Supply Chain Management:
Issues and Models
Introduction to Beer Game
Prof. Dr. Jinxing Xie
Department of Mathematical Sciences
Tsinghua University, Beijing 100084, China
http://faculty.math.tsinghua.edu.cn/~jxie
Email: jxie@ math.tsinghua.edu.cn
Voice: (86-10)62787812 Fax: (86-10)62785847
Office: Rm. 1308, New Science Building
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What is a Beer Game?

The Beer Game is a logistics game
that was originally developed by MIT in the 60s
and has since been played all over the world
by people at all levels, from students
to presidents of big multinational groups.
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A Supply Chain Game:
The Beer Game
Customers
Orders
Retailer
Wholesaler
Distributor
Products
Factory / Brewery
/ Manufacturer
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Four Players on a Team
Orders
Delay
Delay
Delay
Factory
Delay
Delay
Retailer
Delay
Delay
Delay
Delay
Delay
Delay
Delay
Wholesaler
Distributor
Delay
Delay
Delay
Material
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Material delay = (2,2,2,3); Information Delay = (2,2,2,0)
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Events in each period
Retailer
Wholesaler
Distributor
Factory
Each Stage:
•Holds Inventory
•Receives Beer (after Shipping Delay)
•Receives Orders from Downstream (after Mail Delay)
•Ships Beer Downstream to meet Orders
•Orders Beer from Upstream (the only decision)
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Rules
Pick a Team Name
 Holding Cost: $0.50/case/week
 Backorder Cost: $1.00/case/week
 Total Cost = Sum of Costs at all four Stages
 Goal: Minimize Total Supply Chain Cost
 NO COMMUNICATION BETWEEN STAGES!!!
 Retailers must not reveal actual customer orders!!!

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To Remember
All demand is to be satisfied
 Unsatisfied demand becomes Backlog and
is added to next period’s demand
 It takes two weeks for replenishment order
to reach; shipment time is also two weeks
 There are no capacity restrictions

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Game starts now!

First 4 weeks: order 4 cases each week

From 4th week on, you can order any quantity

The game will last 50 weeks

Now start the game
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End of Game: Stop after 36 weeks

Calculate Total Cost at your Stage

Plot your Weekly Orders

Plot your Inventory and Backlog

Plot your Guess on Consumer Demand Pattern

Sum Costs over all Four Stages
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
Tape results on wall as follows:
Retailer
Wholesaler
Distributor
Factory
Orders
Inventory
Guess
the demand
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Debriefing and Discussion
1.
What, if anything, is unrealistic about this game?
Is reality more complicated or less complicated?
2.
Why are there order, production and shipping
delays?
3.
Did you find yourself “blaming” the person
upstream for your problems?
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Debriefing and Discussion
4.
What commonalities do you see in the graphs for the
different teams?
5.
What pattern do you see? What is the cost of this?
6.
What are the reasons that such patterns are seen in
the supply chain?
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Lessons of the Game

Such oscillations are common
– Bullwhip effect (demand distortion)
Everyone blames others - but problem is
with the structure
 Cost of this: Capacity crunch

– Expediting
– High indirect cost
– Low service levels
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Reasons for Oscillations
Demand randomness
 Ill-conceived promotional policies
 Rationing and shortage gaming
 Ordering policy and aggregation
 Incentives

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Motorola's Inventory Problem



Feb. 17, 1996. Announced it has excess
inventory of cellular phones
Stock price tumbled 10%; Profit estimates
down $39 million
Reason
– In 1994, distributors faced shortages
– In 1995, they over-ordered, early and often

Now new-orders are down - idle capacity
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Proctor & Gamble’s New
Pricing Policy
Stopped price discounts on many
products
 Lowered prices
 Marketing budget reduced from 25% to
20%
 Stopped distribution coupons to
customers in many regions

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Law of Supply Chain Dynamics
The magnitude of demand volatility
a company faces
increases the farther upstream
it resides in the supply chain.
This is also called the bullwhip effect.
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Val ue
Beer Ga me Ne t Inventory
76.5779 1
61.3667 6
46.1556 2
30.9444 7
15.7333 2
0.5 2217 89
-14.6889 7
-29.9001 1
-45.1112 6
-60.3224
-75.5335 5
-90.7446 9
-105 .955 8
0
Retai ler
8.3 3333 3
16.6666 7
Who lesa ler
25
Tim e
Distri buto r
33.3333 3
41.6666 7
50
Brewery
$2885
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Value
Beer Game Orders Placed
114.592
105.0427
95.49333
85.944
76.39467
66.84533
57.296
47.74667
38.19733
28.648
19.09867
9.549333
0
0
Retailer
8.333333
16.66667
Wholes aler
25
Time
Distributor
33.33333
41.66667
50
Brewery
24
Information lag reduced to 1 week: Inventory
Val ue
Beer Ga me 1 -Lag Net Inventory
76.5779 1
61.3667 6
46.1556 2
30.9444 7
15.7333 2
0.5 2217 89
-14.6889 7
-29.9001 1
-45.1112 6
-60.3224
-75.5335 5
-90.7446 9
-105 .955 8
0
Retai ler
8.3 3333 3
16.6666 7
Who lesa ler
25
Tim e
Distri buto r
33.3333 3
41.6666 7
50
Brewery
$1773
25
Va lue
Bee r Game 2-Level Net Inventory
76 .577 91
Two Level - Inventory
61 .366 76
46 .155 62
30 .944 47
15 .733 32
0.5221 789
-14 .688 97
-29 .900 11
-45 .111 26
-60 .322 4
-75 .533 55
-90 .744 69
-10 5.95 58
0
Reta iler
8.3333 33
16 .666 67
25
Ti me
33 .333 33
41 .666 67
50
Brewery
$380
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Variants of the game

If there is no information delay?

If the final demand is random but the distribution is
common knowledge?

Minimize the cost for the system or for the individual
himself?

Are there any information sharing?

Two-level system?

…
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Web-based Beer Game

For example
– http://beergame.mit.edu
(h=0.5; p=1.0)
– http://www.masystem.com/beergame
(h=1; p=2)
– …
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How to analyze the beer game?
 Assumptions
 Models
 Control policy
• Decentralized control
• Centralized control
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Summary

What is a beer game?

How do you think about the game?

Can you model and analyze the game
mathematically?

Try to play the game on the Web
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