into (14), the profit of the customer can be obtained as 𝜋₂^𝑡=0=[𝑃₁−𝑃₀−𝐶₁(1+𝜔)][𝑎−𝑏𝐶₁(1+𝜔)].
When the customer chooses mass customization logistics service, according to (9), the profit of the LSI can be obtained as 𝜋₁=[𝐶₁𝜔+𝐶₂𝑡(−1+𝛽)][𝑎−𝑏𝐶₁(1+𝜔)+𝜇𝑡]. According to (14), the profit of the customer can be obtained as 𝜋₂=𝑃₁−𝑃₀−𝐶₁(1+𝜔)−𝐶₂𝑡𝛽𝑎−𝑏𝐶₁(1+𝜔)+𝜇𝑡. (A.1)
By comparison, when 𝜇<0, we can get 𝑎−𝑏𝐶₁(1+𝜔)+𝜇𝑡<𝑎−𝑏𝐶₁(1+𝜔). And because of 0<𝛽<1, we can get 𝐶₁𝜔+𝐶₂𝑡(−1+𝛽)<𝐶₁𝜔,𝑃₁−𝑃₀−𝐶₁(1+𝜔)−𝐶₂𝑡𝛽<𝑃₁−𝑃₀−𝐶₁(1+𝜔). Hence, 𝜋₁<𝜋₁^𝑡=0 and 𝜋₂<𝜋₂^𝑡=0 can be obtained.
In conclusion, when 𝜇<0, the LSI and the customer that choose mass customization logistics service will get lower profit than choosing complete large-scale logistics service.

B. Under the Conditions of 𝑓₁(𝐶₂)>0, 𝑓₂(𝐶₂)>0, Then 𝑡₃>0

Proof. Because that change rate of demand is expressed as 𝜇=𝑄₀−𝑏𝐶₂𝛽 and the demand is expressed as 𝑄₁=𝑎−𝑏𝐶₁(1+𝜔) when the LSI provide mass customization logistics service for the customer, 𝑓₁(𝐶₂),𝑓₂(𝐶₂),𝑡₃ can be changed as follows: 𝑓₁𝐶₂=𝑡₁=𝐶₁𝜔𝑄₀−𝑏𝐶₂𝛽−𝐶₂1−𝛽𝑎−𝑏𝐶₁(1+𝜔)2𝐶₂1−𝛽𝑄₀−𝑏𝐶₂𝛽=𝐶₁𝜔𝜇−𝐶₂1−𝛽𝑄₁2𝐶₂𝜇,𝑓1−𝛽₂𝐶₂=𝑡₂=𝑃₀−𝑃₁+𝐶₁(1+𝜔)𝑄₀−𝑏𝐶₂𝛽+𝐶₂𝛽𝑎−𝑏𝐶₁(×1+𝜔)2𝐶₂𝛽−𝑄₀+𝑏𝐶₂𝛽⁻¹=𝑃₀−𝑃₁+𝐶₁(1+𝜔)𝜇+𝐶₂𝛽𝑄₁−2𝐶₂,𝑡𝛽𝜇₃=𝐶₂𝑎−𝑏𝐶₁(+𝑃1+𝜔)₀−𝑃₁+𝐶₁𝑄₀−𝑏𝐶₂𝛽×−2𝐶₂𝑄₀−𝑏𝐶₂𝛽⁻¹=𝐶₂𝑄₁+𝑃₀−𝑃₁+𝐶₁𝜇−2𝐶₂𝜇=𝑄₁+𝑃−2𝜇¹−𝑃₀−𝐶₁2𝐶₂. (B.1)
According to 𝑓₁(𝐶₂)>0, we can get 𝐶₁𝜔/𝐶₂>(1−𝛽)𝑄₁/𝜇; and according to 𝑓₂(𝐶₂)>0, we can get [𝑃₁−𝑃₀−𝐶₁(1+𝜔)]/𝐶₂>𝛽𝑄₁/𝜇. So (𝑃₁−𝑃₀−𝐶₁)/𝐶₂>𝑄₁/𝜇, if both left and right sides of the two formulae above are added up respectively. Then when can get (𝑃₁−𝑃₀−𝐶₁)/2𝐶₂>𝑄₁/2𝜇, hence 𝑡₃>0.

C. The Proof of Theorem 4

Proof. Subtract the whole profit of supply chain in two conditions that the LSI dominates the decision mode and the customer dominates the decision mode, respectively, from the whole profit of supply chain in the LSSC with centralized decision mode.
We can get 𝜋^case3_𝑇−𝜋^case1_𝑇=𝑄₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀1−𝛽+𝐶₁−1−𝜔+𝛽²4𝐶₂−1+𝛽²;𝜋^case3_𝑇−𝜋^case2_𝑇=𝑄₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀1−𝛽+𝐶₁−1−𝜔+𝛽²4𝐶₂𝛽². (C.1)
Because of the change rate of demand is 𝜇=𝑄₀−𝑏𝐶₂𝛽>0 and the remaining items are all greater than 0 obviously, 𝜋^case3_𝑇−𝜋^case1_𝑇>0 and 𝜋^case3_𝑇−𝜋^case1_𝑇>0 can be obtained. By the methods of subtraction and comparison, the conclusion that the whole profit of supply chain in the LSSC with centralized decision mode is greater than the whole profit of supply chain in the condition that the LSI dominates the decision mode or the customer dominate the decision mode.

D. The Proof of Theorem 5

Proof. Firstly, compare the profit of the LSI in different decision modes: 𝜋^case1₁−𝜋^case2₁=𝑄₀−𝑏𝐶₂𝛽𝐶₁𝜔+1−𝛽𝐶₁+𝑃₀−𝑃₁²4𝐶₂1−𝛽𝛽²;𝜋^case1₁−𝜋^case3₁=𝑄₀−𝑏𝐶₂𝛽𝐶₁𝜔+1−𝛽𝐶₁+𝑃₀−𝑃₁²4𝐶₂.1−𝛽 (D.1)
Because of change rate of demand 𝜇=𝑄₀−𝑏𝐶₂𝛽>0,0<𝛽<1 and the remaining items all obviously greater than 0, 𝜋^case1₁−𝜋^case2₁>0,𝜋^case1₁−𝜋^case3₁>0 can be obtained. The profit of the LSI is greater when the LSI as a leader in the coordination of supply Chain rather than the customer as a leader or in the LSSC with centralized decision mode.
Then, compare the profit of the customer in different coordination modes. Consider 𝜋^case2₂−𝜋^case1₂=𝑄₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝐶₁1−𝛽−𝐶₁𝜔²4𝐶₂1−𝛽²𝛽;𝜋^case2₂−𝜋^case3₂=𝑄₀−𝑏𝐶₂𝛽𝑃₁−𝑃₀−𝐶₁1−𝛽−𝐶₁𝜔²4𝐶₂𝛽. (D.2)
Because change rate of demand 𝜇=𝑄₀−𝑏𝐶₂𝛽>0, 0<𝛽<1 and the remaining items all obviously greater than 0, 𝜋^case2₂−𝜋^case1₂>0, 𝜋^case2₂−𝜋^case3₂>0 can be obtained, the profit of the customer is greater when the customer is a leader in the coordination of supply Chain rather than the LSI as a leader or in the LSSC with centralized decision mode.
Above all, a conclusion can be obtained that whoever dominates the customization degree realizes greater profit than the partner and also greater than the LSSC with centralized decision.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

This research is supported by the National Natural Science Foundation of China (Grant number 71372156), supported by Humanity and Social Science Youth foundation of Ministry of Education of China (Grant number 2013YJC630098), and sponsored by China State Scholarship Fund and Independent Innovation Foundation of Tianjin University. The reviewers’ comments are also highly appreciated.