22/04/23Page 1
Supply Chain Dynamics and Forecasting
Presenter: Mu Niu
22/04/23Page 2 22/04/23Dynamics and ForecastingPage 2
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 .
22/04/23Page 3 22/04/23Dynamics and ForecastingPage 3
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.
22/04/23Page 4 22/04/23Dynamics and ForecastingPage 4
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.
22/04/23Page 5 22/04/23Dynamics and ForecastingPage 5
Draeger supply chain structure
GoodsShipped Order in
GoodsShipped Order in
GoodsShipped
Order in Central Hub
Germany
China
Japan
USA
Canada
France
Denmark
HubUSA
Hub AsiaSingapore
Factory Blyth UK
22/04/23Page 6 22/04/23Dynamics and ForecastingPage 6
Germany- UK Model
Germany Primary Hub Blyth Factory
Hub Forecast
Hforecast
HubRequirement
Hreq
Production
Fprod
Inventory
Finv
Factory Shipments
Fship
Inventory
Hinv
Backlog
Hblk
Backlog
Fblk
1MonthT’ Delay
Hub Sales
Horders
HubShipments
Hship
1MonthM’facture
22/04/23Page 7 22/04/23Dynamics and ForecastingPage 7
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
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]
22/04/23Page 8
Nonlinear block diagram
22/04/23Page 9
Time simulation
0 50 100 150 200 2500
200
400
600
800
1000
1200
Months
Item
s
0 50 100 150 200 250-500
0
500
1000
1500
2000
Month
Item
s
0 50 100 150 200 250 300 350 400 450 500
-500
0
500
1000
1500
2000
2500
3000
3500
Hub Inventory
Month
Item
s
50 100 150 200 250 300 350 400 450 500 550-4000
-3000
-2000
-1000
0
1000
2000
Factory Inventory
Month
Item
s
Stable Limit cycle
Quasi periodic
Chaotic
22/04/23Page 10
Equations
X(k) = A X(k-1) + B U(k)
(t)F(t)F
(t)F2)(tH
2)(tH(t)H
(t)H
X(k)
prod
inv
ship
forcast
req
inv
ship
FFHHHFH
HHHH
αααθβααα011001-000000100000θ00000αθβαα000100100000000
A
(t)Q(t)Q
(t)HU(k)
F
H
orders
FHH
HH
α000000
αθα100000θ1
αθα10101
B)(
z
zU
22/04/23Page 11 22/04/23Dynamics and ForecastingPage 11
System Block Diagram
22/04/23Page 12 22/04/23Dynamics and ForecastingPage 12
Eigenvalues plotted for α = 0:0.01:1 , β = 0 and β = 0:0.01:1 , α = 1 with unit circle
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
α=0.1β=0
α=0.1β=0
α=1β=0
α=1β=0
α=0.5β=0
α=-0.5β=0
α=0.8β=0
α=0.8β=0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
α = 1β = 1
α = 1β = 1
α = 1β = 0
α = 1β = 0
α = 1β = 0.2
α = 1β = 0.2
α = 1β = 0.5
α = 1β = 0.5
α = 0:0.01:1 , β = 0 β = 0:0.01:1 , α = 1
22/04/23Page 13 22/04/23Dynamics and ForecastingPage 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 > 0.25. 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.)
22/04/23Page 14 22/04/23Dynamics and ForecastingPage 14
Model with two additional Production delays
To explore the long lead time production dynamics. The additional delay were added into the production
22/04/23Page 15
System Block Diagram
22/04/23Page 16
Eigenvalues plotted for α = 0:0.01:1 , β = 0 and β = 0:0.01:1 , α = 1 with unit circle
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
α = 0.5β = 0
α = 0.5β = 0
α = 0.5β = 0
α = 0.5β = 0
α = 0.6β = 0
α = 0.6β = 0
α = 0.6β = 0
α = 0.6β = 0
α = 0.8β = 0
α = 0.8β = 0
α = 0.8β = 0
α = 0.5β = 0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
α = 1β = 0.2
α = 1β = 0.32
α = 1β = 0.5
α = 1β = 1
α = 1β = 0.5
α = 1β = 0.5
α = 1β = 0.32
α = 1β = 0.2
α = 1β = 0.32
α = 1β = 0.2
α = 1β = 0.5
α = 1β = 0.32
α = 1β = 0.2
α = 1β = 0.5 α = 1
β = 0.32
α = 1β = 0.2
22/04/23Page 17 22/04/23Dynamics and ForecastingPage 17
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.
22/04/23Page 18 22/04/23Dynamics and ForecastingPage 18
Model with an Planning delays
The planning delay represents two likely scenarios1) Getting forecast wrong2) Compatibility problems between the planning systems at different
locations
22/04/23Page 19
System block diagram
Hub
Factory
22/04/23Page 20
Eigenvalues plotted for α = 0:0.01:1 , β = 0 and β = 0:0.01:1 , α = 1 with unit circle
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
α = 0.62 β = 0
α = 0.62 β = 0
α = 0.62 β = 0
α = 0.4 β = 0
α = 0.4 β = 0
α = 0.4β = 0
α = 0.1β = 0
α = 0.1β = 0
α = 0.1 β = 0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
α = 1 β = 1
α = 1 β = 1
α = 1 β = 1
α = 1 β = 0.5
α = 1 β = 0.5
α = 1 β = 0.5
22/04/23Page 21 22/04/23Dynamics and ForecastingPage 21
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.
22/04/23Page 22 22/04/23Dynamics and ForecastingPage 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 gForecastinSalesCost
;
22/04/23Page 23 22/04/23Dynamics and ForecastingPage 23
The original data
• The original data is 64 months sales history of Lung demand valve
0 10 20 30 40 50 60 700
500
1000
1500
2000
2500
3000
3500
4000Sales history data
Month
Item
s
22/04/23Page 24 22/04/23Dynamics and ForecastingPage 24
ARMA without any preprocessing
0 10 20 30 40 50 60 700
500
1000
1500
2000
2500
3000
3500
4000
time units month
item
s
forecast and sales history
OriginalForecast
tttttt yyyyy 64534221ˆ
The coefficient is produced and updated by Recursive least square
22/04/23Page 25 22/04/23Dynamics and ForecastingPage 25
ARMA with Differencing preprocessing
0 10 20 30 40 50 60 700
500
1000
1500
2000
2500
3000
3500
4000
time units month
item
s
forecast and sales history
tttttttt wwwwww 318554432211ˆ
112 ˆˆ wyy
22/04/23Page 26 22/04/23Dynamics and ForecastingPage 26
Cost function
None Preprocessing
Logarithm Differencing Logarithm and Differencing
Accumulative costs 11806 11535 10219 11258
Average costs 787 769 681 750
22/04/23Page 27 22/04/23Dynamics and ForecastingPage 27
Wavelet Neural Networks
0 10 20 30 40 50 60 70-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1original data s
Wavelet ThresholdDecompose Reconstruct
PredictionNN2
NN3
NN1
NN4)(tg
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.
22/04/23Page 28 22/04/23Dynamics and ForecastingPage 28
Forecasting results
0 10 20 30 40 50 60 700
500
1000
1500
2000
2500
3000
3500
4000
Month
Item
Sales Data
ARMA Neural Network
22/04/23Page 29 22/04/23Dynamics and ForecastingPage 29
None Preprocessing Logarithm DifferencingLogarithm andDifferencing
NeuralWavelet
Accumulative costs 11806 11535 10219 11258 5822
Average costs 787 769 681 750 388
Cost function
22/04/23Page 30 22/04/23Dynamics and ForecastingPage 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.
22/04/23Page 31
Microworld
22/04/23Page 32
Further Research
• Include the dynamics of other Hubs
• Look at different decision making in different Hubs
• look for methods to further improve forecasting
22/04/23Page 33 22/04/23Dynamics and ForecastingPage 33
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.