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

0

10

20

30

40

50

60

1 5 9 13 17 21 25 29 33 37 41

Time (Weeks)

Un

its

Consumer Demand

Retailer's Orders

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

Consider a multi-period inventory system operated under a periodic review policy where :

An Idealized Situation

(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 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 ttt uDdD 1

Dt = the demand in period t,

d = a nonnegative constant = the correlation parameter, -1 < < 1ut = error term i.i.d with mean 0 and var. 2

Dt = the demand in period t,

d = a nonnegative constant = the correlation parameter, -1 < < 1ut = error term i.i.d with mean 0 and var. 2

Demand Signal Processing

11

1 ,mint

vt

tiit

vt

t DSgczE

vt

titi

vt

tiit

vt

tiit SDDShDSg .., where

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)

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)

Demand Signal Processing

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1

0*0

*1

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1

)1(DDDDSSz

v

The optimal order amount is given by*1z

)( )1)(1(

)1)(1(2)()( 02

21

01 DVarDVarzVarvv

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.

Demand Signal Processing

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

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The first order condition is given by

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The second order condition is given by

Rationing Game

The traditional newsvendor solution z` satisfies -p + (p + h)(z`) = 0.

-p + (p + h)(zi0) > 0.

Only then zi0 satisfies dCi/ dzi = 0 and it is the optimal order quantity zi*.

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.

Rationing Game

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.

• 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

222 )1()(

)(

NRNmNZVar

NmZErt

rt

2222 )1()(

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NRNmNZVar

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(a) Random Ordering

– Demands from retailers are independent.

(b) Positively Correlated Ordering

– All the retailers order in the same period

Order Batching

– If R=1, then the variance of orders placed by retailers would be the same as the retailer’s demand.

)1()()(

)(2222

RNmNkRkmNZVar

NmZEbt

bt

(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.

– When N=mR, then “perfectly balanced” retailer ordering can be achieved and bullwhip effect disappears

Order Batching

THEOREM 3. (a)

(b)

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2][][][ NZVarZVarZVar bt

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rdering.balanced oering and random ordordering,

rrelated y under coespectiveltailers, r from N rethe orders

ting ables denoandom vari are the r and Z, Zwhere Z bt

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Order Batching

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.

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

Price Variations

dyVqyqVyLxycxV HLii )()()1()()()(min)(0

Vi (i=H,L) denotes the minimal expected discounted cost incurred throughout an infinite horizon when current price is ci.

Vi (i=H,L) denotes the minimal expected discounted cost incurred throughout an infinite horizon when current price is ci.

y

y

dyhdypyL0

)()()()()( where

L(.) is the sum of one-period inventory and shortage costs at a given level of inventory

L(.) is the sum of one-period inventory and shortage costs at a given level of inventory

The retailers inventory problem is formulated as

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. Orders When Price Changes

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8 9

Time

Un

its

Orders

Sales

Price Variations

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

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.

Rationing Game

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

Order Batching

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

Price Variations

QUESTIONS ?