1. Supply Chain Dynamics and Forecasting
Presenter: Mu Niu
The title of my thesis is Supply china dynamics and forecasting.
The human decision making influences on different structured supply chain has been explored. To improve the supply chain performance. Different forecasting methods are applied and tested in the supply chain model.

2. Dynamics and Forecasting
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 .
To begin with, I’d like to put my research into some kinds of context. Currently, many manufacturing company use logistic software such as SAP, MRP(material requirement planning) as their planning system. However, MRP itself is considered to be a simple calculation engine. such planning system do not consider the human decision making in the planning process and do not promote learning. Therefore the supply chain performance still remain problematic.
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3. Dynamics and Forecasting
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 Draeger’s 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.
So what exactly is the problem? A centralised supply chain system was implemented in a global manufacturing company called Draeger Safety Ltd. It is an international corporation, manufacturing breathing protection and gas detection equipment. It has a presence in approximately 200 countries on all continents. It is difficult to predict the consequence of this reformation would be for the factory plant in Blyth.
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4. Dynamics and Forecasting
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.
The question is what can be done about it. This bring us to the focus of research. The research focus is modelling and simulating......forecasting. A Microwrold is developed to help manager have better understanding about the dynamics of supply chain and enable them to test different planning strategy.
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5. Draeger supply chain structure
Goods
Shipped
Order in
Central Hub
Germany
China
Japan
USA
Canada
France
Denmark
Hub
Hub Asia
Singapore
Factory
Blyth UK
The system I am going to consider is Draeger Global supply chain system. This is the schematic diagram of the draeger supply chain structure.
the primary Hub, based in Germany, receives stock from the UK Factory and ships this to the main EU markets and to the Pacific and US Hubs. Each of the Hubs acts as a business unit and maintains a warehouse. The Hubs receive orders from the Draeger sales agencies linked to them. The sales agencies do not keep inventory or receive shipments from the Hub. The Hubs ship the goods directly to the customer and communicate with production units to help establish production requirements. Since the local agencies do not need to hold inventories. In this structure, the inventory cost is minimised.
Since the Hub structure is similarWe decide to focus on UK Germany part..
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6. Dynamics and Forecasting
Germany- UK Model
Germany Primary Hub
Blyth Factory
Hub
Forecast
Hforecast
Requirement
Hreq
Production
Fprod
Inventory
Finv
Factory Shipments
Fship
Hinv
Backlog
Hblk
Fblk
1Month
T’ Delay
Hub Sales
Horders
Shipments
Hship
1Month
M’facture
To explore it in more detail. We can see this picture.
There are basically two parts in this Germany UK model. Those squares that appear in the top of the Figure are the planning parts including ‘Hub forecast’, ‘Hub requirement’, and ‘Factory production’. The lower part of the diagram represents the warehouse and transporting parts. All the planning components work in one time unit. For example, when the customer places a sales order on the Hub, it takes one single time unit(one month in the simulation) for the sales input into ‘Hub forecast’ and generating output as production plan from ‘Factory production’.
The process is based on a two month ahead forecast. That is, based on the current trends in orders and stock levels, the Hub forecasts its requirements for two months ahead.
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7. Dynamics and Forecasting
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(t+1) - (Finv(t-1) + Fprod(t-1)); Factory
Fship(t) = min(Hreq(t+1) + Fblk(t-1), Finv(t-1) + Fprod(t-1));
Hforcast(t+2) = (1 - θ) Horders(t) + θ Hforcast(t+1);
Hreq(t+2) = max( 0, α( Q – Hinv(t) + Hblk(t) )
–αβ( Fblk(t) +Fship(t) )+ Hforcast(t+2)); Decision
Fprod(t) = max( 0, α ( Q – Finv(t) + Fblk(t) ) + Hreq(t+2) ) Making
In order to do formal analysis, we need to represent the figure as set of equations. After discuss with draeger representative and looking at available technique literatures. We were able to set up these equations.
The equations that are used to describe the inventories, backlogs and shipments are discrete (using a 1 month sample interval) Hub orders and Factory production are based on a simplified anchoring and adjustment heuristic. Expected demand is formed from incoming orders in an adaptive manner based on a simple first-order exponential prediction.
. Provision for this expected demand is taken to be the cornerstone of the order/production policy. ordering policy /Production is adjusted above or below this expected demand value to maintain current inventory and supply lines at their desired levels. where, α, (which lies in the range 0-1) defined the fraction of the discrepancy between the desired inventory Q and the effective inventory (Inventory – Backlog). β (which again lies in the range between 0 – 1) is the fraction of the supply line (requests or production already ordered but not yet received) .
Here, θ represents the rate at which the forecast is adapted
α, is a measure of the aggressiveness with which inventory differences are corrected. [0,1]
β, is a measure of the weight with which inventory ordered but still to arrive. [0,1]
α, is a measure of the aggressiveness with which inventory differences are corrected. [0,1]
β, is a measure of the weight with which inventory ordered but still to arrive. [0,1]
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8. Nonlinear block diagram
It is difficult to interpret any dynamics from the equations. It is easier to understand them with diagram. We map the equation into block diagram.
It is clear from Figure 3.5 that the system comprises four primary elements: These are, the production and Hub dynamics (with their inherent saturations and constraints), the external disturbances or demands, and, the management decision making policies.
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9. Time simulation Stable Limit cycle Quasi periodic Chaotic 19/09/2018
The time simulation is one of the tool we used in analysis.
Quasi periodic
Chaotic
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10. Equations X(k) = A X(k-1) + B U(k) 19/09/2018
If we want to try to use more structured approach to analyse the system. We are going to make use o the fact, the principle of nonlinearity we seen both in equation and diagram are large signal saturation effects. That means we can begin by applying small signal local linear analysis. locally Linearize the system around zero backlog condition. The system can be represent by…. Which in term can be represent by the block diagram.
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11. Dynamics and Forecasting
System Block Diagram
The hub feedback loop is plotted in red and factory feedback loop is plotted in blue. The parameter θ only exists in the first order input and is outside of the feedback structure.
On the other hand, α and β lie inside the feedback loops and will significantly influence the dynamic behaviour of the system.
Therefore, the analysis will concentrate only on variations in α and β .
There is no global feedback loop to link Hub and Factory together. The Factory and the Hub have isolated feedback structures. The individual characteristic euqaions can be analysed independently
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12. Dynamics and Forecasting
Eigenvalues plotted for α = 0:0.01:1 , β = 0 and β = 0:0.01:1 , α = 1 with unit circle
Since our model is discrete, the effect of decision making parameters(which is alpha and beta influence) is explained in egenvalue and unit circle plots.
Αlpha has a destabilising influence, since the complex eigenvalue pair move toward the edge of the unit disc as alpha increase.
Big Alpha represent the aggressive ambitious manager want to reduce the gap between the desire inventory and actual inventory asap. However, if α is too small (representing a very cautious manager) the response becomes too slow and can this lead to significant backlogs and the potential for customer dissatisfaction.
Β on the other hand is clearly stabilising since the igenvalues move toward the center of the unit disc as beta increases.
B>0 represents a manager that thinks outside of immediate area of control and takes some or full account of history. Taking into account the impact of previous decisions, has a stabilising effect
α = 0:0.01:1 , β = 0
β = 0:0.01:1 , α = 1
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13. The stability analysis
For the condition β = 0 (depicted in Figure of eigenvalue plots), the Factory characteristic equation is:
(z + α)(z -1) + α = 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 α = 0 → 1.
The Hub characteristic equation is:
(z2 + α)(z -1) + α = 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 α > It is this pair that is clearly identified in Figure of eigenvalue plots.
Moreover, it is the Hub’s dynamics and not the Factory’s that are the potential source of unstable behavior. The Hub, potentially, becoming unstable for any value of α > 1, (whilst the Factory would be stable for any value of α < 2.)
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14. Dynamics and Forecasting
Model with two additional Production delays
To explore the long lead time production dynamics. The additional delay were added into the production
To explore the long lead time production dynamics. The additional delay were added into the production.
Perhaps a lack of material supply (due to industrial action by a supplier) or a prolonged upturn in business that outstrips the ability to produce.
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15. System Block Diagram
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16. Eigenvalues plotted for α = 0:0. 01:1 , β = 0 and β = 0:0
Eigenvalues plotted for α = 0:0.01:1 , β = 0 and β = 0:0.01:1 , α = 1 with unit circle
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17. Dynamics and Forecasting
Model Analysis
analysis given that the replenishing inventory rate α has a destablising effecs while the consideration of the past decision rate β 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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18. Model with an Planning delays
The planning delay represents two likely scenarios
Getting forecast wrong
Compatibility problems between the planning systems at different locations
The final model we will consider here will consider the effects of the introduction of an additional one month information delay in the communication between Hub and Factory. In terms of our analysis, this delay represents two likely scenarios: the first, simply being ‘getting the forecast wrong’ and the second being ‘compatibility problems between the planning systems at different locations’.
an additional information delay state, Ide(t), is introduced between the Hub requirement and the Factory production
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19. System block diagram
Hub
Factory
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20. Eigenvalues plotted for α = 0:0. 01:1 , β = 0 and β = 0:0
Eigenvalues plotted for α = 0:0.01:1 , β = 0 and β = 0:0.01:1 , α = 1 with unit circle
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21. Dynamics and Forecasting
Model Analysis
Just as in the two previous cases, α has a destabilising influence whilst β 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 Hub’s route to instability now follows the more severe path.
In the presence of the one month information delay, even the stabilising influence of β only lessens the severity of the route to instability. As long as α =1, no matter what β 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.
additional planning state modifies only the Hub loop. The Factory loop reverting to the structure originally seen in the original model
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22. 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 ;
The primary message that we got from analysis is forecasting is important. For the remain of my research, I am going to consider some provisional forecasting techniques.
ARMA and wavelet neural network are what I am very quickly touch on in this presentation.
As the planning delayed model analysis show the Forecasts play a key role in supply chain management. The basic principle of time series forecasting is to use a model to predict the future data based on known past data.
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23. Dynamics and Forecasting
The original data
The original data is 64 months sales history of Lung demand valve
It can be seen from Figure that the overall trend is of growth and the oscillation intervals are not regular.
A performance function, which measures the absolute difference between forecast and real data, is employed to record the cost for each different structured ARMA model.
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24. ARMA without any preprocessing
The coefficient is produced and
updated by Recursive least square
The ARMA forecasting process involves five steps
1) Data preprocessing;
Constructing the structure of the ARMA model;
Applying the model on forecasting of the original data, the model parameters are updated and optimised by using recursive least square algorithm during the prediction;
Changing the structure of the model and back to step three;
Selecting the model with minimum costs.
The green and blue are perfectly matched in the first eight months. It is because the first eight month data are required to construct the model and calculate model parameters. The forecast in this period is set to be the same as the original. There is significant difference in the details of the variation. Since the program need to be initiralised in the beginning of the data. our concentration is still on the last 15 months forecasts. The accumulative absolute difference is units. The average cost for these 15 months is 787 units.
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25. ARMA with Differencing preprocessing
The differencing processing is the successive subtraction between two continued series. The differencing has changed the overall shape of the original,mean of the new series is around zero. the reverse processed forecast performs not as good as the forecasting for the differenced original data. The discrepancy of the amplitude has been enlarged . The accumulative differences are units from month 50 to 64. The average cost is 681 units.
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26. Dynamics and Forecasting
Cost function
None Preprocessing
Logarithm
Differencing
Logarithm and Differencing
Accumulative costs
11806
11535
10219
11258
Average costs
787
769
681
750
From the analysis given here the ARMA model could produce good forecast on the stationary preprocessed data which has a mean of zero and small variation (Figure 6.11 and Figure 6.9). But if the forecasts are converted back to the original series scale, the post processed data is not bale to track the data pattern and predict the trend or variations
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27. Wavelet Neural Networks
Wavelet Threshold
Decompose Reconstruct
Prediction
NN2
NN3
NN1
NN4
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.
To deal with the embed nonlinearity and increase the reliability of forecasting, Discrete wavelet decomposition is applied to divide the original financial time series into multi level approximate and detailed coefficients so that the neural network can then be applied to the denoised data and improve the prediction accuracy.
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28. Dynamics and Forecasting
Forecasting results
The accumulative absolute difference of the forecast and real data from month 50 to 64 is 5822 units. The average absolute difference is 388 units per month. The forecasting performance have been improved a lot.
ARMA
Neural Network
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29. Dynamics and Forecasting
Cost function
None Preprocessing
Logarithm
Differencing
Logarithm and
Neural
Wavelet
Accumulative costs
11806
11535
10219
11258
5822
Average costs
787
769
681
750
388
In comparison with ARMA forecasting model, the wavelet neural network could pick up the nonlienear characters such as trend and varation frequency and produce better forcasts. The neural wavelet average costs are only 388 units compared to 681 units for the best ARMA model.
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30. 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 Hub’s 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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31. Microworld
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32. Include the dynamics of other Hubs
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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33. Dynamics and Forecasting
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 (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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