The paper studied the process of product renewal in a supply chain, which is composed of one manufacturer and one retailer. There are original product and renewal product in the supply chain. A market share shift model for renewal product was firstly built on a increment function and a shift function. Based on the model, the decisionmaking plane consisting of two variables was divided into four areas. Since the process of product renewal was divided into two stages, StackelbergNash game model and Stackelbergmerger game model could be built to describe this process. The optimal solutions of product pricing strategy of two games were obtained. The relationships between renewal rate, cost, pricing strategy, and profits were got by numerical simulation. Some insights were obtained from this paper. Higher renewal rate will make participants’ profits and total profit increase at the same margin cost. What is more important, the way of the optimal decision making of the SC was that RP comes onto the market with a great price differential between OP and RP.
With the development of IT, the speed of product renewal process becomes faster and faster. This situation brings some new problems to traditional supply chain (SC), such as the dynamic nature of an SC and the relationship coordination between participants of an SC. The dynamic nature of an SC includes the dynamic variety of products; that is to say, the market requests SC to satisfy diverse needs of customer with the fastest speed, as well as the best quality, which calls for SC improving performance to adapt to the product variety. A valid way for SC enterprises to follow the variety of market is to renew their existing products, which can make full use of enterprise’s existing resources and supply/distribution outlet of SC. Thus, SC will adapt to a variational market economically and quickly. Product renewal is an effective method that strengthens a SC enterprise’s core competitiveness, and it will even impact on the survival of a enterprise. There are quite a few cases that enterprises collapse because of the mistakes of product renewal decision making, such as the failure of WANGAN Computer Corp.
Now, it is necessary to differentiate “renewal product (RP)” from “innovated product (IP).” IP’s structure and principle are different from original product (OP), while RP’s main structure and principle are the same as OP. Furthermore, RP has some appended components or upgraded functions. Thereby, RP is the renewal of existing product. At present, most researches are mainly focused on complete new product innovation, including management of product innovation process, optimization of product innovation investment, promotion of new product, and design of product innovation drive mechanism. Dereli et al. proposed a framework of the rapid response for innovative product development using reverse engineering approach [
At present, the researches concerning product renewal have been carried out. Bass P. I. and Bass F. M. had proposed a new product expansion model and studied the process of multigeneration renewal products coming onto market [
The other focus of product renewal is on the marketing process of renewal product, especially pricing decision. Luo and Tu studied a price decision problem for product renewal supply chain based on Nash game [
The RP and OP are virtually differentiated products. When they are on sale at the same market, they can substitute for each other. Compared with common differentiated products, the substitution of RP for OP is unidirectional and partial. Therefore, the coming of RP onto market will cause some influences on OP market. At the same time, each entity in SC has independent profit. Therefore, the coordination of SC will become much more complex if there are RP and OP in the SC. A potent tool to coordinate SC is price. The fluctuation of price will make supply and demand tend to an equilibrium. On the other hand, price’s fluctuation can make the profit of each entity in SC distributed reasonably, so as to achieve the aim of coordination of SC. Therefore pricing strategy is the main content of the paper.
The SC including OP and RP is called product renewal SC. The change of market share caused by product renewal in the SC is studied in this paper. When there is a RP in SC, the enterprises in SC will make strategies for both of OP and RP to achieve an equilibrium of enterprises’ profits. Compared with other researches, this paper firstly studied Stackelberg game for product renewal, aiming at solving complex decisionmaking question in actual renewal SC, and obtained some novel insights.
The rest of this paper is organized as follows. Product renewal model is formulated in Section
Consider a twostage SC which is composed of one manufacturer and one retailer. First, suppose the manufacturer produces product
In order to fully describe the model of the SC, we state the following hypotheses.
The retailer is in a monopoly position; that is, only the retailer sells
Suppose that the consumer’s repurchase is possible and each time one customer only buys one product. When there is an RP, some customers of OP may shift to buying RP in other words, there is repetition purchase for the products studied in this paper, such as toys, and small electric appliance equipment.
There is no stochastic demand in the market, so the demand is only decided by price.
Inventory is not considered.
The manufacturer’s productivity is sufficient enough to satisfy demand.
There is no fixed cost for unit product, and margin production cost is an invariant for manufacturer.
The product renewal generally causes its performance promotion.
The SC model of this paper is as follows: there is one manufacturer and one retailer in SC. Suppose that the manufacturer produces products
The structure of renewal products SC.
Product renewal rate is used to measure the change of product performance caused by product renewal. Combined with price and performance price ratio
The RP marketing process can be divided into two stages:
In Stage 1. there is only OP in market. Supposing the OP price of
In expression (
In Stage 2. RP comes onto the market and competes with OP. If RP comes onto the market, it will cause several changes in the market:
There exists an OP
From
The market shift function
If
Existing
If
If
With the increase of
Let
Let
From Theorem
The changes of
According to Figure
According to Figure
The functions (
Letting
In addition, product renewal will make marginal production cost change from
Figure
Area I: the area surrounded by axis
Area II: the area surrounded by lines
Area III: the area surrounded by axis
Area IV: the areas excepting area I, II, and III.
The change of
In area I, Letting
In area II, given
In area III,
Considering
In area IV,
The shift functions and increment functions in different areas are shown in Table
The table of area’s shift function and increment function.

 

Area I 


Area II 


Area III  0 

Area IV  0  0 
According to the feature (vii) of shift function, the zero point of increment function is bigger than that of shift function, namely,
(i) In area I,
(ii) In area II,
(iii) In area III,
(iv) In area IV,
Product renewal process can be regarded as two stages. First, manufacturer and retailer make their optimal decisions for OP
In Stage 1: There is a decision for product
In Stage 2: There is a decision for product
The game solving process is divided into three steps. Following three steps, the optimal solution of product renewal StackelbergNash game can be derived.
In Step 1, given
In Step 2, put the optimal reaction function or the optimal value into the profit functions of Step 1, and the optimal solution
In Step 3, letting
In StackelbergNash game, in areas I, II, and III, given
In area I
Therefore,
The StackelbergNash decisionmaking process can be divided into the following three situations.
In area I, there is no StackelbergNash equilibrium.
In area II, there exists only one optimal pricing strategy for StackelbergNash game.
In area III, there exists only one optimal pricing strategy for StackelbergNash game.
(i) In area I, according to (
From the supply chain’s structure, it is obvious that
(ii) In area II,
From Step 2, two binary cubic equations can be got. Because the analytic solution of the equations cannot be found, the numerical method can be used to find the optimal approximate solution
(iii) In area III,
The value of Nah equilibrium for area I,
From the supply chain structure, it is obvious that:
In the decisionmaking process of StackelbergNash game mentioned previously, if the manufacturer and retailer constitute a manufacturing and sales league to maximize the SC profit, that is, there is no retailer, and manufacturer sells its product in market directly, the product renewal StackelbergNash decisionmaking process will become a Stackelbergmerger decisionmaking process. This process can be divided into two stages, and this process will play a Stackelbergmerger game. In this condition, the league which consists of the manufacturer and the retailer can be regarded as a enterprise, because the league’s decision variables are the retail price
In Stage 1, the league sells OP
In Stage 2, the league sells OP
The solving process of Stackelbergmerger game is divided into three steps, and by three steps the optimal solution of product renewal Stackelbergmerger game can be derived.
In Step 1, OP retail price
In Step 2, put the optimal reaction function
In Step 3, put
In Stackelbergmerger game, in areas I, II, and III, given
In area I
The process of the Stackelbergmerger game is divided into three situations according to areas I, II, III. There exists only one optimal pricing strategy for Stackelbergmerger game in each situation.
(i) In area I,
Base on Theorem
The value of
From
(ii) In area II, the total profit of SC can be got from the sum of (
Based on Theorem
From Step 2,
From Step 3, the optimal value of
(iii) In area III, the total profit of SC can be derived from the sum of (
Based on Theorem
From Step 2, the optimal of
In area I, the optimal value of
In area I, from
In (
The key of the Stackelbergmerger game is how to distribute the total profit between manufacturer and retailer. Using Nash bargaining model can coordinate profit of each entity [
Look at mobile phone, for example. There are two types of mobile phone
The effect of RP cost changing in StackelbergNash game (
Case result 












284.3316  266.0267  286.2994  267.7067  

104.3316  86.0267  106.2994  87.7067  

371.5171  540.0000  393.8308  560.0000  

171.5171  340.0000  163.8308  330.0000  

365.9493  388.6632  352.0533  381.8052  392.5987  355.4133 

365.9493  543.0343  880.0000  381.8052  557.6615  890.0000 

268.1014  222.6737  295.8933  236.3896  214.8025  289.1733 

178.8881  117.0312  75.7487  154.7302  110.3807  71.7150 

268.1014  29.6436  0  236.3896  13.1986  0 

0  193.0301  295.8933  0  201.6040  289.1733 

536.2027  252.3172  295.8933  472.7791  228.0011  289.1733 

38502  43776  35173  41811  

28502  33776  25173  31811  

46298  67005  77553  33729  60346  73621 
The effect of RP cost changing in StackelbergNash decision (
Case result 












279.2893  253.4637  281.5733  255.4993  

99.2893  73.4637  101.5733  75.4993  

399.1822  606.6667  422.1999  626.6667  

199.1822  406.6667  192.1999  396.6667  

366.3029  378.5785  326.9000  382.0862  383.1467  331.0000 

366.3029  598.3644  1013.3000  382.0862  614.3999  1023.3000 

267.3943  242.8429  346.1452  232.8276  233.7066  338.0030 

221.1238  155.7372  107.0742  192.0417  146.8800  101.8516 

267.3943  73.1396  0  235.8276  54.7557  00 

0  169.7034  346.1452  0  178.9509  338.0030 

534.7886  315.9825  346.1452  471.6552  288.4624  338.0030 

54466  59910  49319  57120  

44466  49910  39319  47120  

51701  98933  109820  37958  88639  104250 
From numerical simulation in Tables
There is no StackelbergNash equilibrium in area I, and so Stackelbergmerger is used to simulate this situation. The total profit in this situation is the optimal profit of area I. Obviously, the optimal total profit of area I is less than those of areas II and III. Therefore, area I
For all parameter conditions, the profits of manufacturer, retailer, and the total profit of SC in area III are greater than those of area II (in area II, there is a little difference between the price of RP and OP). Because the manufacturer and retailer are rational, the final decisionmaking result
The profit of retailer in areas II and III is greater than that of manufacturer, mainly because the retailer is a direct participator of market, and it reacts very rapidly when the demand of market changes. Therefore, the retailer can adjust the process of decision making in the fastest time to increase revenue and reduce losses. The manufacturer’s reaction to the market relies on the retailer decision making information’s transmission, and there is a delay in the transmission process. Accordingly, the manufacturer’s profit is less than that of the retailer.
With the cost of RP increasing, the profits of the manufacturer, retailer, and total will decrease.
If the cost of RP is constant, with product renewal rate
The parameters are the same as Section
The effect of RP cost changing in Stackelbergmerger model (
Case result 












365.9493  346.2141  267.8400  381.8052  346.2141  273.5100 

365.9493  458.5284  720.0000  381.8052  473.5284  735.0000 

268.1014  307.5718  464.3200  236.3896  307.5718  452.9800 

178.8881  182.4446  178.2989  154.7302  178.7538  168.5086 

268.1014  98.4720  0  236.3896  61.5634  0 

0  209.0998  464.3200  0  246.0084  452.9800 

536.2027  406.0438  464.3200  472.7791  369.1352  452.9800 

46298  87780  107800  33729  79981  102600 
The effect of RP cost changing in Stackelbergmerger model (
Case result 












366.3029  346.2141  225.4400  382.0862  346.2141  232.3100 

366.3029  505.3881  820.0000  382.0862  520.3881  835.0000 

267.3943  307.5718  549.1200  232.8276  307.5718  535.3800 

221.1238  220.1259  254.7917  192.0417  216.4351  241.9918 

267.3943  187.6227  0  235.8276  150.7141  0 

0  119.491  549.1200  0  156.8577  535.3800 

534.7886  495.1945  549.1200  471.6552  458.2859  535.3800 

51701  123350  150770  37958  111730  143320 
From numerical simulation in Tables
The profits in areas II and III of Stackelbergmerger game are greater than those in area I, so the Stackelbergmerger pricing strategy would not be in area I. The situation is consistent with StackelbergNash game.
If OP adopts lowprice strategy, and RP adopts highprice strategy, the total profit will be maximum value; in other words, area III is the optimal merger pricing area for the SC. The situation and its reason are the same as those of StackelbergNash game.
If the cost of RP is constant, with the product renewal rate increasing, the total profit will increase obviously.
With the cost of RP increasing, the total profit will decrease.
From the analysis of Sections
This paper studied the process of product renewal. A market shift model of RP was built on incremental function and shift function. Based on the model, StackelbergNash game model and Stackelbergmerger game model for RP in SC were built, and their theoretical analysis was carried out. The following conclusions can be drawn. (i) In both two models, the increase of RP cost will make participants’ profits and total profit decrease, while higher renewal rate will make the profits increase at the same margin cost. (ii) Manufacturer and retailer obtain the optimal profits in area III; in other words, the way of the optimal decision making in SC is that RP comes onto the market with a great price differential with OP. (iii) Compared with StackelbergNash game model, Stackelbergmerger game model’s pricing is lower and the profits are higher, which is actually a kind of winwin situation for enterprises and market.
In this paper, a part of premise conditions of the model was built on the basis of some rational hypothesis, and the model parameters need to be confirmed by real statistics data. These problems need to be further studied.
This work was supported by the National Natural Science Foundation of China (Grant no. 71002106).