The dynamics of material flows in supply chains
63
The dynamics of material flows in supply chains Dr Stephen Disney Logistics Systems Dynamics Group Cardiff Business School
description
The dynamics of material flows in supply chains. Dr Stephen Disney Logistics Systems Dynamics Group Cardiff Business School. The future of bullwhip. Methodological approaches to solving the bullwhip problem. The bullwhip effect in supply chains. Implementing a smoothing rule in Tesco. - PowerPoint PPT Presentation
Transcript of The dynamics of material flows in supply chains
The dynamics of material flows in supply chains
Dr Stephen Disney
Logistics Systems Dynamics Group
Cardiff Business School
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
The bullwhip effect in
supply chains
Methodological approaches to
solving the bullwhip problem
Supply chain strategies for taming
the bullwhip effect
The golden replenishment rule
Solutions to the bullwhip problem
Implementing a smoothing rule
in Tesco
Economics of the bullwhip
effect
Square root law for bullwhipThe future of bullwhip
The bullwhip effect in supply chains
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Measures of the bullwhip effect
)(
)(2
2
DemandVar
OrdersVar
Demand
Orders
)(
)(
DemandStdev
OrdersStdev
Demand
Orders
Stochastic measures Deterministic measures
Demand
Orders
Demand
Demand
Orders
Orders
COV
COV
The bullwhip effect is important because it causes
Up to 30% of costs are due to the bullwhip effect!
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Poor customer service due to unavailable products
Runaway transportation and warehousing costsExcessive labour and learning costs
Unstable production schedules Insufficient or excessive capacitiesIncreased lead-times
How the bullwhip effect creates unnecessary costs
DemandVariance
Overtime / Agency work / Subcontracting
+
Stock-outs
+
Costs+
+ +
+
Lead-time+
+
+Obsolescence
+
Capacity+
Utilisation
-
-
Stock
+
+ +
++
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Methodological approaches to
solving the bullwhip problem
Representations of time
Discrete Time Inventory positions are assessed and orders are placed at discrete moments in time
- At the end of every day, or the end of every week, for example
- May be suitable of the way a supermarket operates, or a distribution company
- In between the discrete moments of time nothing is known about the system
Inventory positions are assessed and order rates are adjusted at all moments of time
- May be suitable for a petrol refinery or in a chemical plant
- The system states are known at every moment of time
v Continuous Time
Continuous time approaches
Lambert W functions
WWeWf )(
Johann Heinrich Lambert1728 – 1777
Leonhard Euler 1707 - 1783
t st dtetfstfL0
)()()(
Laplace transforms
Pierre-Simon Laplace1749 - 1827
Differential equations
0
,, dtxtxtftxdt
d
Aleksandr Mikhailovich Lyapunov 1857-1918
Discrete time approaches
Stochastic processes / ARIMA
George Box
noise White
termsAverage Moving
1
termseIntegrativ
1
termsRegressive Auto
1t
q
kktk
d
jjt
p
iitit DDD
The ARMA(1,1) demand process for 16 P&G products in their Homecare range
Discrete time approaches
State space
methods
Joseph Leo Doob1920-2004
Martingales ttt ffffE ,...,11
)(][][
)(][1
ttt
ttt
DuCxY
BuAxX
Rudolfl Kalman 1930-
Stochastic processes / ARIMA
George Box
noise White
termsAverage Moving
1
termseIntegrativ
1
termsRegressive Auto
1t
q
kktk
d
jjt
p
iitit DDD
z-transformsYakov Zalmanovitch Tsypkin
1919-1997
0
)()()(t
tztftfZzF
Table of transforms and their properties
Other useful approaches
Jean Baptiste Joseph Fourier (1768-1830)
Fourier transforms
dxexfkF ikx2
System dynamics / simulation
Jay Forrester (1918-)
The beer gameJohn Sterman
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Supply chain strategies for taming
the bullwhip effect
Traditional supply chainsDefinition: ‘Traditional’ means that each level in the supply chain issues production orders and replenishes stock without considering the situation at either up- or downstream tiers of the supply chain. This is how most supply chains still operate; no formal collaboration between the retailer and supplier.
Bullwhip increases geometrically in a traditional supply chain
Supply chains with information sharingDefinition: Information exchange (or information sharing) means that retailer and supplier still order independently, yet exchange demand information in order to align their replenishment orders and forecasts for capacity and long-term planning.
Bullwhip increases linearly in supply chains with information sharing
Synchronised Supply (VMI)Definition: Synchronized supply eliminates one decision point and merges the replenishment decision with the production and materials planning of the supplier. Here, the supplier takes charge of the customer’s inventory replenishment on the operational level, and uses this visibility in planning his own supply operations.
Bullwhip may not increase at all in VMI supply chains
Integrating internal and external decision in supply chains with long lead-times
RFID technologies now allow us to monitor the distribution leg
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Solutions to the bullwhip problem
Replenishment rules and the bullwhip problem
cydiscrenpan WIP
WIPActual
WIPDesired
1:
ydiscrepancInventory
stockNet stocknet Target
1 periodin demand of at time made
demand ofForecast
1:
at time Orders
)ˆ()(ˆt
T
iittt
Ttt
Ttt
t
t WIPDNSTNSDOp
p
p
• Replenishment decisions influence both inventory levels & production rates.
• A common replenishment decision is the “Order-Up-To” (OUT) policy….
Set via the newsboy approach to achieve
the critical fractile
Forecasts
Generating forecasts inside the OUT policy
• Exponential smoothing
• Moving average
• Conditional expectation
We will assume normally distributed i.i.d. demand & exponential smoothing
forecasting from now on
a
tttt T
DDDD
1
ˆˆˆ 1
1
m
T
iit
t T
DD
m
1ˆ
..0,ˆ, iDDED itxtxtt
The inventory and WIP balance equations
t
t
Tt
Tttt DONSNS
p
p
at time Demand
1 timeat orders Previous
11
111 pTtttt OOWIPWIP
The replenishment lead-time, Tp
The influence of the replenishment policy
The inventory balance equation….
….shows us that the replenishment policy influences both the orders and the net stock.
Therefore, when studying bullwhip we should also consider
)Demand(
)StockNet (2Demand
2StockNet
Var
VarNSAmp
t
t
Tt
Tttt DONSNS
p
p
at time Demand
1 timeat orders Previous
11
The impact of forecasting on net stock variance amplification
• As then NSAmp approaches 1+Tp. • Minimising the Mean Squared Error between the
forecast of demand over the lead-time and review period and its realisation will result in the minimum inventory variance.
• This holds in a single echelon (Vassian 1954) and across a complete supply chain (Hosoda and Disney, 2006) when the traditional OUT policy is used
aT
a
pp
Demand
NetStock
T
TTNSAmp
21
11
2
2
2
The impact of forecasting on bullwhip
As then bullwhip approaches unity.
Thus, we can see that as we make more accurate forecasts the bullwhip problem is reduced (but is not eliminated in this scenario)
2
2
2
2
2
2
231
2
231
232
21
25
211
473225
aa
p
aa
pa
a
a
aa
pappa
Demand
Orders
TT
T
TT
TT
T
T
TT
TTTTTBullwhip
aT
Reducing lead-times• Reducing lead-times usually (but not always)
reduces bullwhip
• However, reducing lead-times will always reduce the inventory variance
2
2
2 231
2
231
232
21
25
aa
p
aa
pa
a
a
TT
T
TT
TT
T
TBullwhip
a
pp T
TTNSAmp
21
11
2
The OUT policy through the eyes of a control engineer…
cydiscrenpan WIP
WIPActual
WIPDesired
1:
ydiscrepancInventory
stockNet stocknet Target
1 periodin demand of at time made
demand ofForecast
1:
at time Orders
)ˆ(*1)(*1ˆt
T
iittt
Ttt
Ttt
t
t WIPDNSTNSDOp
p
p
Unity feedback gains!
• A control engineer would not be at all surprised that the OUT policy generates bullwhip as there are unit gains in the two feedback loops
• Let’s add in a couple of proportional feedback controllers….
cydiscrenpan WIP
WIPActual
WIPDesired
1:
ydiscrepancInventory
stockNet stocknet Target
1 periodin demand of at time made
demand ofForecast
1:
at time Orders
)ˆ(*1
)(*1ˆ
t
T
iitt
wt
i
Ttt
Ttt
t
t WIPDT
NSTNST
DOp
p
p
Inventory feedback gain (Ti) WIP feedback gain (Tw)
The first proportional controller:The Maxwell Governor
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
The golden replenishment rule
Matched feedback controllers
• When Tw=Ti the maths becomes very much simpler
• With MMSE forecasting ( ) we have…
t
T
iitt
it
iTttt WIPD
TNSTNS
TDO
p
p1
:1:ˆ11ˆ
12
12
2
iDemand
Orders
TBullwhip
aT
1212
11
22
2
2
i
ip
i
ip
Demand
NetStock
T
TT
T
TTNSAmp
The golden ratio in supply chains For i.i.d. demand, matched feedback controllers, MMSE forecasting
The golden ratio
1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072...…
618034.12
51
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Economics of the bullwhip
effect
Economics of inventory
Inventory costs are governed by the safety stock (TNS)
The Target Net Stock (TNS*) is an investment decision to be optimized
In each period, when the inventory is positive a holding cost is incurred of £H per unit.
In each period, if a backlog occurs (inventory is negative), a backlog cost of £B per unit
is incurred
The economics of capacity
Capacity per period = Average demand +/- slack capacity
Production above capacity results in some over-time working (or sub-contracting). The cost of this type of capacity is £P per unit of over-time.
Production below capacity results in some lost capacity
cost of £N per unit lost.
The amount of slack capacity (S*) is an investment decision to be optimized
Costs are a linear function of the standard deviation
Setting the amount of safety stock we need via the newsboy…
… and the amount of capacity to invest in…
…for a given set of costs (H, B, N, P) and lead-time, (Tp)
HB
HBerfTNS NS
1* 2
PN
NPerfS O
1* 2
22
costs Total
21
21 2
112
PN
Nerf
OHB
Berf
NS ePNeHB
Inventory costs Bullwhip costsConstantsTotal costs are thus linearly related to the standard deviations
Sample designs for the 4 different scenarios
Lead-time
Tp=1 Tp=3
Ti=
1 TNS*=1.81 S*=0.25 £T=6.34
TNS*=2.56 S*=0.25 £T=7.37
Inve
ntor
y fe
edba
ck
gain
Ti=
Ti*
TNS*=2.27 S*=0.1001 Ti*=3.69 £T=4.63
TNS*=2.99 S*=0.091 Ti*=4.32 £T=5.49
Assuming the costs are; Holding cost, H=£1, Backlog cost, B=£9 Lost capacity cost, N=£4, Over-time cost, P=£6
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Square root law for bullwhip
…
One manufacturer
Distribution Network Design: Bullwhip costs
12 customers
n DC’s
Each customer produces an i.i.d. demand,
normally distributed with a mean of 5 and unit variance
All lead-times in the system are one period long
Number of DC’s (n) 1 2 3 4 6 12
Demand process faced by each DC
Factory demand
…and it all depends on how many distribution centres we have…
Each customer’s demand = N(5,1)
DC demand= )12,60(N
Factory demand=
)12,60(N
)12,60(N
)12,60(N
Number of DC’s (n) 1 2 3 4 6 12
Demand process faced by each DC
Factory demand
… for 2 DC’s…
Each customer’s demand = N(5,1)
DC demand=)6,30(N Factory demand=
)12,60(N
)12,60(N
)12,60(N
)6,30(N
)12,60(N
DC demand=)6,30(N
Number of DC’s (n) 1 2 3 4 6 12
Demand process faced by each DC
Factory demand
… for 3 DC’s…
Each customer’s demand = N(5,1)
Each DC’s demand=)4,20(N Factory demand=
)12,60(N
)12,60(N
)12,60(N
)6,30(N
)12,60(N
)4,20(N
)12,60(N
Number of DC’s (n) 1 2 3 4 6 12
Demand process faced by each DC
Factory demand
… for 4 DC’s…
Each customer’s demand = N(5,1)
Each DC’s demand=
)3,15(N
Factory demand=
)12,60(N
)12,60(N
)12,60(N
)6,30(N
)12,60(N
)4,20(N
)12,60(N )12,60(N
)3,15(N
Number of DC’s, n
1 2 3 4 6 12
Inventory cost £8.59 £12.15 £14.89 £17.20 £21.06 £29.78
£8.59 £8.59 £8.60 £8.60 £8.60 £8.60
The Square Root Law Inventory nBullwhip n
n
costInventory
n
costCapacity
Number of DC’s, n
1 2 3 4 6 12
Capacity cost
£13.38 £18.93 £23.18 £26.77 £32.78 £46.36
£13.38 £13.39 £13.38 £13.39 £13.38 £13.38
“If the inventories of a single product (or stock keeping unit) are originally maintained at a number (n) of field locations (refereed to as the decentralised system) but are then consolidated into one central inventory
then the ratio
exists”, Maister, (1976).
ninventory system dcentralise
inventory system seddecentrali
Proof of “the Square Root Law for bullwhip”
The bullwhip (capacity) costs are given by
In the decentralised supply chain the standard deviation of the orders is ,
In the centralised supply chain the standard deviation of the orders is
Thus,
which is the “Square Root Law for Bullwhip”.
Bullwhip n
Y
ePNC O
PN
Nerf
O
2
21 2
1
£
2cO n
2cO n
n
Yn
Yn
c
c 2
2
costs bullwhip dcentralise
costs bullwhip seddecentrali
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
Implementing a smoothing rule
in Tesco
Tesco project brief
• Tesco’s store replenishment algorithms were generating a variable workload on the physical delivery process
– this generated unnecessary costs
• The purpose of the project was to;– investigate the store replenishment rules to evaluate their
dynamic performance – to identify if they generated bullwhip– offer solutions to any bullwhip problems
Inventory replenishment approaches
High volume products
• Account for 65% of sales volume and 35% of product lines
• Deliveries occur up to 3 times a day
The simulation approach
Weekly workload profile: Before and after
Peak weekly workload amplified by existing system
Peak weekly workload smoothed by modified
system
Summary• Tesco’s replenishment system was found to increase the daily
variability of workload by 185% in the distribution centres
• A small change to the replenishment algorithms was recommended that smoothed daily variability to approximately 75% of the sales variability
• The solution was applied to 3 of the 7 order calculations. This accounted for 65% of the total sales value of Tesco UK
• This created a stable working environment in the distribution system.
The Tesco case study will be discussed in more detail this afternoon in
the President’s Medal presentation
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Ord
ers
The future of bullwhip
Multiple products with interacting demand
tttt
tttt
DDD
DDD
,21,11,21,22,2,2
,11,22,11,11,1,1
Demand for product 2 at time t
Demand for product 1 at time t
Random processesAuto-regressive process with itselfAuto-regressive interaction with the other product
The Inventory Routing and Joint Replenishment Problem
• In a multiple product or multiple customer scenario• Place an order to bring inventory up-to S,
– if inventory is below a reorder point
– OR if inventory is below a “can-deliver” level AND another product (or retailer) has reached its reorder point
Consolidation of orders/ deliveries can generate significant savings
The interaction between bullwhip
inventory variance & lead-times
Manufacturer
Consumer Demand
Production Lead time
Retailerorders
Replenishment orders
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
0 10 20 30 40 50 60 70 80
Retailer uses an OUT policy and places orders onto the manufacturerManufacturer is represented by a queuing model. Operates on a make to order principle
Processes orders on a first come first served basis
If the retailer smoothes his orders (with a proportional controller) then the manufacturer can replenish the retailers orders quicker.
Thus there is an interaction effect between bullwhip and lead-times that allows supply chains to break the inventory / order
variance trade-off!
Multi-echelon supply chain policies
The impact of errors• Demand parameter mis-identification
• Demand model mis-identification
• Lead-time mis-identification
• Information delays
• Random errors in information
• Non-linear, time-varying systems
• …
Thank you
The dynamics of material flows in supply chains
Dr Stephen DisneyLogistics Systems Dynamics Group
Cardiff Business School
www.bullwhip.co.uk
www.cardiff.ac.uk
The IOBPCS family
Stability issues (Tp=1)
Stability issues (Tp=2)
