Information Distortion in a Supply Chain:

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Information Distortion in a Supply Chain The
Bullwhip Effect
Hau L. Lee ? V. Padmanabhan ?
Seungjin Whang
Presented by Isil Tugrul
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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

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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.

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Distortion in Demand Information
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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.

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Causes of the Bullwhip Effect

• 1. Demand signal processing
• 2. Rationing game
• 3. Order batching
• 4. Price variations

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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.
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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

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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 lt ?
lt 1 ut error term i.i.d with mean 0 and var. ?2
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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
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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.
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Demand Signal Processing
THEOREM 1. In the above setting, we
have (a) If 0 lt ? lt 1, the variance of retail
orders is strictly larger than that of
retail sales that is, Var(z1) gt Var(D0)
(b) If 0 lt ? lt 1, the larger the replenishment
lead time, the larger the variance of
orders i.e. Var(z1) is strictly
increasing in v.
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Rationing Game

• If Demand gt 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 .

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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.

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Rationing Game
The first order condition is given by
The second order condition is given by
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Rationing Game
-p (p h)?(zi0) gt 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) gt the order
quantity in the traditional newsvendor problem
(z). Further if F(.) and?(.) are strictly
increasing, the inequality strictly holds.
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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.

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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

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Order Batching

• (a) Random Ordering
• Demands from retailers are independent.

• If R1, then the variance of orders placed by
  retailers would be the same as the retailers
  demand.

• (b) Positively Correlated Ordering
• All the retailers order in the same period

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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 (M1) and (R-k) groups of size M.
  Each group orders in a different period.
• When NmR, then perfectly balanced retailer
  ordering can be achieved and bullwhip effect
  disappears

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

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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 (iH,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
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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 lt SL.
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Price Variations
THEOREM 5. In the above setting, Varzt gt Var?
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Strategies to Reduce the Impact of the Bullwhip
Effect
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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

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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.

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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

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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

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QUESTIONS ?