Transcript No Slide Title

Information Distortion
in a Supply Chain:
“The Bullwhip Effect”
Hau L. Lee

V. Padmanabhan

Seungjin Whang
Presented by Işıl Tuğrul
Content

claims that the demand information in the form of
orders tends to be distorted & misguiding

identifies and analyzes four causes of the bullwhip
effect
develops simple mathematical models to
demonstrate that the amplified order variation is an
outcome of rational and optimizing behavior of
supply chain members


discusses the methods to reduce the impact
of the bullwhip effect
What is Bullwhip Effect?
The increase in demand variability as we
move up in the supply chain is referred to as
the bullwhip effect.
Orders placed by a retailer tend to be much
more variable than the customer demand
seen by the retailer.
Distortion in Demand Information
Orders vs. Sales
60
Consumer Demand
50
Retailer's Orders
Units
40
30
20
10
0
1
5
9
13
17
21
25
Time (Weeks)
29
33
37
41
Previous Work
Sterman attributed the amplified order variability to
players’ irrational behavior or misconceptions about
inventory and demand information. His findings suggest
that progress can be made in reducing the effect through
modifications in individual education.

In contrast, Lee et al. claim that the bullwhip effect is a
consequence of the players' rational behavior within the
supply chain's infrastructure.

Causes of the Bullwhip Effect
1. Demand signal processing
2. Rationing game
3. Order batching
4. Price variations
An Idealized Situation
Consider a multi-period inventory system operated
under a periodic review policy where :
(i) demand is stationary
(ii) resupply is infinite with a fixed lead time
(iii) there is no fixed order cost, and
(iv) price of the product is stationary over time.
Demand Signal Processing





Demand is non-stationary
Order-up-to point is also non-stationary
Project the demand pattern based on observed demand.
• Distributors rely on retailers’ orders to forecast demand
• Manufacturers rely on distributors’ orders
“Multiple forecasting”
As they make their forecasts based on a forecasted data the
variation increases. The supplier loses track of the true demand
pattern at the retail level.
Long lead times lead to greater fluctuations in the order
quantities
Demand Signal Processing
 Consider a single-item multi-period inventory model
 The order sent to the supplier reflects the amount needed
to replenish the stocks to meet the requirements of future
demands, plus the necessary safety stocks.
 The retailer faces serially correlated demands which
follow the process
Dt  d  Dt 1  ut
Dt = the demand in period t,
d = a nonnegative constant
 = the correlation parameter, -1 <  < 1
ut = error term i.i.d with mean 0 and var. 2
Demand Signal Processing
The cost minimization problem in an arbitrary period is formulated as follows:
Parameters:
zt : order quantity at the beginning of period t
h : holding cost
 : unit shortage penalty
c : ordering cost
 : cost discount factor per period
v : replenishment lead time (order lead time + transit time)
t v
 


 
t 1
v
min  E1 czt   g  S t ,  Di  
i t


 

 t 1


where
t v
t v




 t v

g  St ,  Di   h. St   Di    .  Di  St 
i t
i t




 i t


Demand Signal Processing
The optimal order amount
*
1
z
is given by
v 1

(
1


)
*
*
*
z1  S1  S0  D0 
( D0  D1 )  D0
1 
2  (1   v1 )(1   v 2 )
Var( z1 )  Var( D0 ) 
 Var( D0 )
2
(1   )(1   )
For v = 0, the variance of orders reduces to Var( z1) = Var(D0) + 2,
which shows that the demand variability amplification exists, even
when the lead time is zero.
Demand Signal Processing
THEOREM 1. In the above setting, we have:
(a) If 0 <  < 1, the variance of retail orders is
strictly larger than that of retail sales; that is,
Var(z1) > Var(D0);
(b) If 0 <  < 1, the larger the replenishment
lead time, the larger the variance of orders; i.e.
Var(z1) is strictly increasing in v.
Rationing Game
If Demand > Production Capacity, manufacturers often
ration supply of the product to satisfy the ratailers’ orders.

For example, if the total supply is only 50 percent of the
total demand, all customers receive 50 percent of what they
order.

If retailers suspect that a product will be short in supply,
each retailer will issue an exaggerated order more than their
actual needs, in order to secure more units of the product.

If retailers are allowed to cancel orders when their actual
demand is satisfied, then the demand information will be
distorted further .

Rationing Game

A simple one-period model (an extended newsvendor
model) with multiple retailers is developed
Each of the retailers takes others’ decisions as given
and chooses the order quantity that will minimize the
expected cost.

The resulting order quantities (z1*, z2*,….,zN*) chosen
by retailers define a Nash equilibrium. That is, no retailer
can benefit by changing his ordering strategy while other
players keep their strategies unchanged.


Since all retailers are identical, we have a symmetric
Nash equilibrium where zi* = z* i, i  [1,N].
Rationing Game
  
z
Ci    p     i
Q
 0 
 zi / Q 
Q

d( )  h

zi / Q

0

 zi



  d( )dF (  )
Q



zi
 

 (1  F (Q)) p  (  zi )d( )  h  ( zi   )d( )
 zi

0
The first order condition is given by
Q

 z
dC i
   p  ( p  h) i
dz i
 Q
 0 
  1
z
    i2
  Q Q

dF (  )  1  F (Q) p  ( p  h) ( zi )  0

The second order condition is given by


d 2Ci
0
0




p

(
p

h
)

(
z
)
f
(
Q
)

1

F
(
Q
)
(
p

h
)

(
z
)0
i
i
2
dzi
Rationing Game
-p + (p + h)(zi0) > 0.
Only then zi0 satisfies dCi/ dzi = 0 and it is the optimal order quantity zi*.
The traditional newsvendor solution z` satisfies -p + (p + h)(z`) = 0.
THEOREM 2. Optimal order quantity for the
retailer in the rationing game (z*) > the
order
quantity in the traditional newsvendor problem (z`).
Further if F(.) and(.) are strictly increasing, the
inequality strictly holds.
Order Batching

Retailers tend to accumulate demands before issuing
an order.
–
–


transportation costs
order processing costs
Distributor will observe a large order followed by
several periods of no-order, followed by another
large order.
Periodic ordering amplifies variability and
contributes to the bullwhip effect.
Order Batching
• N retailers using a periodic review inventory system
with review cycle equal to R periods.
• Consider 3 cases for retailers’ order cycles:
(a) Random Ordering
(b) Positively Correlated Ordering
(c) Balanced Ordering
Order Batching
(a) Random Ordering
– Demands from retailers are independent.
E ( Z tr )  Nm
Var( Z tr )  N 2  m 2 N ( R  1)  N 2
– If R=1, then the variance of orders placed by retailers would
be the same as the retailer’s demand.
(b) Positively Correlated Ordering
– All the retailers order in the same period
E ( Z tc )  Nm
Var ( Z tc )  N 2  m 2 N 2 ( R  1)  N 2
Order Batching
(c) Balanced Ordering
– Orders from different retailers are evenly distributed in time.
– All N retailers are divided into R groups: k groups of size
(M+1) and (R-k) groups of size M. Each group orders in a
different period.
E ( Z tb )  Nm
Var( Z tb )  N 2  m 2 k ( R  k )  N 2  m 2 N ( R  1)
– When N=mR, then “perfectly balanced” retailer ordering can be
achieved and bullwhip effect disappears
Order Batching
THEOREM 3. (a) E[Ztc ]  E[Ztr ]  E[Ztb ]  Nm
(b) Var[Z c ]  Var[Z r ]  Var[Z b ]  N 2
t
t
t
where Ztc , Ztr and Ztb are the random vari
ables denoting
the ordersfrom N retailers, respectively under correlated
ordering,random ordering andbalanced ordering.
Price Variations
 When a manufacturer offers an attractive price, retailers
engage in "forward buy" arrangements in which items are
bought in advance of requirements
 Retailers buy in larger quantities that exceeds their actual
needs. When the product's price returns to normal, they stop
buying until the inventory is depleted.
 The customer's buying pattern does not reflect its
consumption pattern.
Price Variations


A retailer faces i.i.d demand with density function (.)
Manufacturer may offer two price alternatives:
• cL with probability q
• cH with probability 1 - q
The retailers inventory problem is formulated as



i
i
L
H
V ( x)  minc ( y  x)  L( y )    qV ( y   )  (1  q)V ( y   )  ( )d 
0




Vi (i=H,L) denotes the minimal expected discounted cost
incurred throughout an infinite horizon when current price is ci.

y
y
0
where L( y )  p  (  y ) ( )d  h  ( y   ) ( )d
L(.) is the sum of one-period inventory and
shortage costs at a given level of inventory
Price Variations
THEOREM 4. The following inventory policy is
optimal to the problem:
At price cL, get as close as possible to the stock
level SL, and at price cH bring the stock level SH,
where SH < SL.
Price Variations
Sales vs. O rders When Price Changes
100
Units
80
60
Orders
40
Sales
20
0
0
1
2
3
4
5
6
7
8
9
Time
THEOREM 5. In the above setting, Var[zt] > Var[]
Strategies to Reduce the
Impact of the Bullwhip Effect
Demand Signal Processing

Information sharing among members of the chain
– use electronic data interchange (EDI) to share data
– update their forecasts with the same demand data

Avoiding multiple demand forecast updates
– single member of the chain performs the forecasting and ordering
– centralized multi echelon inventory control system

Vendor Managed Inventory
– manufacturer has access to the information at retailing sites
– updates forecasts and resupplies the retail sites.
– continuous replenishment program (CRP).

Reduction in lead times
– just-in-time replenishment
Rationing Game
Allocate scarce products in proportion to past sales
records rather than based on order.

– no incentive to exaggerate their orders.
Share capacity and inventory information to reduce
customers' anxiety and lessen their need to engage in
gaming.


Enforce more strict cancellation and return policies.
without a penalty, retailers will continue to exaggerate their
needs and cancel orders.
–
Order Batching

Lower the transaction costs
reduce the cost of the paperwork in generating an order
through EDI-based order transmission systems
–
Order assortments of different products instead of
ordering a full load of the same product.

Consolidate loads from multiple suppliers located
near each other by using third-party logistics companies

Price Variations
Reduce the frequency and the level of wholesale
price discounting.


Move to an everyday low price (EDLP)
–
offer a product with a single consistent price
Keep high and low pricing practice but synchronize
purchase and delivery schedules

–
–
deliver goods in multiple future time points
both parties save inventory carrying costs
QUESTIONS ?