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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 15, Issue 1

# Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness

Qi-Jie Jiang
/ Mao-Zhu Jin
/ Pei-Yu Ren
Published Online: 2017-04-06 | DOI: https://doi.org/10.1515/phys-2017-0012

## Abstract

How to optimize agro-product supply chain to promote its operating efficiency so as to enhance the competitiveness of regional agricultural products has posed a problem to academic circles, business circles and governments of various levels. One way to solve this problem is to introduce an information platform into the supply chain, which this essay focuses on. Firstly, a review of existing research findings concerning the agro-product competitiveness, agro-product supply chain (ASC) and information platform was given. Secondly, we constructed a mathematical model to analyze the impact of information platform on the bullwhip effect in ASC. Thirdly, another mathematical model was constructed to help compare and analyze the impact of information platform on information acquisition of members in ASC. The research results show that the implantation of information platform can mitigate the bullwhip effect in ASC, and members can determine order amount or production more close to the actual market demand. And also the information platform can reduce the time for members in ASC to get information from other members. Besides, information platform can help ASC to alleviate information asymmetry among upstream and downstream members. Furthermore, researches about the operating mechanism and pattern, technical feature and running structure of the information platform, along with their impacts on agro-product supply chain and the competitiveness of agricultural products need to be advanced.

PACS: 05.45.-a

## 1 Introduction

Nowadays, among other industries, agriculture has faced a fierce market. Information is the core factor in the agro-product supply chain. Problems like “information asymmetry” and “bullwhip effect”, together with their resulting “adverse choice”, “moral hazard”, “lack of synergy effects” will cause negative effect on the business circle of the agricultural products. By contrast, information sharing can strengthen information quality[1], enhance the information communication and coordination among all the stakeholders [2], and reduce the time and costs of information processing at various stages [3]. As a result, information sharing is considered to be an effective way to solve the problems mentioned above [4, 5].

As international trade barriers and protectionism are weakening, agricultural products worldwide have to deal with competitors at home and abroad. There are several problems bothering local governments, agricultural corporations and farmers as well: how to enhance the competitiveness of local agricultural products, gaining competitive advantages against other competitors; how to meet the varied demands of the agricultural market; how to cut production and transportation costs to increase market share and profits.

Looking at the processes of production, transportation and selling from the perspective of a whole supply chain, we will be able to coordinate all the stakeholders. In this way, the resources will be better integrated and allocated to achieve high efficiency of the supply chain and strong competitiveness of the agricultural products.It's obvious that ASC is a form of complex networks [6], which has been applied in many fields, such as P2P networks [7] and economics [8].

This paper proposes that with the introduction of a platform for information sharing, the stakeholders of ASC will have access to sufficient information and thus give better predictions of the market demand. The influence of “information asymmetry” and “bullwhip effect” will be mitigated and the competitiveness of agricultural products will be improved.

## 2.1 Competitiveness of Agricultural Products

With the ever-deepening globalization and market economy, competitiveness has become a research focus in recent years. Landau [9] defined competitiveness as the ability to sustain an acceptable growth rate and a real standard of living for the citizenry while efficiently providing employment and maintaining the growth potential and standard of living for future generations. Firm-level competitiveness is defined as the ability to deliver goods and services at the time, at the place, and in the form sought by buyers at prices as good as or better than those of other suppliers while earning at least opportunity costs on resources employed [10], and also the ability to profitably gain and maintain market share in domestic or foreign markets [11]. Latruffe, L. [12] thought that competition may be within domestic markets or international markets, and competitiveness is therefore a relative measure because. The Organization for Economic Co-operation and Development (OECD), absorbing all the existing ideas, defines competitiveness as the “ability of companies, industries, regions, nations, and supranational regions to generate, while being and remaining exposed to international competition, relatively high factor income and factor employment levels on a sustainable basis” [13].

The existing researches about agricultural products competitiveness are mainly conducted from a nation-level prospective and are mostly focused on achieving international competitiveness. The international competitiveness of agricultural products is often considered to be the ability to maintain market share and profitability while meeting the demand of international market in a fair and equal economy [14]. A great number of empirical researches have been done to find out indexes that best measure competitiveness and factors that mainly influence it.

Latruffe, L. [12] categorized the existing measures into two groups: trade measures, including real exchange rate and relative real exchange rates [15], purchasing power parity [16], Revealed comparative advantage, relative export advantage, relative import advantage, export market shares, net export index [1720], and Strategic management measures, consists of domestic resource costs [21], social cost-benefit [22], costs of production [23], Profitability [24], Productivity and efficiency [25]. With the help of Regressions, Correlation and ranking analysis, Cluster analysis, researchers analyzed defining factors that influence the competitiveness of agricultural products, including farm size [26], farm specialisation [27], farm manager age, education [28], sophistication of consumers [17], government intervention, public expenditures [29].

Undoubtedly, researches about agricultural products competitiveness are conducive to evaluating the advantages and disadvantages of some specific products compared with other competitors in production and sales, both in domestic and international markets. In this way, the defining factors that influence the competitiveness of agricultural products can be figured out, and then the limited resources will be reasonably allocated to the weak but key processes, thus improving competitiveness of agricultural products.

Nevertheless, with most of the existing researches being macro, it is urgent to conduct researches from the micro perspective of a supply chain, which are of greater pragmatic importance.

## 2.2 Supply chain of agricultural products

Based on the “economy chain” by Peter Drucker and “value chain” by Michael Porter, the concept of supply chain emerged with the rapid development of modern logistics management. First put forward in the 1980s, the concept of supply chain drew much attention to the academic and business circles following the successful application of the supply chain management (SCM) in some world-renowned companies such as Hewlett-Packard [4, 5, 30], Digital Equipment Corporation [31], Procter & Gamble [32].

Jones [33] and Lee [30] suggested that supply chain is a system, consisting of supplier, manufacturer, distributor, retailer and customer, in which a product moves from supplier to customer while the information flows to both sides. Reiter (1996) defined supply chain as a network for an operating entity. Willian C. Copacino defined supply chain management(SCM) as “The art of managing the flow of materials and products from source to user”. The Supply Chain Council, established in Ameica, 1996, defined SCM as a process that encompasses every effort involved in producing and delivering a final product, from the supplier's supplier to customer's customer. The research group Japan SCM Institute defined SCM as the complete and integrated collaboration process of all elements in a supply chain, in which management methods that go beyond individual enterprises are adopted to achieve higher product value and service value for customers. Jones T. C. et al. [33] thought that the operating strategy for a supply chain should be an organization's response to the market.

Started in 1990s, agro-product supply chain, a major application field for supply chain, is an interrelated and interdependent organization system for the producing and selling of common products, just like a super organization (Stern, 1996). Encompassing every relation in trading, agro-product supply chain works as a propeller for it (Pelton, 2002).

Johnson and Hofman (2004) suggested that agro-product supply chain indicates a kind of strategic alliance relationship of integration, in a horizontal and vertical manner, among those actors involving in stages such as raw material supply, production, processing, transportation and selling [34]. Generally speaking, the existing researches are mainly focusing on the content, organization model and its efficiency of agro-product supply chain [35, 36], the safety of agricultural products [37, 38, 39}, the strategies for agro-product safety [40, 41, 42].

Gimnez and Ventura [43] put forward that with the help of internet tools and information technologies like e-commerce, agro-product supply chain management introduces advanced management methods to coordinate all the subjects (mostly enterprises) so that the whole supply chain develops to be ever more systematic, integrated and sophisticated.

Flynn B. B. [34] thought that exchanging and sharing information about products, scheduling and productivity can facilitate farmers in reducing errors, accomplishing production on time, enhancing delivery performance, improving product quality and boosting efficiency of supply chain. Problems in agro-product supply chain like the complexity, congestion and instability in information flow, together with their resulting information lag, information asymmetry and limited means of exchange will severely impede the development of the supply chain. Difficulty in selling and low profitability despite bumper harvests follow.

The efficiency and effectiveness of agro-product supply chain, especially its information communication, is the key for agro-products to achieve competitive advantages.

## 2.3 Information platform

Platform theory is based on modularity, and its appearance is in order to cope with the dynamic and uncertain information from industry technology, market demand and competitor. Because of platform theory's easy understanding and universality, in recent years, it gets more and more attention from theoretical circles and industrial circles. Eisenhardt & Martin [44] believed that platform is a structure, which is based on organization and dynamic capability and can store organization ability. Evans and Schmalensee thought that platform can promote different communities interactions and transactions by attracting and benefiting both sides of the transaction, and ultimately be good for the growth of system [45]. Cusumano [46] considered platform as an intersection center of technology system with indirect network effects. Thomas L. D. W., Autio E. and Gann D. M. [47] develop the logic of leverage by identifying three types of leverage: production leverage, innovation leverage, and transaction leverage.

Gawer [45] epitomized platform theory, in his opinion, platform is an constantly evolving and changing organization, which consists of one or more enterprises aiming at the creation of value. And also, Gawer [48] believes that with the openness extension of interface, the platform will evolve from the enterprise's internal platform to the supply chain platform, and then to the platform ecosystem.

Information is the core of any platform, so an information platform is the key of all platforms. The information platform of a agro-product supply chain serves as a transfer station, collecting information from its subsystems, standardizing and storing it and distributing it anywhere on demand. There is no doubt that a well-managed information platform will help all subjects in the agro-product supply chain communicate and cooperate, exterminating information asymmetry. In this way, information resources can be fully utilized, efficiency of the supply chain can be improved to meet the changing market demand in a timely and high efficient manner and thus competitiveness of local agro products is promoted.

## 3.1 Analysis of bullwhip effect in ASC without information platform

An agricultural supply chain, consists of farmers, processing enterprises, distributors, retailers and consumers, has the characteristics of multiple network structures. Because there is no information platform in ASC, so we suppose that there is no information sharing between members of ASC. Retailers do not provide the real consumer information they have to upstream members in the ASC, and dealers do not provide the correct ordering information of retailers to processing enterprises, and so forth.

Members can only predict the demand with the order quantity of former members. Meanwhile, members use the moving average forecasting technology to predict the future order of its downstream members and determine their order quantity to the upstream members with the order-up-to strategy.

Now we assume that there is one produce in the ASC, and suppose that commercial behaviors between the upstream and downstream members occur in an infinite discrete time range (t = − ∞, …, −1, 0, 1, …, ∞). On the basis of past sales information and stock replenishment period (L), members predict the future order (t+L) of its downstream members with moving average forecasting in the end of t, and use order-up-to strategy to determine their order quantity to the upstream members. And then they make an order qt to the upstream members at the beginning of the next period (t+L).

To facilitate the analysis, we take a two-level ASC including retailers and dealers for example. Suppose that the market demands (dt) retailers face is a simple stationary autocorrelation time series AR(1): $dt=μ+ρd(t−1)+εt,t=0,±1,2,⋯$(1)

In the equation, μ is a non-negative constant, ρ is an autocorrelation coefficient, which indicates the correlation of consumers demand in two adjacent periods, and we suppose |ρ| < 1. And εt are independent random variables with the same distribution, which shows the fluctuation error of market consumption demand. The mean value is 0 and variance is (σ2). We can get the mean value and variance of (dt): $(E(dt)=μ(1−ρ)var(dt)=σ2(1−ρ2)$(2)

According to the foregoing hypothesis, order quantity (qt) issued by the retailers to the dealers will meet the following conditions: $yt=d^tL+zσ^tL$(3) $qt=yt−y(t−1)+dt$(4)

In the equation, ${\stackrel{^}{d}}_{t}^{L}$ represents the estimated value of market demand in the stock replenishment period. And if the estimated value (${\stackrel{^}{d}}_{t}^{L}$) is based on consumer demands, retailers observe in the former few periods, we can get the following equation.

$d^tL=L×d^t=L∑i=0p−1dt−ip$(5)

We define yt as the maximum inventory level, and $z{\stackrel{^}{\sigma }}_{t}^{L}$ as the safety stock (z is the service level coefficient and ${\stackrel{^}{\sigma }}_{t}^{L}$ is the estimated value of the standard deviation of prediction error). To simplify analysis, we suppose the value of z is 0. Then we can get the mathematical expression of the bullwhip effect $\frac{var\left({q}_{t}\right)}{var\left({d}_{t}\right)}$. According to formula (3), formula (4) and formula (5), we can get order quantity (qt) of retailers.

$qt=d^tL−d^t−1L+dt=L∑i=0p−1dt−ip−L∑i=0p−1dt−i−1p+dt=1+Lpdt−Lpdt−p$(6)

Bring formula (1) into formula (6), $qt=1+Lpμ+ρdt−1+εt−Lpμ+ρdt−p−1+εt−p=μ+ρ1+Lpdt−1−Lpdt−p−1+1+Lpεt−Lpεt−p=μ+ρqt−1+1+Lpεt−Lpεt−p$(7)

We define ${\epsilon }_{t}^{\prime }$ and Θ′ as follows.

$εt′=1+Lpεt$(8) $Θ′=L(P+L)$(9)

Then formula (7) can be simplified as: $qt=μ+ρqt−1+εt′−Θ′εt−p′$(10)

Among the formula, the mean and variance of ${\epsilon }_{t}^{\prime }$ can be calculated.

$E(εt′)=0var(εt′)=1+Lp2var(εt)=1+Lp2σ2$(11)

And then, we can deduce the mean and variance of (qt).

$E(qt)=μ(1−ρ)=E(dt)$(12) $varqt=var(μ+ρqt−1+εt′−Θ′εt−p′)=ρ2varqt−1+var(εt′−Θ′εt−p′)+2ρcov(qt−1,εt′−Θ′εt−p′)$(13)

Then we can get: $(1−ρ2)varqt=(1+2Lp+2L2p2)σ2−2ρΘ′cov(qt−1,εt−p′)$(14)

If p ≥ 1, we can prove the following relationship.

$cov(qt−1,εt−p′)=ρp−11+Lpσ2$(15)

Bring formula (15) into (14), $varqt=1+2Lp+2L2p2(1−ρp)vardt$(16)

In summary, our analysis shows that: when the market demands (dt) retailers face is a simple stationary autocorrelation time series AR(1), and retailers forecast their order quantity with moving average forecasting technology and order-up-to strategy, the order quantity (qt) will be a random process ARMA(1,P).

Similarly, dealers forecast their demand (${\stackrel{^}{d}}_{t}^{\left(2\right)}$) with moving average forecasting technology on the basis of retailers’ previous orders.

$d^t(2)=∑i=0p−1qt−i(1)p$(17)

Meanwhile, dealers use order-up-to strategy to determine their order amount (${q}_{t}^{\left(2\right)}$) to processing enterprises.

$qt(2)=L2(d^t(2)−d^t−1(2))+qt(1)=1+L2pqt(1)−L2pqt−p(1)$(18)

The above formula implies the following relationship.

$qt−1(2)=1+L2pqt−1(1)−L2pqt−p−1(1)$(19)

According to formula (10) and (19), $qt(2)=μ+ρqt−1(2)+1+L2pεt(1)−Θ(1)εt−p(1)−L2pεt−p(1)−Θ(1)εt−2p(1)$(20)

We define ${\epsilon }_{t}^{\left(2\right)}$ and Θ(2) as follows.

$εt(2)=1+L2pεt(1)−Θ(1)εt−p(1)Θ(2)=L2L2+p$(21)

Then the order quantity ${q}_{t}^{\left(2\right)}$ has the same expression with ${q}_{t}^{\left(1\right)}$, which is a random process ARMA(1,P).

$qt(2)=μ+ρqt−1(2)+εt(2)−Θ(2)εt−p(2)$(22)

And then, $E\left({\epsilon }_{t}^{\left(2\right)}\right)=0$, $var(εt(2))=1+L2p2varεt(1)−2Θ(1)covεt(1),εt−p(1)+Θ(1)2varεt−p(1)=1+Θ(1)21+L1p21+L2p2σ2$(23)

According to the basic theory of probability theory, no matter how much the value of P, we can get the following relationship.

$varqt(2)=ρ2varq(t−1)(2)+varεt(2)+Θ(2)2varεt−p(2)−2Θ(1)Θ(2)1+L2p2varεt−p(1)−2ρpΘ(1)1+L2p2varεt−p(1)−2ρpΘ(1)L2p2varεt−2p(1)+2ε2pΘ(1)L2p1+L2pvarεt−2p(1)−2ρpL2p1+L2p⋅varεt−p(1)+Θ(1)2varεt−2p(1)$(24)

Then, $varqt(2)vardt=1+2L1p+2L12p21−ρp⋅1+2L2p+2L22p21−ρp+22L1p+L12p2L2p+L22p21−ρ2p$(25)

Similarly, we can deduce the bullwhip effect processing enterprises $\left(\frac{var{q}_{t}^{\left(3\right)}}{var{d}_{t}}\right)$ and farmers $\left(\frac{var{q}_{t}^{\left(4\right)}}{var{d}_{t}}\right)$ encounter. In summary, when there is no information sharing, the bullwhip effect' general mathematical model in the ASC can be expressed as: $varqt(k)vardt=1+2L1p+2L12p2(1−ρp),k=1∏i=1k1+2Lip+2Li2p2(1−ρp)+2(1−ρ2p)∏i=1kLip+Li2p2,k=2,3,4$(26)

## 3.2 Analysis of bullwhip effect in ASC with information platform

After implanting the information platform, the upstream members in ASC can share the market demand information. For easy of understanding, we suppose that there is no information loss here. Under this circumstance, the order amount of dealers, processing enterprises and farmers will meet the following relations when using moving average forecasting technology and order-up-to strategy.

$qtk=qtk−1+ytk−yt−1kytk=Lk×d^td^t=1p∑i=0p−1dt−1$(27)

For dealers, their order quantity (${q}_{t}^{\left(2\right)}$) to processing enterprises can be expressed as: $qt2=qt1+L2p∑i=0p−1dt−1−i−∑i=0p−1dt−1−i=1+L1pdt−L1pdt−p+L2pdt−dt−p=1+L1p+L2pdt−L1p+L2pdt−p$(28)

Similarly, processing enterprises' order amount (${q}_{t}^{3}$) to farmers can be expressed as: $qt(3)=qt(2)+L3p∑i=0p−1dt−1−i−∑i=0p−1dt−1−i=1+L1p+L2pdt−L1p+L2pdt−p+L3p(dt−dt−p)=1+L1p+L2p+L3pdt−L1p+L2p+L3pdt−p$(29)

Accordingly, we can get the general mathematical formula: $qt(k)=1+1p∑i=1kLidt−1p∑i=1kLidt−p$(30)

Then, $varqt(k)=1+1p∑i=1kLi2vardt+1p∑i=1kLi2vardt−21+1p∑i=1kLi1p∑i=1kLicov(dt,dt−p)=1+1p∑i=1kLi2vardt+1p∑i=1kLi2vardt−21+1p∑i=1kLi1p∑i=1kLiρpvardt=1+2p∑i=1kLi+2p2∑i=1kLi2−2ρpp∑i=1kLi−2ρpp2∑i=1kLi2vardt$(31)

To sum up, when there is information sharing between members, the bullwhip effect' general mathematical model in the ASC can be expressed as: $varqt(k)vardt=1+2p∑i=1kLi+2p2∑i=1kLi2(1−ρp),k∈[1,2,3,4]$(32)

## 3.3 Comparison of the bullwhip effect in ASC before and after implanting information platform

For easy to understand, we use (BWE)B to represent the bullwhip effect before the implantation of information platform, and use (BWE)A to represent the bullwhip effect after implanting the information platform. Then we can compare the bullwhip effect in these two situations. When k = 1, it is easy to prove: $(BWE)A−(BWE)B=0$(33)

So, for retailers, the implantation of information platform has no effect to forecast accuracy of market demand. This is because our model is based on whether the market information, retailers receive, is shared to other entities in ASC. When k = 2, we can get the following expression according to formula (26) and (32).

$(BWE)A−(BWE)B=1+2p(L1+L2)+2p2L1+L22(1−ρp)−1+2L1p+2L12p21−ρp⋅1+2L2p+2L22p21−ρp−2L1p+L12p2L2p+L22p2(1−ρ2p)$(34)

We define X, Y, Z as follows: $X=L1+L2Y=L1p+L12p2Z=L2p+L22p2$(35)

Then formula (34) can be shown as: $(BWE)A−(BWE)B=1+2pX+2p2(1−ρp)−[1+2Y(1−ρp)][1+2Z(1−ρp)]−2Y⋅Z(1−ρ2p)=2L1⋅L2p2(ρp−1)+2L1⋅L22+2L2⋅L12p3(ρp−3)+2L12⋅L22p4(ρp−3)(1−ρp)$(36)

Because p<1 and p>1, it is easy to prove: $(ρp−1)<0(1−ρp)>0(ρp−3)<0$(37)

So, when k = 2, $(BWE)A−(BWE)B<0$(38)

We define U1, U2 and U3 as follows: $U1=2L1L2U2=2L1L2(L1+L2)U3=2L12L22<0$(39)

Then, formula (36) can be simplified as: $(BWE)A−(BWE)B=U1p2(ρp−1)+U2p3(ρp−3)+U3p4(ρp−3)(1−ρp)$(40)

We take partial derivation, $∂[(BWE)A−(BWE)B]∂ρ=(−pρp−1)U1p2(ρp−1)+U2p3(ρp−3)+U3p4(ρp−3)+(1−ρp)U1pρp−1+U2p2ρp−1+U3p3ρp−1=2U1p(1−ρp)ρp−1+2U2p2(2−ρp)ρp−1+2U3p3(2−ρp)ρp−1=ρp−12U1p(1−ρp)+2U2p2(2−ρp)+2U3p3(2−ρp)$(41)

1) 0<ρ<1 $∂[(BWE)A−(BWE)B]∂ρ>0$(42)

So the ability, information platform mitigates bullwhip effect, will increase with the decrease of ρ.

2) ρ = 0 $∂[(BWE)A−(BWE)B]∂ρ=0$(43)

So the ability, information platform mitigates bullwhip effect, only related to p. And with the increase of p, the ability will decrease.

3) −1<ρ<0 When p is an even number, $∂[(BWE)A−(BWE)B]∂ρ<0$(44)

So the ability, information platform mitigates bullwhip effect, will increase with the increase of ρ. When p is an odd number, $∂[(BWE)A−(BWE)B]∂ρ>0$(45)

So the ability, information platform mitigates bullwhip effect, will increase with the decrease of ρ. Similarly, when k = 3 or 4, we can also prove these results. In summary, after implanting information platform, dealers' order amount to processing enterprises is closer to the actual consumer demand and the bullwhip effect is mitigated here.

Result 1: the implantation of information platform can reduce the bullwhip effect in ASC, and the ability will increase with the decrease of ρ. Under this circumstance, members can determine order amount or production more close to the actual market demand.

## 4.1 The traditional paths information flows take

We may construct an agro-product supply chain model, taking as variables the five stake holders of the supply chain (farmers or f, agro-produce processing enterprises or e, agro-product dealers or d, retailers or r and consumers or c) and the government (g) whose policies also play an important part in the supply chain. If T is a given period of time, H is the amount of information and m(f,e,d,r,c,g), then ${H}_{T}^{m}$ is the total amount of information from all variables within that time. It can be illustrated as follows: $HT=Hf+He+Hd+Hr+Hc+Hg$(46)

In the agro-product supply chain, capital and service flow one-way while information flows two-way. Without an information platform, the information from different sources can only flow along the supply chain (shown in Figure 1). For instance, in a supply chain comprised of 5 sources of information, information from consumers has to be transferred four times before it can reach farmers (from consumers to retailers, from retailers to wholesalers, then from retailers to processing enterprises, and at last from processing enterprises to farmers).

Figure 1

Along the way, the original information may be omitted, delayed, or distorted on purpose. Therefore, information often becomes less reliable, less punctual, and less useful. If we assume ε of information is damaged when it flow between two near sources, then the amount of information farmers get from processing enterprises is He(1–ε) while the amount of information farmers can get from consumers will be as small as Hc(1–ε)4. Governments are different from other sources in their ways of obtaining and giving away information. In the first place, governments present tourism policies in a public manner but different policies are channeled to different stakeholders accordingly. And the stakeholders vary in their ability to process the information and make appropriate decisions, which is not an issue in question in this paper though. Meanwhile, technically speaking, governments are not a subject in the supply chain and thus lack the motivation to distribute among the stakeholders the information they have obtained from individual stakeholders for the purpose of scientific and reasonable policies. They only exchange information with the sources separately. For example, governments' policies about farmers will be communicated to farmers but farmers won't get information about processing enterprises although governments do possess the information. Similarly, governments won't proactively give information about farmers to processing enterprises (shown in Figure 2).

Figure 2

Information communication by governments

If {Em} is a data set of the information each subject has gained from other subjects and itself, Rm is the amount of information in the data set, m(f,e,d,r,c,g), and we assume every subject can measure its information accurately. We define Z as follow: $Z=(1−ε),ε∈(0,1)$(47)

And then we can come to the following equations.

$Rf=Hf+He×Z+Hd×Z2+Hr×Z3+Hc×Z4+Hg×ZRe=Hf×Z+He+Hd×Z+Hr×Z2+Hc×Z3+Hg×ZRd=Hf×Z2+He×Z+Hd+Hr×Z+Hc×Z2+Hg×ZRr=Hf×Z3+He×Z2+Hd×Z+Hr+Hc×Z+Hg×ZRc=Hf×Z4+He×Z3+Hd×Z2+Hr×Z+Hc+Hg×ZRg=Hf×Z+He×Z+Hd×Z+Hr×Z+Hc×Z+Hg$(48)

## 4.2 The platform paths information flows take

After an information platform is introduced, all the subjects in the supply chain are armed with this new information tool besides the traditional information paths. They can exchange and communicate information on this platform. The information platform serves its purpose in two stages: 1) collecting information from all sources; 2) processing the information and distributing it to all subjects (shown in Figure 3).

Figure 3

Platform paths of information flowss

Result 2: all subjects can obtain information and assess the market and industry in a faster and more convenient manner. If {Fm} is a date set of information all subjects get from the platform within a given period time of T, {Pm} is the amount of information in the data set, and m(f,e,d,r,c,g), then we can come to the following equations.

$Pf=∑Hm×Z2−Hf×Z2+Hf$(49) $Pe=∑Hm×Z2−He×Z2+He$(50) $Pd=∑Hm×Z2−Hd×Z2+Hd$(51) $Pr=∑Hm×Z2−Hr×Z2+Hr$(52) $Pc=∑Hm×Z2−Hc×Z2+Hc$(53) $Pg=∑Hm×Z2−Hg×Z2+Hg$(54)

## 4.3 A comparison of the amount of information before and after the platform is embedded

Our assumption is that the subjects of the supply chain get more information about the market and the industry due to an increase of information nodes and deeper embeddedness. In order to verify our assumption, a comparison is made between the amount of information each subject gets before the platform is introduced and that after. As were mentioned above, {Em} is a data set of the information each subject has gained from other subjects and itself within time T, and {Fm} is a date set of information all subjects get from the platform within a given period time of T. If {(EF)m} is a data set of the information each subject has gained both from other subjects and itself and from the platform within time T, and {(RP)m} is the amount of information in the data set, then {(EF)m} = {Em} ⋃ {Fm}.

Now, we assume that {Xc} is the data set for consumers, and {A} (the amount of information lost in a single transfer by means of the traditional path) equals {B} (the amount of information lost in a single transfer by means of the information platform), then there are the following three possibilities (shown in Figure 4).

Figure 4

Three Types of Information losses

In type (a), there is no intersection between {A} and {B}, so we can get: $({Xc}−{A})∪({Xc}−{B})={Xc}$(55)

In type (b), there is an intersection between {A} and {B}, so we can get: $({Xc}−{A})∪({Xc}−{B})={Xc}−({Xc}−{A})∩({Xc}−{B})$(56)

In type (c), because {A} is the same with {B}, so we can get: $({Xc}−{A})∪({Xc}−{B})={Xc}−{A}$(57)

Comparing the three types, we can see that (c) is the smallest data set of them. So, if possibility (c) can bring desired results, so can (a) and (b). When possibility (a) happens(namely for {Xc}, information lost in the first transfer by means of either the traditional path or the platform comes from the same incident, and so does the second, the third...), under this circumstance, the amount of information each subject gets in time T after the platform is introduced can be shown as follows.

$(RP)f=Hf+He×Z+Hd×Z2+Hr×Z2+Hc×Z2+Hg×Z(RP)e=Hf×Z+He+Hd×Z+Hr×Z2+Hc×Z2+Hg×Z(RP)d=Hf×Z2+He×Z+Hd+Hr×Z+Hc×Z2+Hg×Z(RP)r=Hf×Z2+He×Z2+Hd×Z+Hr+Hc×Z+Hg×Z(RP)c=Hf×Z2+He×Z2+Hd×Z2+Hr×Z+Hc+Hg×Z(RP)g=Hf×Z+He×Z+Hd×Z+Hr×Z+Hc×Z+Hg$(58)

Taking farmers for example, if formula (58)–(43), we can get: $(RP)f−Rf=Hr×Z2(1−Z)+Hc×Z2(1−Z2)$(59)

Because Z ∈ (0,1), then (1 – Z) > 0 and (1 – Z2) > 0. Then(RP)f > Rf. And we can get similar results for (a) and (b). Applying similar methods to processing enterprises, dealers, retailers, consumers and governments, we get: $(RP)e>Re,(RP)r>Rr,(RP)c>Rc,(RP)d=Rd,(RP)g=Rg$(60)

The total amount of information from all sources is HT and it remains the same after the introduction of the platform. So the proportion of information each subject gets can be shown as follows.

$(RP)fHt>RfHt,(RP)eHt>ReHt,(RP)rHt>RrHt(RP)cHt>RcHt,(RP)dHt=RdHt,(RP)gHt=RgHt$(61)

Result 3: After the information platform is introduced, farmers and processing enterprises, retailers, consumers can access to a bigger share of the total information while wholesalers and governments still get the same amount.

## 5.1 Measuring the amount of information

Borrowing the concept of “entropy” of thermodynamics, C. E. Shannon came up with the idea of “information entropy” in his book “A Mathematical Theory of Communication”, 1948. He solved the problem of measuring information amount, using the “bit” for a unit of information. The basic principle is that the amount of information an incident contains complies with the average degree of uncertainty of its occurrence. So the amount of information incident A contains can be illustrated as follows.

$H(A)=−∑λ=1npλlog2⁡pλ$(62)

In the equation, pλ refers to the probability that incident A occurs and n means the possible results or choices facing A. For example, a consumer may be faced with the choices between local products and imported ones, between seasonal and off-season ones, between cheaper ones and more expensive but greener ones. Meanwhile, different incidents that have to be decided about will influence the activities through the supply chain in different ways. So if {Xm} means all the incidents that all sources of information have to decide about in a given period time of T, then the total amount of information that all sources of information in time T can be shown as follows.

$Hm=−∑j=1n1∑i=1n2λjmpxijmlog2⁡pxijm$(63)

In the equation, m ∈ (f,e,d,r,c,g) and j refers to certain incident that certain source of information has to decide about, n1 is the number of incidents and ${\lambda }_{j}^{m}$ refers to the degree of importance the incident has in the tourism activities. The sum of all ${\lambda }_{j}^{m}$ is 1. And i means one possible result of certain incident,n2 is the number of possible results of certain incident. So ${p}_{{x}_{ij}^{m}}$ means the probability of result i when certain source of information decides about incident j. Since every incident has been given its fair weight, it is reasonable to measure the information amount in terms of bite.

## 5.2 An example analysis

If card {Xf} = card {Xc} = 3,card {Xe} = card {Xd} = card {Xr} = card {Xg} = 2, p = 0.1, and the possible results of every information incident (I), their probability (P) and their weights (W) of importance to the agro-product supply chain can be shown in Table 1.

Table 1

An numerical example

According to the equations mentioned above, we are able to figure out the amount of information each source/subject (S) contains and the amount of information each subject can get in the three different situations, which are shown in Table 2 (Keeping three decimal places).

Table 2

Information amount in different situations Unitbite

As is shown in table 2, after the information platform is (IP) embedded in the supply chain, the total amount of information farmers (f) get increases from 1.485 bite to 1.581 bite, processing enterprises (e) from 1.543 bite to 1.582 bite, retailers (r) from 1.566 bite to 1.598 bite, consumers (c) from 1.521 bite to the much larger 1.6 bite, while dealers (d) and governments (g) remain unchanged at 1.568 bite and 1.65 bite respectively. Similarly the proportions of information farmers, processing enterprises, retailers, consumers rise from 82.135% 85.343% 86.615% 84.126% respectively to 87.445% 87.5% 88.385% 88.496% while wholesalers and governments remain unchanged at 86.726% and 91.261%. These figures clearly support Result 3. If ? = 0.5p = 4L1 = L2 = L3 = L4 = 4, we can easily calculate the bullwhip effect in ASC (shown in Table 3).

Table 3

Impact of information platform on bullwhip effect

As is shown in table 3, the value of retailers has no change (both are 4.75 before and after the implantation of information platform), and dealers drop from 30.53 to 12.25, processing enterprises decrease from 123.11 to 23.50, farmers reduce from 540.94 to 38.50. Besides, upstream members of ASC can get more decrement. These figures obviously support Result 1.

## 6 Conclusions

Based on the existing researches on agro-product competitiveness, agro-product supply chain and platform theories, this paper has employed some mathematical models to analyze the mechanism how an information platform can affect ASC and then agro-product competitiveness. According to rigorous mathematical analysis, we find that an information platform can improve efficiency of agro-product supply chain and competitiveness of agro products by mitigating the bullwhip effect in ASC, cutting down time for communication, decreasing information asymmetry and increasing the information each subject gets.

This paper has made advancements in the following ways. First, from the perspective of the agro-product supply chain, taking six sources of information (famers, processing enterprises, dealers, retailers, consumers and governments) into account, scientific mathematical models are introduced to analyze how an information platform can help members in ASC communicate information, obtain information and make predictions. Existing researches focus on the construction and operation mechanism of platform and ignore the mechanism of action. So we enrich the basic theory research of information platform, ASC and agro-product competitiveness. Second, we introduce information entropy to measure the information amount members obtain, which can quantify the effect information platform to members’ information acquisition. So our research has laid a basic foundation for the application of an information platform in the ASC and has opened new fields for the research of agro-product competitiveness.

However, a few problems have yet to be solved. Firstly, since this paper focuses on better ways of acquiring information, processing of the information has not been given much attention though the factors and assessment of information process are well worth studying. Secondly, for the sake of convenience, this paper assumes, by means of both the traditional way and the platform, the same ?% of information is lost while in fact, there are different degrees of information loss by the two means. Thirdly, it is worth furtherly studying the technical architecture, the organizational structure, the value configuration, and the operational mechanism of the information platform.

Embedding an information platform in ASC can help members communicate and acquire information efficiently and effectively, mitigate the bullwhip effect and information asymmetric, make better market prediction and ordering decision and thus the whole ASC will become competitive in the agro-product market. This research is of particular importance to those with agricultural specialties but remotely located.

## Acknowledgement

The authors wish to thank the Major International Joint Research Program of the National Natural Science Foundation of China (Grant No. 71020107027), the National Natural Science Foundation of China (Grant No. 71001075), Doctoral Fund of Ministry of Education of China (No 20110181110034), and Social sciences program of Chengdu (No.SKNHR13-07), Central University Fund of Sichuan University (No.skqy201112) under which the present work was possible.

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Accepted: 2016-11-03

Published Online: 2017-04-06

Citation Information: Open Physics, Volume 15, Issue 1, Pages 108–120, ISSN (Online) 2391-5471,

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