System Dynamics Model to Understand Demand
Conditioning Dynamics in Supply C hains
Lianjun An and Bala Ramachandran
IBM T.J. Watson Research Center
Y orktown, New Y ork 10598, U.S.A.
(914) 945-1565 & (914) 945-3768
{alianjun,rbala}@us.ibm.com
Abstract
Demand Conditioning is one of the methods used to address imbalances between supply and
demand in supply chains. This requires the manufacturer to adjust the demand plan to respond
to supply issues. The supply chain has several sources of delays and uncertainties such as lead
times at different stages, forecast error, supply yield variability etc. that could potentially trigger
or influence the conditioning process. In this paper, we examine dynamical effects in the
conditioning process to study potential instabilities. We developed a Systems Dynamics model of
a PC manufacturing supply chain to examine instabilities in the supply chain. This model
provides insight on supply chain risks and error propagation due to unsynchronized execution.
We also use the model to study the effect of different countermeasures to stabilize the supply
chain.
Keywords: System Dynamics, Demand Conditioning, Supply Chain, Stability, on-demand
operation.
1. Introduction
Managing uncertainties and dynamics in enterprise supply chains require an ongoing emphasis in
aligning supply with demand. With the objective of using the supply chain as a source of
competitive advantage, many enterprises are endeavoring not only to reactively responding to
customer demand, but are also aspiring to proactively condition the supply chain to improve
profits. A common example of this is the cross-selling of goods, using marketing promotions to
avoid overstocking of specific products. The act of conditioning demand may have other
consequences in the supply chain - in particular, due to lead times and uncertainties in the supply
chain. Our objective in this paper is to research the dynamics of demand conditioning in supply
chains using systems dynamics models.
The dynamic behavior of supply chains have been studied extensively, starting with the
pioneering work of Forrester [1] in using systems dynamics models to demonstrate demand
amplification in supply chains (otherwise known as bullwhip effect). Sterman [2] provides a
nice overview of how systems dynamics can be used to study business dynamics. The sources of
oscillations such as a failure to account for time delays are nicely illustrated for a variety of
systems such as supply chains, labor markets etc. It is shown that perfectly rational strategies at a
local level can cause system-wide oscillations, and control strategies to stabilize the system are
proposed. Lee [3] has identified four drivers of the bullwhip effect - namely demand forecast
updating, order batching, price fluctuation, rationing and shortage gaming and proposed
strategies to counter them. The bullwhip effect is also taught in different management courses,
due to its important practical implications.
From the perspective of demand conditioning it has been generally assumed that it is beneficial
and little research has been done into dynamical effects associated with demand conditioning.
Like any human system, conditioning demand in the supply chain is subject to time lags. If the
demand can be conditioned very quickly relative to the time scale of supply variability, it is
intuitive that demand conditioning can lead to supply chain benefits. However, the benefits are
less clear if the time scale for conditioning is large compared with the time scale of supply
variability. This scenario is very likely, since in many organizations, demand conditioning
processes involve significant manual components such as instructing the sales force to tune what
they are selling. In some situations, this may even involve developing new offerings that can be
sold to the marketplace. Our main objective in this paper is to examine the dynamical effects if
there are significant time lags in the conditioning process.
In the next section, we describe dynamical aspects of demand conditioning. In Section 3, we
describe a systems dynamics model of demand conditioning actions in a PC supply chain. In
Section 4, we discuss computational results from our Systems Dynamics model and discuss
implications. We finish with our closing remarks in Section 5.
2. Demand Conditioning Dynamics
The conditioning processes in IBM PC Division are explained in [4] and can serve as a good
example. When imbalance between demand and supply of components and products is detected,
proactive actions can be taken to correct the situation [6]. The basic supply chain structure with
conditioning process is shown in Figure 1. There are three decision points in this figure
representing different types of conditioning.
e Supply conditioning: When the committed supply cannot meet the demand, it is possible
that we can chase additional suppliers or adjust supply among different supply chain
components.
e Demand conditioning: Through price change and promotion, we can provide incentives
to customer to choose product alternatives.
e Offering conditioning: When there are some excessive parts, we can create and offer new
configuration models to consume these parts.
We refer to assembled products as Machine Type Models (MTM). Components procured from
suppliers are assembled to form major building blocks, which can be further assembled to make
the MTM. Customer order creates demand on the MTMs and is backlogged into the order system
(a pull model). The incoming part supply replenishes the inventory and makes parts being
available for assembling (a push model). The demand-supply imbalance would be measured by
the following expression:
by
i
P, - Yc, jm,
J
e where m is the vector representing demand amount for each MTM, p the vector of
available parts for major building blocks, and c the BOM (bill of material) matrix - how
a MTM is built-up from multiple parts.
When component supply is constrained, we have the option of choosing the allocations of
components to different MTMs using different policies, such as priority, proportional allocation
and optimizing allocations to maximize profit. Which rule is used might effect the long term
instability and overall profit measure.
‘Customer
Demand
OnMT™
(pall
Impact
Performance
Measure
Figure 1: Supply Chain Conditioning Process
3. System Dynamics Model
In what follows, we study some instability issues related to the demand conditioning process. In
particular, we examine the dynamic effects relating to time delays in the demand conditioning
process. To gain a fundamental understanding, we only include uncertainty parameters related to
synchronization in the conditioning process without explicitly including incentive actions to
trigger demand shifting. We also further simplify the model by only considering two products in
our model. We also do not consider allocation issues related to constrained supply between
products. We present the stock and flow structure in section 3.1 and decision rules in section 3.2.
3.1. Stock and flow structure
The System Dynamics Model for demand conditioning process is shown in Figure 4. There are
two basic stocks - order backlog and product inventory, in the model. The Backlog has in-and-
out flows: DemandRate and FulfilmentRate. The Inventory has in-and-out flows: ReplenishRate
and ShipmentRate. So the system would be formulated as the following
BackOrder [i](t) = f (DemandRate [i](z) — Fulfilment Rate[i](c))dz + BackOrder [i](t, )
Inventory [i](t) = fRe plenishRate[i](z) — ShipmentRa te[i](c))dz + Inventory [i](t,)
where t is time, t, is the initial time for the processing, and i=1,2 is subscripted for product 1 and
2 in the model. The system consists of four equations here because two products are included.
Note that both BackOrder and Inventory would enter the integrands on the right hand side since
in-and-out flows are actually functions of them. In most cases, the in-and-out flows are
nonlinearly dependent on the stocks variables with time-delays. As a result, the model cannot be
solved analytically, but is amenable to solution through numerical methods.
In the system of equations, the ReplenishRate will be given and DemandRate will be adjusted
based on decision rule given in the next subsection. In order to determine ShipmentRate, we
introduce two variables (for each product, we omit subscripts from now on unless it is necessary):
DesiredShippingRate and MaximalShippingRate defined by
BackOrder
DesiredShippingTime . (2)
Inventory
Minimal Processin gTime
DesiredShippingRate =
MaximalShippingRate =
Since the DesiredShippingRate is determined by BackOrder and MaximalShipping is restricted
by current Inventory level, it is obvious that ShipmentRate should be less than or equal to both in
(2). The DesiredShippingTime is related to transportation delay, and the MaximalShippingRate is
related to the time to process the order. Then ShipmentRate and FulfilmentRate are defined as
follows:
ShipmentRa te = DesiredShippingRate * FulfilmentRatioF unc | fee nna (3)
DesiredShippingRate
FulfilmentRate = ShipmentRate .
The FulfilmentRatioF unc is given graphically as in Figure 2. When MaximalShippingRate is
greater then DesiredShippingRate, ShipmentRate is close to D esiredShippingRate (BackOrder
dominates the rate) since the value the fulfillment ratio function approaches one. When
MaximalShippingRate is less then D esiredShippingRate, ShipmentRate is close to
MaximalShippingRate since the slope of the curve is close to one (Inventory dominates the rate).
As alookup supported in Vensim [7], FulfilmentRatioF unc returns the nearest extreme value
when the input goes outside the range of the lookup.
In this formulation, the following inequality holds
ShipmentRa te < Min(DesiredShi ppingRate, MaximalShi ppingRate) ,
and ShipmentRate is a smooth function of the ratio of MaximalShippingRate over
DesiredShippingRate.
Graph Lookup - FulfilmentRatioFunc
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Figure 2: Fulfillment Ratio Function
3.2. Decision rules of conditioning process
Figure 3 shows the demand conditioning process. We periodically review the potential for
demand conditioning - ConditioningCycleTime represents the review frequency, which triggers
checking of the differences between Inventory and BackOrder (IBDifference) for both product 1
and 2. A positive IBDifference suggests an overage situation and a negative [BDifference
suggests a shortage situation (we do not consider safety stock policy). When the shortage in one
product can be compensated by an overage in the other product, and if both volumes are greater
than the specified Threshold, the conditioning action is triggered and will initiate demand
shifting between two products through some incentive means. We do not model the incentive
process in our systems dynamics model, but directly compute the demand to be shifted and
assume that the demand shift is somehow accomplished. The start and finish time for
Conditioning would relate to the effectiveness of the mechanism to shift demand and may
experience delays due to manual organizational process, etc. We do not investigate causal factors
for synchronization of the conditioning process, but demonstrate the overall supply chain effects
due to time delays in demand conditioning.
Conditioning ii Monitor difference Reference | Threshold
cycle time between Inventory Policy
(periodic review) and BackOrder
yet \ —
Both overage for product 1 Both overage for product 2
and shortage for product 2 and shortage for product 1 Others
are greater then threshold are greater than threshold
Initiate demand shifting Initiate demand shifting
from product 1 to product 2 from product 2 to product 4 Do nothing
Conditioning Conditioning Conditioning
Starting time Execution Turnoff Time
Figure 3: Demand conditioning process for two products
Conditioning Decision Rule Cost Evaluation
Total
Execution —__ ital Deman BacklogPenalty —CumulatedCost
saree _— InitiatDemand
HoldingPrice-—__
/
o: Ses [Cumulated]
ae dent ye et
TrendFactor——___ te
7“ WnChange P
x * Fulfillment
Lr Rae
Threshold
Desired
~
Conditioning ShippingTime
CycleTime /
Modified /\ /
Shifitoz *~——__
.. —~ 3
iP e
F _|__—-tppitterence [peice
. ¥
TumOsDelay——__, Shifttio2 4 —— \ | ShippineRate
Delay \ \ =
\ \
Product Planning Cycle
Planning :
CycleTime ; °
‘rena =Coniiioe: \ Initial
= Change wh —_ Inventory
f gy Arn Demand
/ f \ \ Random 7 FulflmentFune
y \ \ Factor Minimaf
/ stepFactor p.1, Process Time
ES nt StepFactor pujseFactor
Figure 4: System Dynamics model of demand conditioning process
Now, we discuss the decision rules in the system dynamics model, shown in Figure 4. We have
implemented the model through Vensim [7], and use the Vensim syntax to describe the decision
tules. We start with periodic review of the difference of inventory and back order to determine
the potential for demand conditioning. The demand shifting from product 1 to 2 Shiftlto2 is
estimated based on the following:
IfThenAlse ((T > 0): and : Modulo (T +1,CCT )>0:and : Modulo (T +1,CCT ) <1,
IfThenAlse ((IBD [1]> 0): and : (IBD [2] < 0), Min (IBD [1],-IBD [2]), , (4)
IfThenAlse ((IBD [1]< 0): and : (IBD [2] > 0), - Min (—IBD [1], IBD [2)), 0), 0), )
where T is for Time, CCT for ConditioningCycleTime, and IBD for IBDifference. The review
time constraint is expressed in the first part of equation (4). Note that the formulated condition 0
< Modulo(T+1,CCT) <=1 guarantees that the system behavior does not depend on the time step
chosen for numerical simulation. The second line is to check whether product 1 has overage and
product 2 has shortage. Similarly, the third is to check whether product 1 has shortage and
product 2 has overage. In both cases, the value would be the minimum of amplitudes of both
overage and shortage. Otherwise, the value would be zero. The shifting is tumed off by adding
the negative of Shiftlto2 with delay CCT+TurnOffDelay. So the total possible shifting from
product 1 to 2 would defined as
ModifiedShiftito 2[i] =
Shift1to 2 — D elayFixed (Shift1to2,CCT +TurnOffDelayli], Shiftlto2) i=1,2°
By introducing TurnOffDelay, we could study the influence from the uncertainty associating
with the switching off of the conditioning process. The DesiredRateInC hange, which causes the
demand change, is formulated as
DesiredRatelnC hange[1] =
IfThenAlse (Abs(ModifiedShiftlto2[1]) > Threshold, ModifiedShift1to2[1]/CCT , 0) (5)
DesiredRatelInC hange[2] =
IfThenAlse (Abs(ModifiedShiftlto2[2]) > Threshold , — ModifiedShiftlto2[2]/CCT, 0) .
When the ModifiedShift1to2 is greater then Threshold, demand for product 1 is increased by
ModifiedShift1to2[1]/CCT and demand for product 2 is decreased by ModifiedShift1to2[2]/CCT.
Our formulation implies that we intend to correct the situation in a time period of duration CCT.
To model delays in the execution of conditioning actions, we introduce another parameter
ExecutionDelay. The real DemandRateInChange would be delayed with respect to
DesiredRateInC hange
DemandRate InChange =
DelayFixed (DesiredRateInChange, ExecutionD elay, DesiredRateInChange) .
Finally, the Demand is determined through integrating D emandRateInC hange
A
Demand (t) = J DemandRatelnChange(z)dz + Demand(t,) .
4
DemandRate is non-negative and can be expressed as
DemandRate = Max(Demand , 0). (6)
Without the above constraint, Demand could become negative with execution delay and turmoff
delay, This can happen because the effects of previous conditioning actions may not be seen due
to the delays.
3.3. Cost formulation
We associate excessive inventory with holding costs and backlogged order with penalty costs.
The excessive inventory is represented by the positive part of IBDifference and the backlogged
order is represented by the negative part of IBDifference. So the cost is given by
Cost[i] = HoldingCost* Max(IBD [i],0) + Back log Penalty * Max(-IBD [i],0),
where IBD is for IBDifference. And CumulatedC ost will be integrated from Cost
t
CumulatedCost[i] = JCostfil(2)dz .
i
As seen from formulation that, we end up with the system of differential equations (four from
subsection 3.1, two from 3.2 and two from 3.3) with nonlinearities, time delays and uncertainty.
The work on the stability of stochastic delay differential equations in literature [8] is related to
our context here and may be applicable to study the stability of demand conditioning processes.
In this paper, we limit ourselves to a system dynamics study of the stability of demand
conditioning processes.
4. Computational Results and Implications
In order to study dynamical effects in Demand Conditioning, we consider a simple two product
supply chain. We introduce a supply spike in one product, along with a corresponding shortfall
in another product that can trigger conditioning actions. We then explore the dynamics of
inventories, backorders and costs for different values of the delays in the start and finish of the
conditioning actions. These delays can be interpreted to be the result of different manual
processes in Demand Conditioning.
4.1, Ideal case
We use the following for ReplenishRate
Re plenishRate[1] = 100+ Pulse(10,20)
, (7
Re plenishRate[ 2] = 90— Pulse(10,20) (7)
which is shown in Figure 5. The function Pulse has two parameters: starting time (10) and
duration (20). We use the Pulse function here to introduce spike in product 1 and drop in product
2 that can trigger conditioning actions. The initial inventory levels are set to be 200 and 100 for
two products, and the initial backorders are set to be 100 and 90.
ReplenishRate
7 a0 90100
Figure 5: Replenishing rate from suppliers
For the demand rate, initially we also have 100 for product 1 and 90 for product 2. Because of
the change in supply (Pulse in equation (7)), IBDifference for product 2 becomes negative and
the imbalance occurs at Time=11 as shown in the right of Figure 6. First we demonstrate system
behavior in an idealized case in which there are no execution delay (ExecutionD elay=0) and no
conditioning turnoff delay (TurnO ffD elay=0). We also set the conditioning cycle time (CCT) to
be 7 and threshold to be 0. When Time reaches 14, demand conditioning is triggered based on
decision rules expressed in (4), as shown in the left of Figure 6. In fact, there are subsequent
demand conditioning actions at Time=21 and 28. Finally, the conditioning action is totally tumed
off at Time=42. The right of Figure 7 shows corresponding IBDifference curve for both products.
The IBDifference roughly returns to the initial state after Time=42.
DemandRate IBDifference
100 att a <i
0 ae 100
0 200
o 0 0 3 % 30 6 70 60 9 100 o 1 2% 3 4 5 Go 70 a) 90 100
Time (Dey) Time (Day)
DemaneRat tect): Cure, ———_____ IBDitfereneltech] : Curent;
DemaneRatel tet]: Curent [BDilerecel tei]: Curent —
Figure 6: Demand conditioning effect in ideal case
4.2. Influence from delays
In reality, we do not have control on execution delay and conditioning turnoff delay. Figure 7
shows the demand rate and IBDifference profiles, when the execution delay is 4 and tumoff
delay is 5. Due to the execution delay, the demand rate changes at Time=18 instead of 14. The
IBDifference for product 1 changes from a large positive number to zero. In the other words, the
product 1 changes from an overage to being just on the verge of a shortage situation.
If we continue to increase the tumoff delay, we end up with oscillations alternating with
overages and shortages for products 1 and 2. Figure 8 shows the IBDifference for different
TurnOffDelay with given ExecutionDelay=4. When the tumoff delay is 8, oscillation is
dampened after two cycles and both products end up in an overage state, as shown in the left of
Figure 8. However, when the tumoff delay is 10, the oscillation continues, growing in amplitude
as shown in the right of Figure 8.
DemandRate IBDifference
140 200
120 TANI 100 AT
100 0
| ine
~ ‘a ml
80 Vt tT 100
Uy
Co 200
o w 2 3 4 50 6 70 a 90 100 oc 0 2 3 4 50 6 70 8 9% 100
‘Time (Day) ‘Time (Day)
DemandRate{techt] : Curent ———————___ IBDifference{techt] : Cures. ——
DemandRateltech2} : Curent, $$ IBDifference{ tech] : Current, $$
Figure 7: Demand conditioning effect in
the case of ExecutionDelay=4 and TurnO ffD elay=5
IBDifference IBDifference
200
2 0 6 10120 oo 4 10012010
a0 Cy
‘Time (Day) Time (Day)
1Differencetecht + Curent, IBDifference{tech!) : Current
pDiflerence[tech2}: Current, — ifeaxteel: Coe <——<£ ——————
Figure 8: IBDifference in case of ExecutionD elay=4 and TurnOffD elay=8, 10
Figure 9 shows the IBDifference profile for a longer time horizon, under the same parameter
settings as in Figure 8. The oscillation stops at a point with both products experiencing large
shortages. In the context of this paper, we refer to this as unstable, even though the values
converge to a large product shortage. The reason is that the inherently unstable parameter
selection converges to a large shortage due to the demand non-negativity constraint on the
demand rate (Equation. 6). Interestingly, if we remove this constraint, the oscillation continues
with growing amplitude as shown in the right of Figure 9. However, it is unrealistic to remove
equation 6 from the formulation. Hence, the model ends up with both products having shortages
with amplified magnitudes for the unstable case compared with both products stabilizing to a
reasonable profile for the stable case.
IBDifference IBDifference
3,000 30,000
Too 125 150-175-200 «225250 035 80 75 100 125 150 175 200 228 25
‘Time (Day) Time (Day)
[BDiterenceftecht} : Cures. ££ 'BDiflerencetecht] : Curent
[BDiflerenceltech2] : Curent, IeDifawnoa eo), Care
Figure 9: IBDifference in case of ExecutionD elay=4 and TurnO ffD elay=10
If we study the effect of varying the execution delay keeping the turmoff delay fixed, we observe
the same qualitative behavior. Figure 10 shows [BDifference for different ExecutionDelay with
given TurnOffD elay=4. When the execution delay is 6, oscillation dampens after one cycle in the
left of Figure 10; when the execution delay is 8, the oscillation continues to grow in amplitude,
as shown in the right of Figure 10.
IBDifference IBDifference
Q i
| SV
200
400
oo 4 oF oo io 120 1 o 2 4 6 8 100 120 140
‘Time (Day) Time (Day)
IBDifferenceltech!] : Curent —————————__— [BDifference{techl] : Current;
IBDifferenceltech2) : Curent, IBDiflerencefteck2} : Curent
Figure 10: IBDifference in case of ExecutionD elay=6, 8 and TurnO ffD elay=4
The right of Figure 11 shows the phase plot of IBD[1] versus IBD[2] for the case where the
execution delay is (4, 5) (i.e. 4 for product 1 and 5 for product 2) and the turnoff delay is (8,9). It
starts as a big oval and then shrinks in its diameter, ultimately stabilizing at the point (65.55,
56.06). The left of Figure 11 is the corresponding state plot. Since this choice of parameters
corresponds to a stable case, both products stabilize to an overage state. Note that if we use the
delay parameter settings (4,4) instead of (4, 5), the phase plot ends up as a straight line,
oscillating between line segments of smaller lengths before converging to a point.
IBDifference
IBD[1] vs. IBD[2]
80 100 120 140 120
Time (Day) 88S
a OTS
bitferencel tech
IBDifferenceltech] : Care ——— eet
BDifferenceftechd} : Curent [Difference tect2] : Current
10713907
Figure 11: IBDifference for ExecutionD elay=(4,5) and TurnOffD elay=(8,9)
The right of Figure 12 shows the phase plot of IBD[1] versus IBD[2] for the case where the
execution delay is (4, 5) and the tumoff delay is (9, 10). It starts a small oval, then continues to
grow in diameter, ultimately stabilizing to the point (-126.27, -2476). The left of Figure 12 is the
corresponding state plot. Since this parameter setting corresponds to an unstable case, both
products stabilize to a shortage state with increased magnitude.
IBDifference IBD[1] vs. IBD[2]
33000
1,500
o
+1,500
3,000
038075 100105150175 200 Zo 2,600
Time (Day) 2319
ist ca
BDitference tech]
Difference echt]: Currea; ———__________
[Difference tech] : Curren, BDifference{tct2} : Curent
30
Figure 12: IBDifference for ExecutionD elay=(4,5) and TurnO ffD elay=(9,10)
4.3. Cost Impacts
The left of Figure 13 shows the cost plot for ExecutionD elay=(4,5) and TurnOffD elay=(8,9). The
cost curves have several peaks with the sum of amplitudes gradually becoming smaller, and then
the costs stabilize at certain levels. Note that if the first bump is due to overage and holding cost
of excessive inventory, then the next bump would be due to shortage and the penalty cost of
backlogged order. The points at which the curves cross zero are switching points between
overage and shortage. Starting at Time=14, the first bump for product 2 is shortage cost and the
first bump for product 1 is overage cost.
Cost
1,000
750
0 2 50 75 100 125 150 175 200 225 250
Time (Day)
Costtech] : Curent
Costtech2}: Curent
Figure 13: Cost for ExecutionDelay=(4,5) and TunOffD elay=(8,9)
The left of Figure 14 shows the cost plot for ExecutionD elay=(4,5) and TurnOffD elay=(9,10).
The cost curves keep growing in amplitude, ultimately stabilizing at very high levels due to a
large shortage. The right is the corresponding phase plot of Cost[1] vs. Cost[2]. The phase
change range becomes bigger and bigger before stabilizing at a point far away from the origin.
Cost
0 125150, 250
Time (Day)
Cost{techl]: Current
Cost{tech] : Current
Figure 14: Cost for ExecutionDelay=(4,5) and TumOffD elay=(9,10)
These simulations suggest that there exists a transition point at which the system transitions from
a stable behavior to an unstable behavior. Figure 15 shows the plot of the average cost versus
turnoff delay with given ExecutionD elay=4 and initial inventory level being (200,100). When the
tumoff delay is less than or equal to 9, the average cost has small variation and is small. When
the tumoff delay is beyond 9, the average cost has a sharp transition.
Average Costs. Delay
Tumneft Delay
Figure 15: Cost Jump during Transiting from Convergence to Divergence
4.4, Countermeasures
Both subsections 4.2 and 4.3 demonstrate dynamical effects for different values of time delays in
the conditioning process. We now discuss how these instabilities can be potentially managed.
4.4.1, Inventory level influence
Increasing inventory levels would in general increase the time before product shortages are seen
and further reduce the frequency of oscillations. Figure 16 shows that, when we change initial
inventory for product 2 from 100 to 150 and keep TurnOffDelay=10 and ExecutionDelay=4,
behavior of IBDifference changes significantly comparing with the right of Figure 8 in which
inventory baseline is (200,100) and oscillates one cycle, before stabilizing.
IBDifference
0 20 40 60 80 10120140
Time (Day)
IBDifference{ tech! : Current
IBDifferencel tech2] : Current
Figure 16: IBDifference after increasing inventory level
for ExecutionD elay=4 and TurnO ffD elay=10
Figure 17 shows plot of average cost versus the tumoff delay for different initial inventory levels.
When the initial inventory is (100, 90), average cost will jump when the turnoff delay is 3. When
the initial inventory is (200,100), average cost will jump when the tumoff delay is 9. When the
initial inventory moves up to (200,150), average cost will jump when the tumoff delay is 13. It
implies that, in order to make the system more stable, a potential countermeasure is to increase
the inventory level (safety stock level). However, notice from Figure 17 that the average costs
are higher when the inventory levels are increased. This suggests a tradeoff between operational
costs and risk of instability. This also suggests that stability issues need to be considered when
enterprises drive cost reduction initiatives, because inventory reduction brings along with it an
increased risk of instability.
‘Average Cost vs. Turnoff Delay
12000
10000
g 8
*
.
N
|
‘Turnoff Delay
Fo = (10080) a= (200,500) = BOOTH)
Figure 17: Cost Transition Change for Different Inventory Levels
4.4.2. Conditioning line consideration
Another countermeasure is to avoid excessive conditioning which could happen if conditioning
actions are done based on partially or completely ignoring the effects of earlier conditioning
actions. This is important because in the presence of time delays, the effects of past conditioning
actions may not be immediately manifested in the inventories and backlogs that drive
conditioning actions according to equations (4) and (5). In the ideal case, this situation never
happens since there are no delays and the effects of past conditioning actions are seen before any
further conditioning actions are decided upon. This situation is not unlike the systems dynamics
models in Reference [2], where it is shown that ignoring the supply lines partially or completely
is an important source of amplifications. Hence, the decision rule for new conditioning actions
should account for the conditioning line, as shown in Figure 18.
Conditioning
Conditionin_____—» "i
poe oes ROT
° = (Condition)
Conditioning Decision Rule — eatin \
Conditioning
sahiage
ioe
oft InitialDemand
°
—— pemaniRate
o> TnChange
TrendFactor__ io
ae Besiredtite
Adjuster
Execution
Delay
__» InChange
s A Dane
Threshold <a
Conditioning ~~~
4 CycleTime Re
Modified as AdjustedIBD
ShiftIto2““——-—__ /'
Delay _ =
TumO#Delay- Shin ag >
Delay
Figure 18: Decision Rule with Conditioning Line
Instead of using IBDifference to determine Shiftlto2 in Eg. 4, we used AdjustedIBD (this is
adjusted by the current conditioning pipeline),
AdjustedID B = IBDifference —C onditioningD iff * Adjuster ,
ConditioningD iff = ConditioningLine —
FixedD elay(ConditioningLine, CCT , ConditioningLine) .
By choosing Adjuster=1, we take the last CCT period conditioning lines into account. The
conditioning line is calculated as the following
t
ConditioningLine(t) = | FixedDelay (DRIC (zr), ExecutionD elay, DRIC (r))dz ,
i
where DRIC is for DesiredRateInChange. Figure 19 shows the result for the execution delay
being 4 and tumoff delay being 19. We observe stable behaviors even for large tumoff delays.
IBDifference
0 2 50 75 100 125 150 175 200 225 250
‘Time (Day)
1BDifference{tech1] : Current
1BDifference{tech2] : Current
Figure 14: IBDifference after Conditioning Line Adjustment
5. Closing Remarks
In this paper, we have discussed dynamical effects arising out of demand conditioning in the
supply chain, using a systems dynamics model. We showed the presence of oscillations in
supply shortages created due to the conditioning actions, if the time delays in managing the
conditioning are long. There are other interesting dynamical issues relating to demand
conditioning, arising from the presence of uncertainties in the supply chain. For instance, we
may forecast a future inventory surplus for a specific product and trigger conditioning actions to
sell the excess inventory. However, since supply is uncertain, it is possible that the inventory
surplus may not materialize due to a number of reasons - for example, the suppliers yield may be
variable. If this happens, we may have triggered the conditioning action too soon and as a result,
create an inventory shortage instead of a surplus, as an unintended consequence of the action
taken. An interesting question for future work in this regard is how to trigger the conditioning
actions, given the supply and demand uncertainty and lead times in the supply chain.
We suspect that the instabilities discussed in this paper are equally applicable to supply
conditioning. This is particularly relevant, since all the suppliers in different tiers are not
integrated; hence, it is likely that some of the supply lines are not accounted for in supply chain
planning. Since there are considerable time delays in supply management, this is a potential
source of instabilities. It would be interesting to explore this deeper, to understand the drivers of
instability in supply conditioning and also to examine potential countermeasures.
References
[1] J.W. Forrester, Industry Dynamics, MIT Press, Cambridge, MA, 1961.
[2] J.D. Sterman, Business Dynamics: System Thinking and Modeling for a Complex World,
Irwin McGraw-Hill, Boston, 2000.
[3] Hau L. Lee, V. Padmanabhan, S. Whang, Information Distortion in a Supply Chain: the
Bullwhip Effect, Management Science, Vol. 43, No. 4, April 1997, pp. 546-558.
[4] S. Kapoor, K. Bhattacharya, S. Buckley, P. Chowdhary, M. Ettl, K. Katircioglu, E.
Mauch, L. Phillips, “A Technical Framework for Sense & Respond Business
Management”, IBM Systems Journal, Vol. 44, No. 1, pg 5, 2005.
[5] J.D. Sterman, Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic
Decision Making Experiment, Management Sciences, Vol. 35, No. 3, March 1989, pp.
321-339.
[6] P. Huang, Y.M. Lee, L. An, M. Ettl, K. Soururajan, S. Buckley, Utilizing Simulation to
Evaluate Business Decisions in Sense-and-Respond Systems, Proceedings of the 2004
Winter Simulation Conference, 2004.
[7] Vensim: http://www.vensim.com
[8] A.F. Ivanov, Yu. Kazmerchuk and A.V. Swichchuk, Theory, Stochastic Stability and
Applications of Stochastic Delay Differential Equations: A Survey of Recent Results,
Differential Equations and Dynamical Systems, Vol. 11, Nos. 1&2, 2003, pp. 55-115.
