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For durable products, the high quality after-sales service has been playing an increasingly important role in consumers’ purchase behaviors. We mainly study a supply chain composed of a manufacturer and a retailer. In a process of products sales, the manufacturer will provide a basic free quality assurance service. On this basis, the retailer provides paid optional quality assurance service to consumers to promote sales. Users are divided into two categories in this paper: users with no optional service and users with optional services. We derive the equilibrium decisions between the manufacturer and the retailer under the following two cases: (i) the optional after-sales service level and the wholesale price determined by the manufacturer and the retail price determined by the retailer; (ii) the wholesale price determined by the manufacturer and the optional after-sales service level and the retail price determined by the retailer.

In recent years, as the living standard of people is improving with the rapid development of economy, people become more and more sensitive to nonprice factors they could enjoy rather than a price attribute. In 2007 the global consumer electronics products consumer research showed that service has become the second important factor that affects consumer’s purchase behaviors. More and more enterprises have realized this point in time. Relying solely on price advantage, it is difficult to maintain a lasting competitive edge, such as Lenovo, WAL-MART, SONY, General Electric, and DELL. These enterprises also have to provide better services to customers so that they can maintain their market shares.

For the same product, providing different services in daily life is also becoming more common. When we buy a computer, we will encounter this kind of situation. Basic quality assurance services are to be purchased, but not all consumers are satisfied with this basic service; there is a part of the consumers who want to get more and better service. Therefore, for retailers and manufacturers, it is necessary to set up a reasonable and optional service policy to meet more consumers.

Kameshwaran et al. [

In the model of Cohen and Whang [

In fact, the optional service to a certain extent to meet the needs of customers is a stimulating factor, so we assume that the demand is subject to the impact of optional services. This is consistent with the study of Xu et al. [

Our problem is most relevant to Kurata and Nam [

The remainder of this paper is organized as follows. The second part is the problem description and modeling. In the third part, we establish the model where the optional service level is decided by the manufacturer. The fourth part is the model analysis and the solution. In the fifth part, we establish the model where the optional service level is decided by the retailer. The sixth part is the model analysis and the solution. The seventh part is the comparisons of the two kinds of equilibrium decisions by numerical results. Finally, conclusions and the future research directions are addressed in Section

We consider a supply chain composed of a manufacturer and a retailer, in which the manufacturer sells the product to the retailer at the wholesale price

There are two categories of users in the market. The first category of users only use basic service items, such as the basic quality assurance services; the second category of users are not satisfied with the basic services but also need enterprises to provide more optional services, such as extended warranty service. We use

If one user chooses the optional service, she/he needs to pay a certain service charge, which we call the optional service price. Of course, the optional service price changes with the optional service level. Let

In order to maximize their own profits, the manufacturer and the retailer need to make decisions based on their own pieces of information. We assume that the basic service level is known as well as the optional service price given by the retailer. We consider the decision-making problem of supply chain members under the condition of determined environment.

In this part, the optional service level

Hence, the manufacturer’s profit function is

In the above equation, the first item is the sales revenue, and the second is the cost of the optional service, as Tsay and Agrawal [

Then, the retailer’s profit function can be formulated by the following:

Based on (

We can see that, based on the analysis stated above, in this model the manufacturer determines the wholesale price

We now derive chain members’ optimal strategies by maximizing their profits in the above general optimization model.

For any given wholesale price

Consider the following derivatives:

Because

In the following, all best response functions are denoted by the superscript “′” and let the superscript “

For any given

It can be easily proved by solving the first condition

Paying attention to the impact of wholesale price and optional service level on the retailer’s best response function, we derive the first derivatives of

Obviously, if the manufacturer increases the wholesale price

The inequality

As the retailer’s operation problem, its profit must have a maximum value in any practical case.

Bringing the formulation of

Consider the following derivatives:

From the existence condition of extreme function for multivariable function, there must be

The manufacturer equilibrium decisions satisfy

With the best response function for retail price

Let

Bring it into

Bringing

The equilibrium wholesale price

From (

From (

From (

If

From (

It is easy to know that if

If

From (

It is easy to know that if

The equilibrium optional service level

From (

From (

From (

From (

(i) If

From (

It is easy to know that if

From (

It is easy to know that if

In this part, the optional service level

Hence, the manufacturer profit function is

Then, the profit function of retailer can be formulated by the following:

In the above equation, the first item is sales revenue, and the second is the cost of the optional service, as Tsay and Agrawal [

Based on (

We can see that, based on the analysis stated above, in this model the manufacturer determines the wholesale price

We now derive chain members’ optimal strategies by maximizing their profits in the above general optimization model.

Firstly, the following parameters hold.

The inequalities

As the retailer’s operation problem, its profit must have a maximum value in any practical case. Consider the following derivatives:

From the existence condition of extreme function for multivariable function, there must be

For any given

Let

Bring it into

It is easy to get that

Among them,

Paying attention to the impact of wholesale price on the retailer’s best response function, we derive the first derivatives of

The profit function

Bringing the retailer best response functions into the manufacturer profit function

Consider the following derivatives:

Because

The manufacturer equilibrium decisions satisfy

Let (

Bringing

In this section, we will analyze the changes of different parameters of supply chain members by numerical simulation. The objective of numerical analyses is to examine how the equilibrium profit functions change when the values of parameters change. And we compare the equilibrium decisions and the equilibrium profits under two models. The baseline parameters are set as follows:

The ordinate axes in Figures

Effects of unit production cost.

Effects of optional service cost coefficient.

Effects of service elastic coefficient of the first category of customers.

Effects of market base of the first category of customers.

Effects of market base of the second category of customers.

Effects of price sensitive coefficient.

Effects of service elastic coefficient of the second category of customers.

Effects of service elastic coefficient.

Figure

Figure

Figure

Figure

Figure

Considering the existence of price and service competition, the supply chain equilibrium decision problem has become an important problem in the field of management science. Optional service is one aspect of the service and also becomes more and more common in real life. In this paper, we assume that the basic service level is known and we use a general demand function to describe the impact of product price and optional service level on market demand in such a competitive environment. Moreover, a Stackelberg model structure is proposed between the retailer and the manufacturer in a two-echelon supply chain. We obtain the optimal wholesale price, the optimal retail price, and the optimal optional service level when the optional service level is, respectively, determined by the manufacturer and the retailer. Finally, in order to compare the two models in the optimal equilibrium decision, the profit of the members, and the whole supply chain, we carried out numerical simulation, which has certain guiding significance to the enterprise management.

However, our research leaves several unanswered questions for future research. In this paper, we assume that the demand function is determined, while, in real life, the market demand is often random. Assuming that the demand function is random is a good extension of this paper. We also add some constraints to some known parameters. The other limitation of the model is that we cannot compare the equilibrium decisions of the two models in theory because of the complexity of the equilibrium decision. Hence, how to simplify the model is another important research direction.

The authors declare that they have no competing interests.

This research is supported by the National Natural Science Foundation of China (NSFC), Research Fund no. 71302112.