Matching Supply with Demand:
An Introduction to Operations Management
Gérard Cachon
ChristianTerwiesch
All slides in this file are copyrighted by Gerard Cachon and Christian
Terwiesch. Any instructor that adopts Matching Supply with
Demand: An Introduction to Operations Management as a required
text for their course is free to use and modify these slides as desired.
All others must obtain explicit written permission from the authors to
use these slides.
Slide ‹#›
The Bullwhip Effect
Slide ‹#›
Supply chain demand and variability

Over the long run the average inflow to a firm must equal the average
outflow
Inflow

Firm
Outflow
(sales)
However, the volatility of the inflow can differ substantially from the volatility
of the outflow
Inflow
Firm
Slide ‹#›
Outflow
(sales)
What is the bullwhip effect?

Demand variability increases as you move up the supply chain from
customers towards supply
Equipment Tier 1 Supplier
Factory
Distributor
Slide ‹#›
Retailer
Customer
Bullwhip effect in autos to machine tools
80%
Machine tools
Autos
60%
% change in demand
40%
20%
0%
-20%
-40%
-60%
GDP = solid line
-80%
Source:Anderson, Fine and Parker (1996)
Slide ‹#›
Bullwhip effect in the US PC supply chain
Changes in
demand
80%
60%
Semiconductor
Equipment
40%
20%
PC
0%
-20%
Semiconductor
-40%
1995
1996
1997
1998
1999
2000
2001
Annual percentage changes in demand (in $s) at three levels of the semiconductor
supply chain: personal computers, semiconductors and semiconductor manufacturing
equipment.
Slide ‹#›
Consequences of the bullwhip effect

Inefficient production or excessive inventory.

Low utilization of the distribution channel.

Necessity to have capacity far exceeding average demand.

High transportation costs.

Poor customer service due to stockouts.
Slide ‹#›
Causes of the bullwhip effect

Order synchronization

Order batching

Trade promotions and forward buying

Reactive and over-reactive ordering

Shortage gaming
Slide ‹#›
Order synchronization

Customers order on the same
order cycle, e.g., first of the
month, every Monday, etc.
The graph shows simulated
daily consumer demand (solid
line) and supplier demand
(squares) when retailers order
weekly: 9 retailers order on
Monday, 5 on Tuesday, 1 on
Wednesday, 2 or Thursday and
3 on Friday.
70
60
50
40
Units

30
20
10
0
T im e (e a c h p e rio d e q u a ls o n e d a y )
Slide ‹#›
Order batching

Retailers may be required to
order in integer multiples of
some batch size, e.g., case
quantities, pallet quantities, full
truck load, etc.
70
60

The graph shows simulated
daily consumer demand (solid
line) and supplier demand
(squares) when retailers order
in batches of 15 units, i.e.,
every 15th demand a retailer
orders one batch from the
supplier that contains 15 units.
Units
50
40
30
20
10
0
T im e (e a c h p e rio d e q u a ls o n e d a y )
Slide ‹#›
Trade promotions and forward buying


Supplier gives retailer a temporary discount, called a trade promotion.
Retailer purchases enough to satisfy demand until the next trade promotion.

Example: Campbell’s Chicken Noodle Soup over a one year period:
One retailer’s buy
Total shipments and consumption
7000
6000
S hipm e nts
Cases
Cases
5000
4000
3000
C ons um ption
2000
1000
Slide ‹#›
Nov
Oct
Sep
Aug
Jul
Jun
Apr
Mar
Feb
May
T im e (w e e ks )
Jan
Dec
0
Reactive and over-reactive ordering

Each location forecasts demand to determine shifts in the demand process.

How should a firm respond to a “high” demand observation?
 Is this a signal of higher future demand or just random variation in
current demand?
 Hedge by assuming this signals higher future demand, i.e. order more
than usual.

Rational reactions at one level propagate up the supply chain.

Unfortunately, it is human to over react, thereby further increasing the
bullwhip effect.
Slide ‹#›
Shortage gaming

Setting:
 Retailers submit orders for delivery in a future period.
 Supplier produces.
 If supplier production is less than orders, orders are rationed, i.e.,
retailers are “put on allocation”.

… to secure a better allocation, the retailers inflate their orders, i.e., order
more than they need…

… So retailer orders do not convey good information about true demand …

This can be a big problem for the supplier, especially if retailers are later
able to cancel a portion of the order:
 Orders that have been submitted that are likely be canceled are called
phantom orders.
Slide ‹#›
Strategies to combat the bullwhip effect

Information sharing:
 Collaborative Planning, Forecasting and Replenishment (CPFR)

Smooth the flow of products
 Coordinate with retailers to spread deliveries evenly.
 Reduce minimum batch sizes.
 Smaller and more frequent replenishments (EDI).

Eliminate pathological incentives
 Every day low price
 Restrict returns and order cancellations
 Order allocation based on past sales in case of shortages

Vendor Managed Inventory (VMI): delegation of stocking decisions
 Used by Barilla, P&G/Wal-Mart and others.
Slide ‹#›
An antidote to the bullwhip effect
Is there any force in a supply chain that counteracts the bullwhip effect?

Yes: If demand is seasonal (i.e., there are anticipated peaks and valleys in
demand), then use production smoothing:
 If the firm’s orders are correlated with its production, the firm’s suppliers
will see orders that are smoother than the firm’s demand.
Quantity

Demand exceeds
production, drawing
down inventory
Production
Production exceeds
demand, building
inventory
Demand
Time
Slide ‹#›
Production smoothing - U.S. monthly trade sector sales and
production
Slide ‹#›
Production smoothing at Walmart
(quarterly sales and production)
Slide ‹#›
Supply chain contracting
Slide ‹#›
Double marginalization at Umbra Visage (UV)

Suboptimal supply chain performance occurs because …
 Each firm makes decisions based on their own margin, not the supply
chain’s margin.
 This is called double marginalization.

Example:
 Zamatia makes sunglass at a cost of $35 and sells them to UV for $75.
 UV sells them for $115 and salvages left over inventory for $25 per unit.
 Demand is normal with mean 250 and standard deviation 125.
 UV faces a newsvendor problem.
 UV:
Cu = 115 - 75 = 40, Co =75 - 25 = 50, Critical ratio = 40 / 90 = 0.44
 Supply chain:
Cu = 115 - 35 = 80, Co =35 - 25 = 10, Critical ratio = 80 / 90 = 0.89
Supply chain’s critical ratio is much higher than UV’s critical ratio!



Slide ‹#›
The cost of double marginalization

UV:




Optimal order quantity = 234 (critical ratio = 0.44)
 Expected sales = 192
 Expected profit = $5,580
Zamatia:
 Sales = 234
 Profit = $9,360
Total supply chain profit = $5,580 + $9,360 = $14,940
Supply chain potential:
 Order quantity = 404 (critical ratio = 0.89)
 Expected sales = 243
 Expected profit = $17,830 …. 19% higher than $14,940.
Slide ‹#›
A solution to double marginalization: share risk

Suppose Zamatia offers to buy-back unsold sunglasses at b per unit:
 UV incurs a $1.5 cost to ship sunglasses back.
 b < $75 so that UV doesn’t make money returning merchandise.
 b > $26.50 so UV prefers to return rather than salvage.
 Zamatia salvages sunglasses for $26.50.

UV’s overage cost, Co =75 – (b – 1.5) > 50, is reduced …
 … so UV’s critical ratio increases!

Choose b to make UV’s critical ratio equal the supply chain’s critical ratio:
Buy back price  Shipping cost  Price
 Price  Salvage value 
  Price - Wholesale price   

Price  Cost


 $115  $25 
Buy back price  $1.5  $115   $115  $75  
  $71.5
$115

$35


Slide ‹#›
Potential allocations of profit:
Wholesale price ($)
35
45
55
65
75
85
95
105
Buy back price ($)
26.50 37.75 49.00 60.25 71.50 82.75 94.00 105.25
C u ($)
80
70
60
50
40
30
20
10
C o ($)
10.00
8.75
7.50
6.25
5.00
3.75
2.50
1.25
Critical ratio
0.8889 0.8889 0.8889 0.8889 0.8889 0.8889 0.8889 0.8889
z
1.23
1.23
1.23
1.23
1.23
1.23
1.23
1.23
Q
404
404
404
404
404
404
404
404
Expected sales
243
243
243
243
243
243
243
243
Exp. left over inv.
161
161
161
161
161
161
161
161
Expected profits:
Umbra
17,830 15,601 13,373 11,144 8,915 6,686 4,458 2,229
Zamatia
0 2,229 4,458 6,686 8,915 11,144 13,373 15,601
Supply chain
17,830 17,830 17,830 17,830 17,830 17,830 17,830 17,830

As the buy-back price is increased, risk is shifted from UV to Zamatia
along with profits.

There is a wholesale/buy back price combination that makes both firms
better off!
Slide ‹#›
Buy-back contracts summary

What are they?
 Retailer is allowed to return to the supplier goods left over at the end of
the selling season.

How do they improve supply chain performance?
 The retailer’s overage cost is reduced, so the retailer stocks more.
 Allows for the redistribution of inventory risk across the supply chain.
 Could protect the supplier’s brand image by avoiding markdowns.
 Allows the supplier to signal that significant marketing effort will occur.

What are the costs of buy-backs?
 Administrative costs plus additional shipping and handling costs.

Where are they used?
 books, cosmetics, music CDs, agricultural chemicals, electronics …
Slide ‹#›
Other solutions to supply chain coordination failure

Quantity discounts:
 Used to induce larger downstream order quantities so that downstream
service is improved and/or handling and transportation efficiency is
improved.

Franchise fees:
 Marginal cost pricing coordinates actions, but leaves the upstream party
with no profit.
 So charge a franchise fee to extract profit from the franchisee.
 Also known as a “two-part tariff”.
Slide ‹#›
Options contract example: semiconductors

Setting:
 Supplier invests in capacity (fabs cost $3Billion+), then …
 Random demand occurs.

Scenario 1:
 Buyer decides how much to buy after observing demand.
 Supplier bears all risk of idle capacity, so supplier under invests in capacity …
 … buyer can’t get needed product if demand is high

Scenario 2: option contact:
 Buyer purchases options before demand is observed, p0 per option
 Buyer exercises options, pe to exercise each option, after observing demand
 Now risk is shared (supplier gets p0 per option up front even if demand is low)
 Supplier builds more capacity because she bears less risk …
 … and more capacity is available to the buyer if demand is high …
 … so they both can be better off.

Where else are option contracts used?
 Energy markets (electric power), commodity chemicals, metals, plastics, apparel
retailing, air cargo, …
Slide ‹#›
Summary

Coordination failure:
 Supply chain performance may be less than optimal with decentralized
operations (i.e., multiple firms making decisions) even if firms choose
individually optimal actions.

A reason for coordination failure:
 The terms of trade do not give firms the proper incentive to choose
supply chain optimal actions.

Why fix coordination failure:
 If total supply chain profit increase, the “pie” increases and everyone
can be given a bigger piece.

How to fix coordination failure:
 Design terms of trade to restore a firm’s incentive to choose optimal
actions.
 e.g., with revenue sharing a retailer can justify holding more tapes.
Slide ‹#›