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A Study on the Information Sharing Model of the Supply Chain Based on Transmission Dynamics and Its Application
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 4041 – 4046 www.elsevier.com/locate/procedia
Advanced in Control Engineeringand Information Science
A Study on the Information Sharing Model of the Supply Chain Based on Transmission Dynamics and Its Application Junhai Ma1,2* ，Guanhui Wang1
1 College of Management Economic, Tianjin University, Tianjin 300072, China 2 Tianjin University of Finance & Economics, Tianjin 300222, China
Abstract Supply chain management has been a subject of both theoretical and empirical studies in the operations management literature. One of the reasons for supply chain inefficiencies is the inadequacy of information sharing among the supply chain node enterprises, which has drawn wide concerns among scholars and reseracher in this field. Based on a review of current studies in transmission dynamics, this paper constructs a three-phased model. The models and critical thresholds in homogeneous, heterogeneous, and heterogeneous conditional networks are worked out to reveal the quantitative relationship between some statistics of the supply chain network. The finding of statistical emulation, arrived at with the adjustment of the parameters, is that the alteration in the threshold can effectively improve the level of enterprise information sharing among the supply chain node enterprises. This study finding is of theoretical value and practical significance.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Key words: Spreading dynamics, Information sharing, Supply chain models, Complexity
1. Introduction It has always been the case that many manufacturing companies find high demand for their products. However, the fluctuation of the demand exceeds that of the actual consumption quantity of the products in the market, with the result that companies are bedeviled with excess capacity and inventory. Many scholars have made research in information sharing. Cachon and Fisher[1] examines information sharing in supply chain. Yanfeng Ouyang[2] analyzes the bullwhip effect in multi-stage supply chains operated with linear and time-invariant A basic hypothesis in transmission dynamics is homogenous mixing hypothesis
[3-4]
. It assumes that each individual has an equal chance of contacting any other
* Corresponding author. Tel.: +86 15222025960 E-mail address: [email protected], [email protected]
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.758
4042 2
Junhai Ma and Wang /Engineering Procedia Engineering 15 (2011) 4041 – 4046 Junhai MaGuanhui et al/ Procedia 00 (2011) 000–000
individual in the group. Some contacts take place in real life complex networks[5]. Supply chains are regarded as complex networks. Based on the SIR model developed by Kermack and McKendrick[6], this paper puts forward a theory on critical value of information sharing in supply chain. A typical supply chain consists of the suppliers, manufacturers, distributors, and customers. These players in the supply chain can be classified into three categories: information senders, information receivers, and actors. 2. Hypothesis of the Supply Chain Model Information senders include suppliers, manufacturers, distributors. At time t, the proportion of the information senders is denoted as s(t), the proportion of the information receivers is denoted as r(t), the proportion of the actors is denoted as a(t). Let us assume: (1). The supply chain is in a closed environment. (2). No urgent orders of large volumes are involved. (3). The number of companies along the supply chain is fixed at time t. The actors might alter their previous order in response to the information from the senders. The number of actors is in direct ratio to s(t)r(t). Let the coefficient of the actors be β, then the number of new actors at time t is βs(t)r(t). At time t, the number of senders who do not alter their actions in response to other senders’ actions is in direct ratio to the number of actors. Let the coefficient of the actors be γ, then the number of actors at time t is γr(t). Assume β be the probability that the senders will be affected and therefore become receivers, γ be the probability that the receivers become actors. Let δ be the probability that the receivers are influenced by the information from the actors, and ζ be the probability that the senders become actors. As the supply chain network is heterogeneous, Let k be the average degree of all the players in this network.But k cannot describe the characteristics of the network. Therefore, the heterogeneousness of the node degree must be taken into consideration. So assume sk(t), rk(t), ak(t) be the relative density. 3. Model Construction 3.1 In the Case of Homogenous Networks The supply chain networks can be regarded as homogeneous networks where the degree of each distributor approximates the average degree, because the status and importance of these small and
4043 3
Junhai MaJunhai and Guanhui Wang / Procedia Engineering 15 (2011) 4041 – 4046 Ma et al / Procedia Engineering 00 (2011) 000–000
medium-sized distributors is comparable. − − ds(t ) dr (t ) da(t ) = − β k s(t )r (t ) − ζ s (t ), = β k s (t )r (t ) − γ r (t ), = ζ s (t ) + γ r (t ) dt dt dt
(1) −
−ζ t − β k
In the above equations, ζ, γ, β are fixed sharing coefficient. Let s (t ) = e e
t
∫0 r (τ ) dτ
(2) When the system reaches a state of stability, make dr(t)/dt=0. Therefore, Let
r(t)=0,
The
relationship
can
be
r (t ) =
β − k s (t ) r (t ) γ
rewritten
as
−
β / γ > eζ t / k
(3) As no signifcant difference exsists between the degree of small-sized and medium-sized distributors k, −
−
ζt the average degree approximation of k can be put at 6. e / k is the threshold for information sharing −
ζt control where the value of ζ is generally regarded as a constant. When β / γ < e / k , information sharing −
ζt can be achieved with the progress of time t. However, when β / γ > e / k , information sharing is
confined to certain areas instead of being fully achieved. To improve information sharing, distributors should be given greater say to lower the value of β. 3.2 In the Case of Heterogenous Networks According to the Pareto principle, the supply chain networks can be regarded as heterogeneous networks, because the degree of large distributors is larger than that of the small and medium-sized distributors. Based on the above statement, differential equations are expressed as
dsk (t ) dr (t ) da (t ) = − β ksk (t )ωk (t ) − ζ sk (t ), k = β ksk (t )ωk (t ) − γ rk (t ), k = ζ sk (t ) + γ rk (t ) dt dt dt (4) ωk(t) denotes the random probability of the receivers being linked at time t. In the supply chain network, the probability of a node with a degree of λ being linked is in direct ratio to λp(λ). P(λ) denotes node degree distribution which is defined as a node chosen randomly from the supply chain network. The degree of the node equals the probability of λ. Therefore,
4044 4
ωk (t ) =
Junhai Ma and Wang /Engineering Procedia Engineering 15 (2011) 4041 – 4046 Junhai MaGuanhui et al/ Procedia 00 (2011) 000–000
∑ kp(k )r ∑ λ λ p (λ )
k
k
=
1 ∑ k kp(k )rk k
stability, make drk(t)/dt=0. Then
t
, then
rk (t ) =
then
, When the system reaches a state of
β ωk (t ) = ks (t )ωk (t ) γ k , As
− β kω (τ ) dτ β ωk (t ) = − ∑ kp (k ) kω (t )e−ζ t e ∫ γ k k
1
−
− β k ω (τ ) dτ sk (t ) = e −ζ t e ∫0
k
k
−
k
, −
df (ω (t )) >1 dω (t ) ω (t )=0
t
0
,
∑ kp(k )r (t )
let
,
β eζ t k > − γ 2 k
then,
(5) −
−
−
−
ζt 2 ζt 2 Make e k / k the threshold for information sharing control. When β / γ < e k / k , information −
−
ζt 2 sharing can be achieved with the progress of time t. However, when β / γ > e k / k , information sharing,
concentrating in certain areas, cannot be fully achieved. Under such cirumstances, the supply chain −
−
−
2 ζt 2 networks are heterogeneous networks. The larger is the value of k , the smaller the threshold of e k / k .
As a result, information sharing is difficult to achieve. To increase the value of the threshold, an option is to classify the distributors into different groups for management purposes. 3.3 In the Case of Heterogenous Conditional Networks Based on the second scenario, positive node degree correlation exists when nodes of high degree are linked, and negative node degree correlation exists when nodes of low degree are linked. The edges between the marketing departments of manufacturers and large distributors show positive correlation. We can use conditional probability
P ( k ' k)
to illustrate this correlation.
P ( k ' k)
is the probability that a
randomly chosen node with degree k arrives at a node with degree k’. ωk(t) denotes the random probability of the receivers being linked at time t. Therefore,
ω (∞ ) = ∑ k P ( k k )rk (∞ ) '
'
= ∑ k P(k ' k )
ω (t ) = ∑ k P ( k ' k )rk (t ) '
, In a stable state,
β k 'δω (∞) γ (ζ + δ ) + (γ + δ ) β k 'ω (∞)
,
(6) Therefore, (7)
ζ β / γ = (1 + ) / ∑ k k ' p (k ' k) δ '
4045 5
Junhai MaJunhai and Guanhui Wang / Procedia Engineering 15 (2011) 4041 – 4046 Ma et al / Procedia Engineering 00 (2011) 000–000
ζ β / γ < (1 + ) / ∑ k k ' p (k ' k) δ In the case of , the information will be evenly disseminated among the '
ζ β / γ > (1 + ) / ∑ k k ' p (k ' k) δ nodes in the networks with the progress of time t. In the case of , the '
information will not be evenly disseminated among the nodes in the networks with the progress of time t. We can take several measures to increase the threshold value. For example, we can make the information dissemination a one-way process, the decision making of nodes with large degrees is independent of nodes with small degrees. Besides, measures could be taken to reduce the communication between the nodes. These meausres will help to decrease the value of δ. An alternative is to increase the value of ζ through regular government information disclosure. In the three scenarios mentioned above, different results for the critical threshold β/γ are arrived at. Information sharing can be achieved if we adjust the three parameters ζ, γ, β. In the first scenario where the degrees are evenly distributed, the synchronization of ζ,, γ, β poses greater challenge in adjusting than in the latter two scenarios. In the second scenario which is close to reality, large distributors can be adjusted by making the information follow a one-way flow. That is, the information is allowed to flow from large distributors to small and medium-sized distributors, whereas the opposite is forbidden. In the third scenario, we can approximate the sum of the conditional probability based on conditional distribution to get the criteria for the measurement of information sharing. Some measures can be taken to achieve information transparency. 4. Conclusion This paper constructs three models on information sharing which cover the companies along the different stages of the supply chain. A theory on threshold value is also developed. The study shows that in multi-stage supply chains comprising manufacturers and distributors, distributors can base their decision-making on the information they acquired. Under the circumstances of homogeneous and heterogeneous networks, information sharing can be achieved in a time trend through adjusting the critical threshold and relevant parameters. A more precise measurement of the value of information sharing can be achieved if cost calculation is added to quantitative study. References
4046 6
Junhai Ma and Wang Engineering / Procedia Engineering 15 (2011) 4041 – 4046 Junhai Ma Guanhui et al/ Procedia 00 (2011) 000–000
[1] Murray J. D., Mathematical Biology: (І) An Introduction. Berlin: Springer Verlag, 2003. [2] Yanfeng O., The effect of information sharing on supply chain stability and the bullwhip effect, European Journal of Operational Research, In Press, Corrected Proof, Available online 13 December 2006. [3] Cachon G. Fisher, Supply chain inventory management and the value of shared information, Management Science, 2000, 46(8), 1032-1048. [4] P. Fiala, Information sharing in supply chains, Omega, Volume 33, Issue 5, Or and its Applications, October 2005, Pages 419-423 [5] Moreno Y, Pastor-Satorras R, Vespignani A. Epidemic outbreaks in complex heterogeneous networks. The European Physical J, 2002, 26(4): 521-529. [6] Deffuant G., Neau D., Amblard E., Weisbuch G., Mixing beliefs among interacting agents[J]. Adv. Complex Syst., 2000, 3:87-98.
Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 4041 – 4046 www.elsevier.com/locate/procedia
Advanced in Control Engineeringand Information Science
A Study on the Information Sharing Model of the Supply Chain Based on Transmission Dynamics and Its Application Junhai Ma1,2* ，Guanhui Wang1
1 College of Management Economic, Tianjin University, Tianjin 300072, China 2 Tianjin University of Finance & Economics, Tianjin 300222, China
Abstract Supply chain management has been a subject of both theoretical and empirical studies in the operations management literature. One of the reasons for supply chain inefficiencies is the inadequacy of information sharing among the supply chain node enterprises, which has drawn wide concerns among scholars and reseracher in this field. Based on a review of current studies in transmission dynamics, this paper constructs a three-phased model. The models and critical thresholds in homogeneous, heterogeneous, and heterogeneous conditional networks are worked out to reveal the quantitative relationship between some statistics of the supply chain network. The finding of statistical emulation, arrived at with the adjustment of the parameters, is that the alteration in the threshold can effectively improve the level of enterprise information sharing among the supply chain node enterprises. This study finding is of theoretical value and practical significance.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Key words: Spreading dynamics, Information sharing, Supply chain models, Complexity
1. Introduction It has always been the case that many manufacturing companies find high demand for their products. However, the fluctuation of the demand exceeds that of the actual consumption quantity of the products in the market, with the result that companies are bedeviled with excess capacity and inventory. Many scholars have made research in information sharing. Cachon and Fisher[1] examines information sharing in supply chain. Yanfeng Ouyang[2] analyzes the bullwhip effect in multi-stage supply chains operated with linear and time-invariant A basic hypothesis in transmission dynamics is homogenous mixing hypothesis
[3-4]
. It assumes that each individual has an equal chance of contacting any other
* Corresponding author. Tel.: +86 15222025960 E-mail address: [email protected], [email protected]
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.758
4042 2
Junhai Ma and Wang /Engineering Procedia Engineering 15 (2011) 4041 – 4046 Junhai MaGuanhui et al/ Procedia 00 (2011) 000–000
individual in the group. Some contacts take place in real life complex networks[5]. Supply chains are regarded as complex networks. Based on the SIR model developed by Kermack and McKendrick[6], this paper puts forward a theory on critical value of information sharing in supply chain. A typical supply chain consists of the suppliers, manufacturers, distributors, and customers. These players in the supply chain can be classified into three categories: information senders, information receivers, and actors. 2. Hypothesis of the Supply Chain Model Information senders include suppliers, manufacturers, distributors. At time t, the proportion of the information senders is denoted as s(t), the proportion of the information receivers is denoted as r(t), the proportion of the actors is denoted as a(t). Let us assume: (1). The supply chain is in a closed environment. (2). No urgent orders of large volumes are involved. (3). The number of companies along the supply chain is fixed at time t. The actors might alter their previous order in response to the information from the senders. The number of actors is in direct ratio to s(t)r(t). Let the coefficient of the actors be β, then the number of new actors at time t is βs(t)r(t). At time t, the number of senders who do not alter their actions in response to other senders’ actions is in direct ratio to the number of actors. Let the coefficient of the actors be γ, then the number of actors at time t is γr(t). Assume β be the probability that the senders will be affected and therefore become receivers, γ be the probability that the receivers become actors. Let δ be the probability that the receivers are influenced by the information from the actors, and ζ be the probability that the senders become actors. As the supply chain network is heterogeneous, Let k be the average degree of all the players in this network.But k cannot describe the characteristics of the network. Therefore, the heterogeneousness of the node degree must be taken into consideration. So assume sk(t), rk(t), ak(t) be the relative density. 3. Model Construction 3.1 In the Case of Homogenous Networks The supply chain networks can be regarded as homogeneous networks where the degree of each distributor approximates the average degree, because the status and importance of these small and
4043 3
Junhai MaJunhai and Guanhui Wang / Procedia Engineering 15 (2011) 4041 – 4046 Ma et al / Procedia Engineering 00 (2011) 000–000
medium-sized distributors is comparable. − − ds(t ) dr (t ) da(t ) = − β k s(t )r (t ) − ζ s (t ), = β k s (t )r (t ) − γ r (t ), = ζ s (t ) + γ r (t ) dt dt dt
(1) −
−ζ t − β k
In the above equations, ζ, γ, β are fixed sharing coefficient. Let s (t ) = e e
t
∫0 r (τ ) dτ
(2) When the system reaches a state of stability, make dr(t)/dt=0. Therefore, Let
r(t)=0,
The
relationship
can
be
r (t ) =
β − k s (t ) r (t ) γ
rewritten
as
−
β / γ > eζ t / k
(3) As no signifcant difference exsists between the degree of small-sized and medium-sized distributors k, −
−
ζt the average degree approximation of k can be put at 6. e / k is the threshold for information sharing −
ζt control where the value of ζ is generally regarded as a constant. When β / γ < e / k , information sharing −
ζt can be achieved with the progress of time t. However, when β / γ > e / k , information sharing is
confined to certain areas instead of being fully achieved. To improve information sharing, distributors should be given greater say to lower the value of β. 3.2 In the Case of Heterogenous Networks According to the Pareto principle, the supply chain networks can be regarded as heterogeneous networks, because the degree of large distributors is larger than that of the small and medium-sized distributors. Based on the above statement, differential equations are expressed as
dsk (t ) dr (t ) da (t ) = − β ksk (t )ωk (t ) − ζ sk (t ), k = β ksk (t )ωk (t ) − γ rk (t ), k = ζ sk (t ) + γ rk (t ) dt dt dt (4) ωk(t) denotes the random probability of the receivers being linked at time t. In the supply chain network, the probability of a node with a degree of λ being linked is in direct ratio to λp(λ). P(λ) denotes node degree distribution which is defined as a node chosen randomly from the supply chain network. The degree of the node equals the probability of λ. Therefore,
4044 4
ωk (t ) =
Junhai Ma and Wang /Engineering Procedia Engineering 15 (2011) 4041 – 4046 Junhai MaGuanhui et al/ Procedia 00 (2011) 000–000
∑ kp(k )r ∑ λ λ p (λ )
k
k
=
1 ∑ k kp(k )rk k
stability, make drk(t)/dt=0. Then
t
, then
rk (t ) =
then
, When the system reaches a state of
β ωk (t ) = ks (t )ωk (t ) γ k , As
− β kω (τ ) dτ β ωk (t ) = − ∑ kp (k ) kω (t )e−ζ t e ∫ γ k k
1
−
− β k ω (τ ) dτ sk (t ) = e −ζ t e ∫0
k
k
−
k
, −
df (ω (t )) >1 dω (t ) ω (t )=0
t
0
,
∑ kp(k )r (t )
let
,
β eζ t k > − γ 2 k
then,
(5) −
−
−
−
ζt 2 ζt 2 Make e k / k the threshold for information sharing control. When β / γ < e k / k , information −
−
ζt 2 sharing can be achieved with the progress of time t. However, when β / γ > e k / k , information sharing,
concentrating in certain areas, cannot be fully achieved. Under such cirumstances, the supply chain −
−
−
2 ζt 2 networks are heterogeneous networks. The larger is the value of k , the smaller the threshold of e k / k .
As a result, information sharing is difficult to achieve. To increase the value of the threshold, an option is to classify the distributors into different groups for management purposes. 3.3 In the Case of Heterogenous Conditional Networks Based on the second scenario, positive node degree correlation exists when nodes of high degree are linked, and negative node degree correlation exists when nodes of low degree are linked. The edges between the marketing departments of manufacturers and large distributors show positive correlation. We can use conditional probability
P ( k ' k)
to illustrate this correlation.
P ( k ' k)
is the probability that a
randomly chosen node with degree k arrives at a node with degree k’. ωk(t) denotes the random probability of the receivers being linked at time t. Therefore,
ω (∞ ) = ∑ k P ( k k )rk (∞ ) '
'
= ∑ k P(k ' k )
ω (t ) = ∑ k P ( k ' k )rk (t ) '
, In a stable state,
β k 'δω (∞) γ (ζ + δ ) + (γ + δ ) β k 'ω (∞)
,
(6) Therefore, (7)
ζ β / γ = (1 + ) / ∑ k k ' p (k ' k) δ '
4045 5
Junhai MaJunhai and Guanhui Wang / Procedia Engineering 15 (2011) 4041 – 4046 Ma et al / Procedia Engineering 00 (2011) 000–000
ζ β / γ < (1 + ) / ∑ k k ' p (k ' k) δ In the case of , the information will be evenly disseminated among the '
ζ β / γ > (1 + ) / ∑ k k ' p (k ' k) δ nodes in the networks with the progress of time t. In the case of , the '
information will not be evenly disseminated among the nodes in the networks with the progress of time t. We can take several measures to increase the threshold value. For example, we can make the information dissemination a one-way process, the decision making of nodes with large degrees is independent of nodes with small degrees. Besides, measures could be taken to reduce the communication between the nodes. These meausres will help to decrease the value of δ. An alternative is to increase the value of ζ through regular government information disclosure. In the three scenarios mentioned above, different results for the critical threshold β/γ are arrived at. Information sharing can be achieved if we adjust the three parameters ζ, γ, β. In the first scenario where the degrees are evenly distributed, the synchronization of ζ,, γ, β poses greater challenge in adjusting than in the latter two scenarios. In the second scenario which is close to reality, large distributors can be adjusted by making the information follow a one-way flow. That is, the information is allowed to flow from large distributors to small and medium-sized distributors, whereas the opposite is forbidden. In the third scenario, we can approximate the sum of the conditional probability based on conditional distribution to get the criteria for the measurement of information sharing. Some measures can be taken to achieve information transparency. 4. Conclusion This paper constructs three models on information sharing which cover the companies along the different stages of the supply chain. A theory on threshold value is also developed. The study shows that in multi-stage supply chains comprising manufacturers and distributors, distributors can base their decision-making on the information they acquired. Under the circumstances of homogeneous and heterogeneous networks, information sharing can be achieved in a time trend through adjusting the critical threshold and relevant parameters. A more precise measurement of the value of information sharing can be achieved if cost calculation is added to quantitative study. References
4046 6
Junhai Ma and Wang Engineering / Procedia Engineering 15 (2011) 4041 – 4046 Junhai Ma Guanhui et al/ Procedia 00 (2011) 000–000
[1] Murray J. D., Mathematical Biology: (І) An Introduction. Berlin: Springer Verlag, 2003. [2] Yanfeng O., The effect of information sharing on supply chain stability and the bullwhip effect, European Journal of Operational Research, In Press, Corrected Proof, Available online 13 December 2006. [3] Cachon G. Fisher, Supply chain inventory management and the value of shared information, Management Science, 2000, 46(8), 1032-1048. [4] P. Fiala, Information sharing in supply chains, Omega, Volume 33, Issue 5, Or and its Applications, October 2005, Pages 419-423 [5] Moreno Y, Pastor-Satorras R, Vespignani A. Epidemic outbreaks in complex heterogeneous networks. The European Physical J, 2002, 26(4): 521-529. [6] Deffuant G., Neau D., Amblard E., Weisbuch G., Mixing beliefs among interacting agents[J]. Adv. Complex Syst., 2000, 3:87-98.