1. Information Distortion in a Supply Chain: “The Bullwhip Effect”
Hau L. Lee  V. Padmanabhan  Seungjin Whang
Presented by Işıl Tuğrul

2. 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

3. 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.

4. Distortion in Demand Information

5. 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.

6. Causes of the Bullwhip Effect
1. Demand signal processing
2. Rationing game
3. Order batching
4. Price variations

7. 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.

8. 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

9. 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 = 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

10. 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)
where

11. Demand Signal Processing
The optimal order amount is given by
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.

12. 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.

13. 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 .

14. 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].

15. Rationing Game The first order condition is given by
The second order condition is given by

16. 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.

17. 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.

18. 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

19. Order Batching (a) Random Ordering (b) Positively Correlated Ordering
Demands from retailers are independent.
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

20. 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.
When N=mR, then “perfectly balanced” retailer ordering can be achieved and bullwhip effect disappears

21. Order Batching
THEOREM 3. (a)
(b)

22. 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.

23. The retailers inventory problem is formulated as
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
Vi (i=H,L) denotes the minimal expected discounted cost incurred throughout an infinite horizon when current price is ci.
L(.) is the sum of one-period inventory and shortage costs at a given level of inventory

24. 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.

25. Price Variations
THEOREM 5. In the above setting, Var[zt] > Var[]

26. Strategies to Reduce the Impact of the Bullwhip Effect

27. 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

28. 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.

29. 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

30. 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

31. QUESTIONS ?