CN104732410A - Method for establishing price and service competitiveness model between supply chains - Google Patents

Abstract

The invention discloses a method for establishing a price and service competitiveness model between supply chains. The method researches the competitiveness behavior between the supply chains in the environment of uncertain market demands. Each supply chain is composed of a supplier neural in risk and a retail dealer averse in risk, and every two retail dealers have a competitiveness relation on the aspects of retail prices and service level. In the same supply chain, the supplier is a leader, and the retail dealer is a follower. The method mainly discusses influences, on the retail dealer prices and service decisions, of uncertainty of the market demands, wholesale prices of the suppliers, risk aversion attitudes of the retail dealers and service investment efficiency. In the future research, risk aversion attitudes of the suppliers, dominance, in the supply chains, of the retail dealers and repeated competition between the supply chains can be considered. In brief, the method is provided for judging and implementing decisions made on products, prices and service levels.

Description

The method for building up of the price between a kind of supply chain and service competitive model

Technical field

The present invention relates to a kind of method for establishing model, specifically, relate to the price between a kind of supply chain and the method for building up of serving competitive model.

Background technology

Along with progress and the economic globalization of science and technology, the competition between enterprise and enterprise has changed the competition between supply chain and supply chain into.Product price and service horizontal competition are modal two kinds of competitive ways between supply chain.But enterprise wants the service provided, certain investment must be had.How does supply chain members make optimum retail price and Service Level Decision? how does the service efficiency of investment of retailer affect the decision-making of rival? these are all the problems that the present invention will study.

Due to uncertainty that is social and economic environment, the market demand is also uncertain usually.Supply chain members generally all does decision-making under market demand uncertain environment.The decision behavior of supply chain when the market demand is uncertain that the dealer that Bernstein and Federgruen have studied a manufacturer and multiple price competition is formed.Bernstein and Federgruen considers selling price under market demand uncertain condition between dealer and Service Level Decision behavior simultaneously.Ai Xingzheng analyzes the control structure model that chain and chain are competed under uncertain market demand environment, has inquired into the uncertainty of the market demand, the intensity of product competition to the impact of supply chain control structure performance.The balanced competitive strategy of Ibtinen and Koichi supply chain system that single supplier and multiple retailer are formed under have studied Stochastic Market demand, there is competitive relation in retailer in price and stock.Yi Yuyin and Chen Yuexiao constructs the Closed Loop Supply Chain Price Competition Model with product remanufacturing ability of the uncertain next manufacturer of the market demand and two retailer's compositions.The coordination problem of the supply chain that the retailer of single supplier and multiple price competition is formed under Hou Linlin and Qiu aster China have studied Stochastic Market demand.Ai Xingzheng, based on the uncertain market demand, constructs chain and chain Price Competition Model, have studied the Revenue Sharing Contract between manufacturer and retailer.Hou Ling etc. use the equilibrium pricing behavior of supply chain under Discussion on Game Theory market demand uncertain environment.

In supply chain, the attitudes toward risk that retailer treats the uncertain market demand has important impact to its decision-making.The retailer of a risk aversion can be target with maximization of utility when doing decision-making usually, instead of is target with maximizing of expected profit.Because the effectiveness of retailer is the increasing function of Expect Profits, it is the subtraction function of attitudes toward risk.How do the uncertainty of the market demand and the attitudes toward risk of retailer affect the decision behavior of retailer and competition? this is the problem that the present invention wants selective analysis.

At present, also seldom there is document to consider the uncertainty of the market demand and the attitudes toward risk of supply chain members in the price and service competition of supply chain simultaneously.

Summary of the invention

In order to overcome the defect existed in prior art, the present invention proposes the price between a kind of supply chain and the method for building up of serving competitive model, consider two independently supply chains, every bar supply chain is made up of the supplier of a risk neutral and the retailer of a risk aversion.In the uncertain situation of the market demand, there is competitive relation in two retailers in retail price and service level.

Its technical scheme is as follows:

A method for building up for price between supply chain and service competitive model, comprises the following steps:

Step 1. determines the influence factor that basic model is set up

The Stochastic Market demand that retailer i faces, average is variance is

The unit product production cost of supplier i;

The mutual substitution coefficient of two kinds of products, 0< α <1;

The retail price of retailer i;

The service level of retailer i;

The unit product wholesale price of supplier i;

The market demand of retailer is relative to the sensitivity of he self service level;

The market demand of retailer relative to the sensitivity of the service level of rival, β > γ >0;

The risk aversion level of retailer i, φ _i>=0;

The service efficiency of investment coefficient of retailer i, θ _i>0;

Step 2. sets up retailer's demand function model

Retail price and service level are two key factors affecting the market demand, suppose that the market demand function of retailer i is:

${\tilde{q}}_i={\tilde{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+\mathrm{\&beta;}{s}_i-{\mathrm{\&gamma;s}}_j,$ i,j＝1,2，j≠i

Step 3. calculates and solves retailer's chance of a profit model

${\widetilde{\mathrm{\&pi;}}}_i=(p_i-w_i)({\tilde{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2,$ i,j＝1,2，j≠i

Step 4. sets up retailer's utility function model

$u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)=E\left({\widetilde{\mathrm{\&pi;}}}_i\right)-{\mathrm{\&phi;}}_i\mathrm{Var}\left({\widetilde{\mathrm{\&pi;}}}_i\right)$

Step 5. determines the utility function of retailer's price and service and decision-making

$u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)=(p_i-w_i)({\stackrel{\&OverBar;}{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+\mathrm{\&beta;}{s}_i-{\mathrm{\&gamma;s}}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2-{\mathrm{\&phi;}}_i{(p_i-w_i)}^2{\mathrm{\&sigma;}}_i^2$

Further preferably,

(1) if B ₁, B ₂>0, the optimum retail price of retailer and service level are:

$p_i^{*}=M_i-w_i$

$s_i^{*}=\mathrm{\&beta;}{M}_i/{\mathrm{\&theta;}}_i$

(2) suppose the optimum retail price of retailer i and service level meet:

If 1. A _j>=1, then have with

If 2. A _j<1, for 0< α < β γ/[θ _j(1-A _j)], have with for α=β γ/[θ _j(1-A _j)], have with for β γ/[θ _j(1-A _j)] < α <1, have with

(3) suppose then have

1. with

If 2. β γ/θ _j< α <1, so with

If 3. α=β γ/θ _j, so with

If 4. α < β γ/θ _j, so with

(4) if with β A _j+ γ B _j>0, the service efficiency of investment of retailer is larger, and retail price and the service level of its optimum are higher.

Beneficial effect of the present invention is: the present invention have studied the competitive behavior under market demand uncertain environment between supply chain.Each supply chain is made up of the supplier of a risk neutral and the retailer of a risk aversion, and two retailers have competitive relation in retail price and service level.In same supply chain, supplier is leader, and retailer is follower.The present invention mainly discusses market demand uncertainty, the wholesale price of supplier, the risk aversion attitude of retailer and service efficiency of investment to the impact of retailer's price and service and decision-making.Future studies can be considered in repeatedly competition game of the risk aversion attitude of supplier, the dominance of retailer in supply chain, supply chain etc.In a word, this invention is a kind of in product, the one judgement carrying out decision-making between price and service level and implementation method for we providing.

Accompanying drawing explanation

Fig. 1 is optimum retail price with service efficiency of investment θ ₁between relation;

Fig. 2 is optimum logistics service level with service efficiency of investment θ ₁between relation.

Embodiment

Below in conjunction with the drawings and specific embodiments, technical scheme of the present invention is described in more detail.

Two supply chains of competing mutually when the present invention considers that the market demand is uncertain, every bar supply chain is made up of the supplier of a risk neutral and the retailer of a risk aversion.Competitive relation is there is in two retailers in retail price and service level.The product of Liang Ge supplier can substitute mutually, and they are by respective retail seller sells product.

The symbol used in the present invention following (i=1,2):

the Stochastic Market demand that retailer i faces, average is variance is

C _ithe unit product production cost of supplier i

The mutual substitution coefficient of α two kinds of products, 0< α <1

P _ithe retail price of retailer i

S _ithe service level of retailer i

W _ithe unit product wholesale price of supplier i

The market demand of β retailer is relative to the sensitivity of he self service level

The market demand of γ retailer relative to the sensitivity of the service level of rival, β > γ >0

φ _ithe risk aversion level of retailer i, φ _i>=0

θ _ithe service efficiency of investment coefficient of retailer i, θ _i>0

Retail price and service level are two key factors affecting the market demand, suppose that the market demand function of retailer i is:

${\tilde{q}}_i={\tilde{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j,i,j=\mathrm{1,2},j\&NotEqual;i---\left(1\right)$

The market demand of each retailer is the increasing function of his rival's retail price and own services level, and be the subtraction function of his self retail price and rival's service level, what suppose retailer i is s in service level _itime cost of serving function be then the chance of a profit of retailer is:

${\widetilde{\mathrm{\&pi;}}}_i=(p_i-w_i)({\tilde{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2,i,j=\mathrm{1,2},j\&NotEqual;i---\left(2\right)$

Consider the risk aversion of retailer, suppose that the utility function of retailer is:

$u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)=E\left({\widetilde{\mathrm{\&pi;}}}_i\right)-{\mathrm{\&phi;}}_i\mathrm{Var}\left({\widetilde{\mathrm{\&pi;}}}_i\right)---\left(3\right)$

Section 2 in formula (3) is the risk cost of retailer i, φ _irepresent that retailer i is to the risk aversion degree of the uncertain market demand, formula (3) shows that retailer i can do between the expectation and variance of the chance of a profit and weighs.

Hereafter first provide in formula (3) with so that the derivation of formula hereinafter.

$\begin{array}{c}E\left({\widetilde{\mathrm{\&pi;}}}_i\right)=(p_i-w_i)[E\left({\tilde{a}}_i\right)-p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j]-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2\\ =(p_i-w_i)({\stackrel{\&OverBar;}{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2\end{array},$

$\mathrm{Var}\left({\widetilde{\mathrm{\&pi;}}}_i\right)={(p_i-w_i)}^2\mathrm{Var}\left({\tilde{a}}_i\right)={(p_i-w_i)}^2{\mathrm{\&sigma;}}_i^2.$

In the present invention, the competition game order of supply chain is:

(1) Liang Ge supplier determines respective wholesale price simultaneously;

(2) two retailers determine respective retailer's price and service level respectively.

The present invention only studies the decision behavior of retailer after the given wholesale price of supplier temporarily as space is limited, and the price policy behavioral study of supplier will be delivered in a separate paper.

The price of retailer and service and decision-making model

According to formula (2) and (3), after the given wholesale price of supplier, retailer i (i=1,2) can determine its retail price p simultaneously _iwith service level s _ito maximize its effectiveness, utility function is as follows:

$u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)=(p_i-w_i)({\stackrel{\&OverBar;}{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2-{\mathrm{\&phi;}}_i{(p_i-w_i)}^2{\mathrm{\&sigma;}}_i^2---\left(4\right)$

Yi Zhi, hesse matrices be: $H_i=\left[\begin{array}{cc}-2(1+{\mathrm{\&phi;}}_i{\mathrm{\&sigma;}}_i^2)& \mathrm{\&beta;}\\ \mathrm{\&beta;}& -{\mathrm{\&theta;}}_i\end{array}\right].$ And if only if Hesse matrices H _iwhen being negative definite, utility function about (p _i, s _i) concave function.Order

If theorem 1 B ₁, B ₂>0, the optimum retail price of retailer and service level are:

$p_i^{*}=M_i-w_i---\left(5\right)$

$s_i^{*}=\mathrm{\&beta;}{M}_i/{\mathrm{\&theta;}}_i---\left(6\right)$

Wherein, $M_i=[({\stackrel{\&OverBar;}{a}}_i-w_i+{\mathrm{\&alpha;w}}_j)A_j-({\stackrel{\&OverBar;}{a}}_j-w_j+{\mathrm{\&alpha;w}}_i)B_j]/(A_i{A}_j-B_i{B}_j)\text{,}$ B _i＝βγ/θ _i-α。

Prove basis hesse matrices H _iif, known A _i>0, about (p _i, s _i) concave function.Therefore, according to A ₁, A ₂>0 is known satisfied the solution of first-order condition is optimum.

For i, j=1,2, j ≠ i, single order optimal conditions be:

$\&PartialD;u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)/{\&PartialD;p}_i=(-2-2{\mathrm{\&phi;}}_i{\mathrm{\&sigma;}}_i^2)p_i+\mathrm{\&alpha;}{p}_j+{\mathrm{\&beta;s}}_i-{\mathrm{\&gamma;s}}_j+{\stackrel{\&OverBar;}{a}}_i+(1+2{\mathrm{\&phi;}}_i{\mathrm{\&sigma;}}_i^2)w_i=0---\left(7\right)$

${\&PartialD;u}_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)/{\&PartialD;s}_i=\mathrm{\&beta;}(p_i-w_i)-{\mathrm{\&theta;}}_i{s}_i=0---\left(8\right)$

S is had by formula (8) _i=β (p _i-w _i)/θ _i, substituted in formula (7), can be obtained:

$A_1{p}_1+B_2{p}_2={\stackrel{\&OverBar;}{a}}_1+(A_1-1)w_1+(B_2+\mathrm{\&alpha;})w_2---\left(9\right)$

$B_1{p}_1+A_2{p}_2={\stackrel{\&OverBar;}{a}}_2+(B_1+\mathrm{\&alpha;})w_1+{(A_2-1)w}_2---\left(10\right)$

From formula (9) and (10), the optimum retail price of retailer i is i=1,2, the optimum logistics service level that can also obtain retailer i is i=1,2.Card is finished.

If lemma 1 a can be obtained ₁a ₂-B ₁b ₂>0, wherein

${\mathrm{\&alpha;}}_{\&PlusMinus;}^{*}=\frac{\mathrm{\&beta;\&gamma;}({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)\&PlusMinus;\sqrt{\mathrm{\&Delta;}}}{2{\mathrm{\&theta;}}_1{\mathrm{\&theta;}}_2},$

$\begin{array}{c}\mathrm{\&Delta;}={\mathrm{\&beta;}}^2{\mathrm{\&gamma;}}^2{({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}^2\\ +4{\mathrm{\&theta;}}_1{\mathrm{\&theta;}}_2\left\{{\mathrm{\&beta;}}^2\right[{\mathrm{\&beta;}}^2-{\mathrm{\&gamma;}}^2-2{\mathrm{\&theta;}}_2(1+{\mathrm{\&phi;}}_2{\mathrm{\&sigma;}}_2^2)]-2{\mathrm{\&theta;}}_1(1+{\mathrm{\&phi;}}_1{\mathrm{\&sigma;}}_1^2)[{\mathrm{\&beta;}}^2-2{\mathrm{\&theta;}}_2(1+{\mathrm{\&phi;}}_2{\mathrm{\&sigma;}}_2^2)\left]\right\}\end{array}.$

Prove order

$\begin{array}{c}f\left(\mathrm{\&alpha;}\right)=A_1{A}_2-B_1{B}_2\\ =(2+2{\mathrm{\&phi;}}_1{\mathrm{\&sigma;}}_1^2-{\mathrm{\&beta;}}^2/{\mathrm{\&theta;}}_1)(2+2{\mathrm{\&phi;}}_2{\mathrm{\&sigma;}}_2^2-{\mathrm{\&beta;}}^2/{\mathrm{\&theta;}}_2)-(\mathrm{\&beta;\&gamma;}/{\mathrm{\&theta;}}_1-\mathrm{\&alpha;})(\mathrm{\&beta;\&gamma;}/{\mathrm{\&theta;}}_2-\mathrm{\&alpha;})\end{array}$

Easily know that f (α) is a concave function about mutual substitution coefficient α, solving equation f (α)=0 therefore, if then there is A ₁a ₂-B ₁b ₂>0.Card is finished.By theorem 1 and lemma 1, following theorem 2 can be obtained.

Theorem 2 is supposed the optimum retail price of retailer i and service level meet:

(1) if A _j>=1, then have with

(2) if A _j<1, for 0< α < β γ/[θ _j(1-A _j)], have with for α=β γ/[θ _j(1-A _j)], have with for β γ/[θ _j(1-A _j)] < α <1, have with

Proving will to w _jdifferentiate, has note α A _j+ B _j=α (A _j-1)+β γ/θ _j.If A _j>=1, there is α A _j+ B _j>0.If A _j<1, for 0< α < β γ/[θ _j(1-A _j)] there is α A _j+ B _j>0; For α=β γ/[θ _j(1-A _j)] there is α A _j+ B _j=0; For β γ/[θ _j(1-A _j)] < α <1 has α A _j+ B _j<0.According to lemma 1, there is A ₁a ₂-B ₁b ₂>0.Thus can obtain, if A _i>0, A _j>=1 He then have in like manner can prove the other parts of theorem (2).Card is finished.

It is how affect by the wholesale price of the supplier in competitive supply chains that theorem 2 analyzes the optimum retail price of retailer and service level.

Theorem 3 is supposed then have

(1) with

(2) if β is γ/θ _j< α <1, so with

(3) if α=β is γ/θ _j, so with

(4) if α < β is γ/θ _j, so with

Prove according to lemma 1 and A _iabout φ _iincreasing function, if can obtain then about φ _isubtraction function, namely

Will to φ _jdifferentiate, has

$\frac{{\&PartialD;s}_i^{*}}{{\&PartialD;\mathrm{\&phi;}}_j}=\frac{2{\mathrm{\&beta;\&sigma;}}_j^2[({\stackrel{\&OverBar;}{a}}_j-w_j+\mathrm{\&alpha;}{w}_i)A_i-({\stackrel{\&OverBar;}{a}}_i-w_i+{\mathrm{\&alpha;w}}_j)B_i]B_j}{{\mathrm{\&eta;}}_i{(A_i{A}_j-B_i{B}_j)}^2}=\frac{2\mathrm{\&beta;}{\mathrm{\&sigma;}}_j^2{M}_j{B}_j}{{\mathrm{\&eta;}}_i(A_i{A}_j-B_i{B}_j)}---\left(11\right)$

According to lemma 1, there is A ₁a ₂-B ₁b ₂>0.And, according to formula (11) and M _j>0, known with B _jthere is identical symbol, namely $\mathrm{sign}({\&PartialD;s}_i^{*}/{\&PartialD;\mathrm{\&phi;}}_j)=\mathrm{sign}\left(B_j\right).$ Card is finished.

Can be drawn the following conclusions by theorem 3:

(1) service level of the retailer of risk aversion will lower than the retailer of risk neutral.And when the substitutability of product is larger, the risk aversion degree of retailer is higher, and the optimum logistics service level of rival is lower, and this can reduce the service level of whole industry.

(2) when the substitutability of product is larger, retailer can show larger risk aversion level; When the substitutability of product is smaller, retailer can show less risk aversion level, and these are all to attract more client.

(3) raising of retailer's risk aversion degree can cause the reduction of its service level, and due to the competition in market, retailer can initiatively bring down retail price to attract more client.

(4) retailer also can improve the price of retail accordingly when providing high-caliber service.

(5) when the substitutability of product is larger, if rival shows more conservative, retailer can bring down retail price to attract clients, and also can turn down service level with investment reduction; If rival shows more radical, retailer can improve retail price to earn more profit, also can improve service level to attract clients.

If theorem 4 with β A _j+ γ B _j>0, the service efficiency of investment of retailer is larger, and retail price and the service level of its optimum are higher.

Prove according to lemma 1 and β A _j+ γ B _j>0, has

f＝A ₁A ₂-B ₁B ₂>0

$\&PartialD;f/{\&PartialD;\mathrm{\&theta;}}_i={\mathrm{\&beta;\&theta;}}_i^{-2}({\mathrm{\&beta;A}}_j+{\mathrm{\&gamma;B}}_j)>0$

$\&PartialD;\left({\mathrm{f\&eta;}}_i\right)/{\&PartialD;\mathrm{\&theta;}}_i=(\&PartialD;f/{\&PartialD;\mathrm{\&theta;}}_i){\mathrm{\&theta;}}_i+f>0$

According to theorem 1, lemma 1 and, theorem 4 must be demonstrate,proved.

Example Verification

Verifying conclusion above below by way of two examples, for the ease of analyzing, suppose that supply chain is symmetrical, we are only by an analysis supply chain wherein.Parameter value in first example is as follows:

φ ₁＝φ ₂＝0.2，σ ₁＝σ ₂＝3，θ ₁＝θ ₂＝1.2，γ＝0.5，w ₂＝7。

Because A ₁=A ₂=2.8-β ², B ₁=B ₂=0.6 β-α, so

A ₁A ₂-B ₁B ₂＝(2.8-β ²+0.6β-α)(2.8-β ²-0.6β+α)。

And if only if α ^*during=0.35, β=1.5, it equals 0.When β=1.5, α ^*during >0.35, it is greater than 0.Therefore, condition or A ₁a ₂-B ₁b ₂>0 is satisfied.According to theorem 1 and 2, table 1 can be obtained.

The optimum retail price of table 1 retailer and service level

"-" represents that retailer has exited market.

From table 1, we can find that the size of products substitution factor alpha and market demand sensitivity β is depended in the impact of the wholesale price of supplier on the optimum retail price of retailer.Haply, when the wholesale price of supplier is higher, the optimum logistics service level of retailer is lower, and optimum retail price is higher.

Parameter value in second example is as follows:

φ ₁＝φ ₂＝0.2，σ ₁＝σ ₂＝3，β＝1.2，γ＝0.5，w ₁＝w ₂＝9，θ ₂＝1.1。

Fig. 1 and 2 respectively illustrates the optimum retail price of service efficiency of investment on retailer 2 and the impact of service level of retailer 1.

From Fig. 1 and 2, we can know that the service efficiency of investment of rival is higher, the optimum retail price of retailer and service level lower.This is because because own services efficiency of investment does not have advantage, retailer can bring down retail price to attract consumer, also can reduce service level with investment reduction.When product substitution is higher, the service efficiency of investment of rival on the optimum retail price of retailer and the impact of service level more obvious.

The above; be only the present invention's preferably embodiment; protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses, the simple change of the technical scheme that can obtain apparently or equivalence are replaced and are all fallen within the scope of protection of the present invention.

Claims (2)

1. a method for building up for the price between supply chain and service competitive model, is characterized in that, comprise the following steps:

Step 1. determines the influence factor that basic model is set up

The Stochastic Market demand that retailer i faces, average is variance is

The unit product production cost of supplier i;

The mutual substitution coefficient of two kinds of products, 0< α <1;

The retail price of retailer i;

The service level of retailer i;

The unit product wholesale price of supplier i;

The market demand of retailer is relative to the sensitivity of he self service level;

The market demand of retailer relative to the sensitivity of the service level of rival, β > γ >0;

The risk aversion level of retailer i, φ _i>=0;

The service efficiency of investment coefficient of retailer i, θ _i>0;

Step 2. sets up retailer's demand function model

Retail price and service level are two key factors affecting the market demand, suppose that the market demand function of retailer i is:

${\tilde{q}}_i={\tilde{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+\mathrm{\&beta;}{s}_i-\mathrm{\&gamma;}{s}_j,i,j=\mathrm{1,2},j\&NotEqual;i$

Step 3. calculates and solves retailer's chance of a profit model

${\widetilde{\mathrm{\&pi;}}}_i=(p_i-w_i)({\tilde{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+\mathrm{\&beta;}{s}_i-\mathrm{\&gamma;}{s}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2,i,j=\mathrm{1,2},j\&NotEqual;i$

Step 4. sets up retailer's utility function model

$u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)=E\left({\widetilde{\mathrm{\&pi;}}}_i\right)-{\mathrm{\&phi;}}_i\mathrm{Var}\left({\widetilde{\mathrm{\&pi;}}}_i\right)$

Step 5. determines the utility function of retailer's price and service and decision-making

$u_i\left({\widetilde{\mathrm{\&pi;}}}_i\right)=(p_i-w_i)({\stackrel{\&OverBar;}{a}}_i-p_i+\mathrm{\&alpha;}{p}_j+\mathrm{\&beta;}{s}_i-\mathrm{\&gamma;}{s}_j)-\frac{1}{2}{\mathrm{\&theta;}}_i{s}_i^2-{\mathrm{\&phi;}}_i{(p_i-w_i)}^2{\mathrm{\&sigma;}}_i^2.$

2. the method for building up of the price between supply chain according to claim 1 and service competitive model, it is characterized in that, (1) is if B ₁, B ₂>0, the optimum retail price of retailer and service level are:

$p_i^{*}=M_i-w_i$

$s_i^{*}=\mathrm{\&beta;}{M}_i/{\mathrm{\&theta;}}_i$

(2) suppose the optimum retail price of retailer i and service level meet:

If 1. A _j>=1, then have $\&PartialD;p_i^{*}/\&PartialD;w_j>0$ With $\&PartialD;s_i^{*}/\&PartialD;w_j>0;$

If 2. A _j<1, for 0< α < β γ/[θ _j(1-A _j)], have with for α=β γ/[θ _j(1-A _j)], have with for β γ/[θ _j(1-A _j)] < α <1, have with $\&PartialD;s_i^{*}/\&PartialD;w_j>0;$

(3) suppose $\max \{0,{\mathrm{\&alpha;}}_{-}^{*}\}<\mathrm{\&alpha;}<\min \{{\mathrm{\&alpha;}}_{+}^{*},1\},$ Then have

① $\&PartialD;s_i^{*}/\&PartialD;{\mathrm{\&phi;}}_i<0$ With $\&PartialD;p_i^{*}/\&PartialD;{\mathrm{\&phi;}}_i<0;$

If 2. β γ/θ _j< α <1, so $\&PartialD;s_i^{*}/\&PartialD;{\mathrm{\&phi;}}_j<0$ With $\&PartialD;p_i^{*}/\&PartialD;{\mathrm{\&phi;}}_j<0;$

If 3. α=β γ/θ _j, so $\&PartialD;s_i^{*}/\&PartialD;{\mathrm{\&phi;}}_j=0$ With $\&PartialD;p_i^{*}/\&PartialD;{\mathrm{\&phi;}}_j=0;$

If 4. α < β γ/θ _j, so $\&PartialD;s_i^{*}/\&PartialD;{\mathrm{\&phi;}}_j>0$ With $\&PartialD;p_i^{*}/\&PartialD;{\mathrm{\&phi;}}_j>0;$

(4) if with β A _j+ γ B _j>0, the service efficiency of investment of retailer is larger, and retail price and the service level of its optimum are higher.