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 .


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.


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.


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


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


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]

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Nonlinear block diagram

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Time simulation

0 50 100 150 200 2500

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Months

Item

s

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Month

Item

s

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Hub Inventory

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s

50 100 150 200 250 300 350 400 450 500 550-4000

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Factory Inventory

Month

Item

s

Stable Limit cycle

Quasi periodic

Chaotic

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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


System Block Diagram


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


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.)


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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-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

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0

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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


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.


Model with an Planning delays

The planning delay represents two likely scenarios1) Getting forecast wrong2) Compatibility problems between the planning systems at different

locations

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System block diagram

Hub

Factory

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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

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0

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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

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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


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.


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

;


The original data

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

0 10 20 30 40 50 60 700

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4000Sales history data

Month

Item

s


ARMA without any preprocessing

0 10 20 30 40 50 60 700

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time units month

item

s

forecast and sales history

OriginalForecast

tttttt yyyyy 64534221ˆ

The coefficient is produced and updated by Recursive least square


ARMA with Differencing preprocessing

0 10 20 30 40 50 60 700

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time units month

item

s

forecast and sales history

tttttttt wwwwww 318554432211ˆ

112 ˆˆ wyy


Cost function

None Preprocessing

Logarithm Differencing Logarithm and Differencing

Accumulative costs 11806 11535 10219 11258

Average costs 787 769 681 750


Wavelet Neural Networks

0 10 20 30 40 50 60 70-1

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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.


Forecasting results

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Sales Data

ARMA Neural Network


None Preprocessing Logarithm DifferencingLogarithm andDifferencing

NeuralWavelet

Accumulative costs 11806 11535 10219 11258 5822

Average costs 787 769 681 750 388

Cost function


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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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


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.

Documents

Supply Chain Dynamics and Forecasting