Supply Chain Dynamics and Forecasting

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Supply Chain Dynamics and Forecasting

• Presenter Mu Niu

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The Context

• Companies make huge investments in Manufacturing
  Resource Planning systems. However, even with the
  introduction of resource planning systems, the
  performance of the supply chain remains
  problematic ( Lyneis, 2005 ).
• They do not take into account the inherent
  messiness of situations that contain human
  decision making within the process.
• Such tools do not promote learning or effective
  decision support as they do not include the
  powerful technique of simulation to allow for
  what-if analysis of alternative strategies .

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The Problem

• A centralised supply chain system was recently
  implemented in Draeger Safety Ltd, with the
  purpose of diminishing costs and avoiding
  backlogs. However, the central Hub in Germany
  still hold big amount of inventory.
• This made Draegers planning managers even more
  worried as it was difficult to predict what the
  consequences of centralised inventories would be
  for the manufacturing plant in Blyth.

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The Research Focus

• Modelling and simulation of the material and
  information flows including the decision
  processes of the centralised supply-chain at
  Draeger Safety, UK
• Analyses of the behaviour of inventories with
  relation to different decision strategies and
  characteristics of managers
• Evaluate the sensitivity of the supply chain to
  different methods of forecasting
• Develop a Microworld (Senge, 1990) to enable
  managers to conduct what-if scenarios and learn
  about the behaviour of the supply chain.

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Draeger supply chain structure
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Germany- UK Model

• 1Month
• Mfacture

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Model Equations

• Hinv(t) max(0, Hinv(t-1) Fship(t-1)
  Hship(t))
• Hblk(t) max(0, Hblk(t-1) Horders(t) -
  (Hinv(t-1) Fship(t-1)) HUB
• Hship(t) min(Horders(t) Hblk(t-1), Hinv(t-1)
  Fship(t-1))
• Finv(t) max(0, Finv(t-1) Fprod(t-1)
  Fship(t))
• Fblk(t) max(0, Fblk(t-1) Hreq(t1) -
  (Finv(t-1) Fprod(t-1)) Factory
• Fship(t) min(Hreq(t1) Fblk(t-1), Finv(t-1)
  Fprod(t-1))
• Hforcast(t2) (1 - ?) Horders(t) ?
  Hforcast(t1)
• Hreq(t2) max( 0, a( Q Hinv(t) Hblk(t) )
• aß( Fblk(t) Fship(t) )
  Hforcast(t2)) Decision
• Fprod(t) max( 0, a ( Q Finv(t) Fblk(t) )
  Hreq(t2) ) Making

a, is a measure of the aggressiveness with which
inventory differences are corrected. 0,1 ß, is
a measure of the weight with which inventory
ordered but still to arrive. 0,1
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Nonlinear block diagram
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Time simulation
Stable
Limit cycle
Quasi periodic
Chaotic
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Equations
X(k) A X(k-1) B U(k)
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System Block Diagram
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Eigenvalues plotted for a 00.011 , ß 0
and ß 00.011 , a 1 with unit circle
a 00.011 , ß 0
ß 00.011 , a 1
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The stability analysis

• For the condition ß 0 (depicted in Figure of
  eigenvalue plots), the Factory characteristic
  equation is
• (z a)(z -1) a 0
• This has two eigenvalues, one at z 0 and a
  second, which is always real and which lies in
  the range z 1 ? 0 as a 0 ? 1.
• The Hub characteristic equation is
• (z2 a)(z -1) a 0
• This has three eigenvalues. Again one of these
  is at z 0, the other two form a second order
  pair that become complex when a gt 0.25. It is
  this pair that is clearly identified in Figure of
  eigenvalue plots.
• Moreover, it is the Hubs dynamics and not the
  Factorys that are the potential source of
  unstable behavior. The Hub, potentially,
  becoming unstable for any value of a gt 1, (whilst
  the Factory would be stable for any value of a lt
  2.)

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Model with two additional Production delays
To explore the long lead time production
dynamics. The additional delay were added into
the production
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System Block Diagram
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Eigenvalues plotted for a 00.011 , ß 0
and ß 00.011 , a 1 with unit circle
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Model Analysis

• analysis given that the replenishing inventory
  rate a has a destablising effecs while the
  consideration of the past decision rate ß has a
  stablising effects on the dynamics of this
  production delayed supply chain model.
• The extra production delay has made the system
  more sensitive to the management decisions.
  Comparing with the original model, the production
  delay model could be unstable, even the
  eigenvalues locating inside of the unit circle.
• managers have a flexible option by improving the
  safety stock Q to stabilize the supply chain and
  achieve the on time delivery. However the
  warehouse has to pay more costs for holding the
  extra mount of safety stock.
• With the introduction of the two additional lead
  time states, it is the Factory which provide the
  primary route toward instablility. In this
  situation, the Hub can do little about the poor
  management decisions in the Factory.

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Model with an Planning delays

• The planning delay represents two likely
  scenarios
• Getting forecast wrong
• Compatibility problems between the planning
  systems at different locations

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System block diagram
Hub
Factory
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Eigenvalues plotted for a 00.011 , ß 0
and ß 00.011 , a 1 with unit circle
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Model Analysis

• Just as in the two previous cases, a has a
  destabilising influence whilst ß is stabilising.
• For this situation it is again the Hub management
  policy that is the primary route to instability.
  However, with the additional information delay
  the Hubs route to instability now follows the
  more severe path.
• In the presence of the one month information
  delay, even the stabilising influence of ß only
  lessens the severity of the route to instability.
  As long as a 1, no matter what ß is, the model
  is always oscillating. Operations on the safety
  stock Q cannot make effects for the unstable
  behavior.
• Thus, for this situation good management and
  management policies are critical if significant
  problems are to be avoided. Therefore, the
  accurate forecasting is essential to improve the
  supply chain performance.

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Time series Prediction

• The basic principle of time series prediction is
  to use a model to predict the future data based
  on known past data.
• Many kinds of forecasting methods implemented
  with system dynamic approach, ARMA
  (auto-regression and moving average) model,
  wavelet neural networks model has been applied.
• A performance function, which measures the
  absolute difference between forecast and real
  data, is employed to record the cost for each
  different structured model

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The original data

• The original data is 64 months sales history of
  Lung demand valve

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ARMA without any preprocessing
The coefficient is produced and updated by
Recursive least square
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ARMA with Differencing preprocessing
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Cost function
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Wavelet Neural Networks
This hybrid scheme includes three stages. 1)The
time series were decomposed with a wavelet
function into three sets of coefficients. 2)
Three new time series is predicted by a separate
NN 3)The prediction results are used as the
inputs of the third stage, where the next sample
of is derived by NN4.
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Forecasting results
ARMA
Neural Network
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Cost function
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Summary and Contributions

• The behaviors of Draeger supply chain model has
  been analyzed with different decision parameters.
  The small signal analysis shows that when the
  system behaves normally (no backlog) the factory
  and the hub are decoupled.
• We identified the principle source of unstable
  behavior could be the factory or hub depnding on
  the operating condition. In the original model
  the route toward instability is via via the Hub
  management policy. With the introduction of the
  extra states (additional lead-time), it is the
  Factory which now provides the primary route
  toward instability .In the presence of one month
  planning delay, the Hubs route to instability
  follows the more severe path.
• Because the systems are isolated poor
  management decisions in the Hub cannot be
  corrected by good decisions in the Factory
• We have shown the most severe route to the
  instability come from the errors in forecasting.
  The wavelet neural network forecasting apparently
  offers to improvement over the Draeger current
  forecasting approach.

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Microworld
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Further Research

• Include the dynamics of other Hubs
• Look at different decision making in different
  Hubs
• look for methods to further improve forecasting

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Publication

• Niu M.,Sice P.,French I., Mosekilde E., (2007)
  The Dynamics Analysis of Simplified Centralised
  Supply Chain, The Systemist Journal, Oxford, UK,
  Nov.2007.
• Niu M.,Sice P.,French I., Mosekilde E., (2008)
  Explore the Behaviour of Centralised Supply Chain
  at Draeger Safety UK, International Journal of
  Information system and Supply Chain Management,
  USA, Jan. 2008 (print copy availibel in Dec
  2008).
• French I., Sice P., Niu M., Mosekilde E.,(2008)
  The Dynamic Analysis of a Simplified Centralised
  Supply Chain and Delay Effects, System Dynamic
  Conference, Athens, July.2008.
• Sice P., Niu M., French I., Mosekilde E., (2008)
  The Delay Impacts on a Simplified Centralised
  Supply Chain, UK Systems Society Conference,
  Oxford, UK, Sep.2008.
• Niu M, Sice P., French I., (2008) Nonlinear
  Forecasting Model, Northumbria Research Forum
  2008, Newcastle upon Tyne, UK.

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