A Computerized Beer Game and Decision Making
Experiments
Ezgi Can Eren
Texas A&M University, Department of Industrial Engineering
Tel: 1-979-764 72 38
Email: ezgicaneren@yahoo.com
Omer Hanger
Cornell University, School of Operations Research and Industrial Engineering
Tel: 1-607-257 01 85
Email: omer@orie.cornell.edu
Mehmet Gékhan Samur
Bogazi¢i University, Department of Industrial Engineering
Tel: 90-532-706 52 09
Email: samur@boun.edu.tr
Belkis Burcu Tunakan
Cornell University, School of Operations Research and Industrial Engineering
Tel: 1-607-342 34 68
Email: burcu@orie.cornell.edu
Abstract
This paper has two goals: The first is to present a computerized version of “Beer Game’
originally developed as a board game to teach managers the principles of supply chain
management. The multiplayer interactive simulation game we develop is 100 percent
faithful to the original game, so that experimental results from the physical and
computerized environments can be safely compared. The simulation model used to
represent the game also illustrates some subtleties that a model builder must be careful
about while simulating a discrete and physical game. Secondly, the game was used as an
experimental platform and experiments were done in order to analyze game medium
(computer vs. board), demand pattern and learning effects on performances of players. One
striking result is the fact that subjects who played the board game scored significantly
better than those who played the computerized version in the same conditions.
' Supported by Bogazici University Research Fund, grant number: 02R102
1. Introduction
Beer Game is a well known example of a supply chain structure. This game was developed
originally as a board game by the System Dynamics Group of MIT Sloan School of
Management to teach principles of management science. In the game each player of a team
manages a single inventory along a supply chain through deciding on her order rate each
period. Each team consists of four players positioned as: Retailer, Wholesaler, Distributor
and Factory. Each sector of the game orders from the sector in the upstream position and
supplies goods downstream. In case of stock-outs, there are no lost sales in that backlogs
are allowed. Between each level of the supply chain there are two periods of shipping
delays and two periods of order receiving delays. For the factory, the delay between
placement of production orders and receipt of products is three periods. The team’s
objective is to minimize the total team cost, where costs are calculated cumulatively (on-
hand inventory costs are $0.50/case/week and backlog costs are $1.00/case/week). Each
player has local information but severely limited global information. Each player has
information regarding her inventory/backlog level and her orders placed, he/she is also
allowed to check the amount of goods he/she will receive in the next term. Communication
between the players is not allowed during the game to better simulate real-life cases.
The analysis of experiments with the board game reveals that the inventory and order levels
of sectors, independent of the given demand pattern, exhibit three major patterns of
behavior: Oscillations, amplifications and phase lags. These behavior patterns occur even
under very stable market conditions. °! Players recognize the fact that their own actions are
the real causes of these cyclic behavior patterns, whereas in real life most people are
inclined to attribute the causes of undesirable effects to external factors rather than the
internal system structure.
Several computerized versions of Beer Game exist, however none of them simulates the
multiplayer board game with 100 percent fidelity. For example, the computerized beer
game on the website of MIT ™! uses a different cost calculation than the one described in
the board game instructions 1 and it assumes there is a total of three periods of delays
between when a facility places an order, and when the results of that order arrive in
inventory. However in the board game, this delay is four periods. We place special
emphasis on this fidelity issue. The computer network simulation game we develop is a 100
percent exact replication of the Beer Game’s board version. This equivalence was proven in
the verification stage of the model design.
In the second part of the paper, we carry out a series of gaming experiments using the
computerized game so as to analyze the effects of game medium (computer vs. board),
demand pattern and transfer of learning (from one medium to the other) on the
performances of players.
2. Constructing the Simulation Model
The model used for the computer network simulation game was based on the model
developed by Sterman J.D. We modified the model so that order quantities became the
inputs from players. Powersim Constructor Version 2.51 was used as the simulation
software.
The model is discrete, in that all the adjustment time variables and DT is selected equal to
one; and the formulations in the model are based on discrete modeling techniques. The
basic model consists of four inventories, which are arranged along a single supply chain:
Retailer, Wholesaler, Distributor, and Factory. Orders are placed from retail end towards
manufacturing end, and goods flow in reverse direction. Each sector of this chain has a
single customer, whose orders it should satisfy, and a single supplier, which it places all of
its orders to. The same shipping and ordering delay structures exist as in the board game.
In the model the order rates of each sector were defined as constants which were replaced
by the ordering decisions of players in the game version. The order rates were rounded to
the nearest integer, since in the game version players can enter non-integer order decisions,
which would be unrealistic.
In the game, the orders given by the players at each period are the only external inputs to
the model. The shipment rates are automatically calculated, since each sector must ship all
of the requested orders from them, as long as they have sufficient inventory on hand. Below
are the critical issues we encountered while developing the model. Note that time t
corresponds to the beginning of period t+1.
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Figure 1. Part of the model used for the computerized game
Customer Demand Pattern
In the board game, customer orders have the classical pattern of 4,4,4,4,8,8,8,8,8,..., where
there is a step increase in the beginning of fifth period. Since the fifth period begins at time
4, the orders must become 8 at time 4 in order to be consistent with the original game
instructions. ©!
Output (Customer_Orders)
10-
Figure 2. Default customer demand pattern
Shipment Formulations
Shipment rates from each inventory were formulated based on a comparison of the
available supply and the requested orders from the sector under concern.
ShipRate = MIN(Incoming _ Orders + Backlog, ReceivingRate + Inventory) qd)
Incoming orders represent the orders from the sector’s own customers, which arrive in the
current period. This term is added to the accumulated backlog amount to find the total
amount of orders the sector try to satisfy. This amount is compared to the available
inventory on hand before shipping the order, which is exactly equal to Jnventory plus
ReceivingRate. In the board game, players first add the incoming shipments to their
inventory during a period and then try to satisfy the demand for the period, so the
formulation is consistent with the board game.
Verification phase and delay structure analysis
In order to verify that the model simulated the supply chain structure in the intended way,
available data from the board game were utilized for benchmarking. The inventories and
shipping delays in between -formulated as material delay structures- are basic stock-flow
formulations. However, the design of ordering delay structure is more complex. Order
receiving delays are represented by information delays in the model, where the number of
information delays necessary to reproduce exactly the same structure as that of the board
version of Beer Game was found after analyzing alternative delay structures thoroughly. To
check the consistency of the models with the board game, a game with some arbitrary
retailer orders was played on board. Then, these orders were entered as order-rate decisions
into the model and tests were run to examine the stock values; since during the board game
only the stock variables are observed. The resulting variable values were compared with the
records in the board game. Three alternative ordering-delay structures were considered. We
focused on the propagation of retailer orders only, because the delay formulations for
wholesaler and distributor orders are similar. Retailer shipments are determined by
customer orders with no delay, so no delay structure is necessary for customer orders. For
the factory, three periods of product receiving delay was obtained without any need for
information delay.
The retailer orders used for benchmarking and the corresponding wholesaler stock records
from the board game are as follows:
Time _Retail_OrderRate Wholesaler Inventory |\Wh_ ReceivingRate
i 400 12,00 400
1 10,00 12,00 400
2 800 | 12,00) 400
3 0,00 600 | 4,00
4 5,00 2,00 400
Table 1. Board game records for benchmarking
Alternative 1: Two-stock information delay structure
The formulations for the variables in this alternative are:
R_order = (Retail_OrderRate — R_Orders_Placed) / 1 (2)
R_Orders_Placed = 4 + dt*R_order (3)
W_OrderReceiptRate=(R_Orders_Placed — Wincoming_Orders) / 1 (4)
W_Incoming_Orders = 4 + dt*W_OrderReceiptRate (5)
Orde 7
R Placed “Y-Orel
% | Order's Pl
eo ee WizOrder
|_OrderRate W_GrderRate
sel ws
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Customer] Orders
Nl
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claiiey/ invertor 1oR, Del lo ShipDeley1 sates Dt rs maecaley,
one fs Ret fe «SOC WHS Wh_Stipret® J
Figure 3. Ordering-delay structure of alternative model 1
Time _JRetail OrderRatelR_ Orders Placed] Wincoming Orders |Wh_ShipRatet |Wholesaler_Inventory|DtoW_ ShipDelay2
0 4.00 4.00 4,00 4.00 12.00 4.00
1 70,00) 4,00) 4,00 4,00 12,00 4,00]
2 8,00) 70,00] 4.00 4,00 42,00 4.00)
3 0.00 8.00 70,00 10,00 42.00 4.00
4 5.00 0.00 3.00 3.00 6.00 4.00
Table 2. Orders and inventory levels of alternative model 1
The rationale behind the above structure is that two delay stocks match the two delay boxes
that exist in the board version. But simulation is needed for full verification. The Retailer
order at time | is 10 units and at time 2, this order passes to the stock “R_Orders_Placed”
and at time 3 to the “WIncoming_Orders” stock. Again at time 3, “Wh_Ship_Ratel” is 10.
However, there is a major problem due to calculation sequence of the simulation software:
This 10-unit order influences the “Wholesaler_Inventory” at time 4, i.e. the wholesaler
inventory decreases at time 4. Nevertheless, in the board game it decreases at time 3. So, in
this model there is one redundant delay structure, which results in a shift of inventory levels
by one time period.
Alternative 2: One-stock information delay structure
To address the above problem, the formulations for the variables in this alternative are:
W_OrderReceiptRate = (roundROR — Wincoming_Orders) / 1 (6)
W_Incoming_Orders = 4 + dt*W_OrderReceiptRate (7)
Note that roundROR is the nearest integer to Retail_OrderRate.
Time _|Retail_OrderRate |Wincoming Orders|Wh_ShipRate’ |Wholesaler_Inventory| Wh_ReceivingRate
0 4,00 4,00) 4,00] 12,00 4,00]
1 10,00/ 4,00] 4,00| 12,00 4,00 |
2 4 8,00! 10,00] 10,00/ 12.00 4.00)
3 0,00 | 8.00} 8.00 | 6,00 4.00 |
Table 3. Orders and inventory levels of alternative model 2
The delay problem encountered in alternative model 1 was resolved in this model by
deleting the second stock “R_Orders Placed” from the information delay structure. The
order decision made by the retailer at time t is effective on the wholesaler inventory at time
t+2, which is the case in the board game. All the stock values exactly fit to the figures in the
board game, i.e. stocks take the right values at the right time points. However, a problem
does exist in this game regarding the information available to players. The information
directly available to a board game player (except the calculations he/she makes) while
placing orders at time t are:
i) Inventory/Backlog level at time t
ii) Shipments that will have arrived at time t+1 (i.e. the next box on his/her right
in the board game)
iii) Incoming Order at time t-1, placed by the downstream player (This is the
order that the player automatically meets at time t if he has sufficient
inventory or this order increases player’s backlog)
In the above version, the player does have correct information regarding his/her
inventory/backlog level and shipments to arrive (“Wh_ReceivingRate”), whereas incoming
orders are not correctly displayed to decision-makers. The shipment rate from wholesaler
inventory (“Wh_ShipRate1”’) at time t is calculated using the orders arrived to the player at
time t (“WIncoming Orders” at t). However, this shipment will be subtracted from the
inventory at time t+1; in the board game, the player sees this order at time tt+1. So, the
value of “WIncoming Orders” at time t-1 should be displayed to the decision maker at time
t. This can be accomplished by adding an information delay structure consisting of a stock
to store the 1-period past value of “WIncoming Orders” for display purposes only, as seen
below.
Correct delay structure: One-stock information delay structure with an additional
information delay for display purposes
The formulations for the variables in the information delay structure are:
W_OrderReceiptRate = (roundROR — Wincoming_Orders) / 1 (8)
W_Incoming_Orders = 4 + dt*W_OrderReceiptRate (9)
WOrderCorrect = WIncoming_Orders — WdelOrder (10)
WDelOrder = 4 + dt*WOrderCorrect (11)
Incoming) Orders wog®rder_{
/OrderRéceiptRa WOrderCorrect cM
Retail_OrderRate
roundROR
W_OrderRate
ROrderCorrect
Réftective_Invehtory neerne Woackog — WEHTecti_inv
Customer| Orders
Backlog
OR, iow in
Wh_Ship
fate
Figure 4. Ordering-delay structure of alternative model 3
Time _ [Retail OrderRate|WiIncoming Orders| WDelOrder Wholesaler _Inventory Wh_ReceivingRate
0 4,00 4,00 4,00 12,00 4,00
1 10,00 4,00 | 4,00} 12,00} 4,00
2 8.00 10,00 | 4.00) 12,00) 4.00
$ 0,00 8.00 10,00 6.00 4.00
Table 4. Orders and inventory levels of alternative model 3
In this final version of the SC model, 1-period past value of “WIncoming_ Orders” is stored
in the stock “WDelOrder” to be displayed to the decision-maker in game version. This
information delay allows the display of the correct incoming orders to players in
Wholesaler, Distributor and Factory positions. The same problem existed for Retailer and
the same additional information delay structure was employed although customer orders are
stored in a converter instead of a stock variable. The stock “RDelOrder” takes the same
values as the variable “Customer Orders” but with a shift of one time period.
This finalized version of the Supply Chain model was selected as the appropriate design
due to the reasons listed above. This way, consistency between board game records and
computerized game records was obtained and players are provided with the correct
information at correct time points. This step completes the design and verification phases of
supply chain modeling.
The computerized game interface
The computer network simulation game is the computerized version of the board game in
which players decide on their orders for each period. Since the user interfaces are very
similar, wholesaler interface will be explained also representing the other sectors. Below is
the user interface used in the game:
a
i Revertte Bare
=
Figure 5. Wholesaler user interface
¢ Wholesaler Inventory: This box displays the current inventory at hand.
e Wholesale Backlog: This box displays the current backlog.
e Shipments to Arrive: This box displays the amount of goods to be received in the
next period. It corresponds to the “DtoW_ShipDelay2” stock in the model.
e Incoming Orders from Retailer: This box displays the orders that the retailer has
received in that period. It corresponds to the “WDelOrder” stock in the model the
use of which is already mentioned.
The following equation is valid while calculating the variables:
(Inv: — Inv +1) + (Backlog: — Backlog:)=Inc.Orderst-1— Ship. to Arrive: (12)
The graph displays the effective inventory versus time, whereas the table on the right keeps
the past inventory, backlog and orders which are variables recorded by the player in the
board game.
At the bottom of the screen the player sees the total cost of the team and his own during the
game. Also the current period of the game is displayed on the simulation screen. Simulation
time advances as all the players make their decisions.
3. Experimentation
After four sets of experiments with the board game, sixteen trials with the computerized
game were carried out in order to see if the typical behavioral patterns of oscillation,
amplification and phase lag were observed in the computerized game setting. The duration
of all of the experiments was 35 periods. The subjects were recruited from undergraduate
and graduate students. The results of the experiments were also analyzed to compare the
performances in two different mediums of the game. Table 5 gives a summary of the design
of the experiments.
version number of teams number of subjects
icomputerized|16 (4 teams with each demand pattern)| 64
board game 44 (with the first demand pattern) 16
total 20 80
Table 5. Design of experiments
The experiments in the computer medium were carried out with different customer demand
patterns to test the demand pattern effect on the performances of the groups. Another
purpose of the experimental study was to test the learning effect. Three teams played the
board game prior to playing the computerized game in order to detect any learning process
occurring during the board game trial. Conclusions were made without claiming any
statistical significance, considering the limited number of the experiments.
Board game vs. computerized game
Both the inventories and the order rates showed common behavioral patterns of oscillation,
amplification and the phase lag in both settings. (See Sterman 1989 paper for a thorough
discussion of these patterns.) Generally large amplitude fluctuations were observed in every
team (See Figure 6). One common characteristic of the results from different teams was
that the amplitude of orders increased from retailer to factory in the same team, known as
bullwhip effect (See Figure 7). An example to phase lag behavior is illustrated in Figure 8.
RETAILER WHOLESALER
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Figure 6. Order rate graphs of group
16 as an example to oscillation behavior
RETAILER WHOLESALER
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Figure 7. Order rate graphs of group 4 as an example to bullwhip effect
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Figure 8. Order rate graphs of group 7 as an example to phase lag
Another major observation regarding the comparison of the board and computerized games
was that the players performed better in the board game compared to the computerized
game. This was figured out by comparing the board game results with the computerized
game results belonging to the same demand pattern group. The variables used in the
analysis were:
Total cost of the team: This is the primary measure of the performance of the teams since
they are instructed to minimize the total cost of the team.
Minimum inventory: For each of the four parties, minimum inventory level reached during
the game was recorded. “Minimum inventory” is the minimum of those minimum
inventories.
Maximum inventory: For each of the four parties, maximum inventory level reached during
the game was recorded. “Maximum inventory” is the maximum of those maximum
inventories.
Maximum amplitude: For each of the four parties the difference between the maximum
inventory level and the minimum inventory level reached during the game was recorded.
“Maximum amplitude” is the maximum of those differences.
Computerized | Cost Min Inv | Max Inv | Max Amp
44448888
PATTERN I:
Group 1 4958.5 -37 340 344
Group 2 3,301.5 -120 89 148
Group 3 3794 -99 26 121
Group 4 1931 -55 95 138
Average 3496.25 | -77.75 137.5 187.75
Board Game
Group1 1703 -44 36 62
Group2 2590 -76 42 107
Group3 2536 -59 29 85
Group4 2484 -71 32 83
Average 2328.25 -62.5 34.75 84.25
Table 6. The data relevant to computerized game vs. board game comparison
The data used for the comparison of performances in two mediums of the game are
summarized in Table 6. The average cost generated by the players of board game was
$2328, significantly smaller than that of computerized version, $3496. This result was also
supported by the two tailed t-test for total cost values with a p-value of 0,079. Also note
that the averages of all the variables have higher magnitude for the computerized game than
the board game. T-test results regarding all the variables of analysis are summarized in
table 7.
Cost 0.079
Min Inv 0.250
Max Inv 0.117
Max Amp 0.071
Table 7. T-Test results for the computerized game vs. board game comparison
There are a couple of facts that can be argued to be the reason behind this performance
difference. First, players of computerized version were more isolated from each other
compared to the board game players. Players in the board game tended to watch their
neighbor’s inventory levels although they were told to stay isolated as much as possible.
This increased the player’s ability to keep track of the team’s overall position. Second, the
board game was played with bunches of beans which symbolized the “beer inventory”.
Hence, players physically counted the shipments and inventories. This lowered the
tendency of players to give huge orders compared to the “computerized game”, in which
they could give orders of high amounts just by dragging a slide bar. Finally, the progress of
the board game was slower than the progress of the computerized game, giving subjects
more time to think about what was going on. They were able to capture the delay effects in
the game in fewer periods.
Customer Demand Pattern Effect:
Experiments with four different customer patterns were conducted. Only the data from the
computerized game were used for customer demand pattern effect analysis.
The four different customer demand patterns are:
I-) Step-Up Customer Demand (4,4,4,4,8,8.8,8,8,8,.....): Customer demand was constant at
4 until the fifth period. At time five a sudden doubling of demand occurred without any
pre-declaration.
Il-) Step-Up-and-Down Customer Demand (4,4,4,4,12,8,8,8,8,8......): After a one-period
peak of 12 at time five followed by a step-down of four units, the demand pattern stabilized
at the upgraded level of 8.
IlI-) Step-Down Customer Demand: (8,8,8,8.4,4,4.4.4.4.4......): Customer demand remained
constant at 8, till the introduction of a step-down of four units at time 5.
IV-) Steady Customer Demand: (4.4,4,4.4.4.4.4.4.4.4......): Demand pattern was kept
constant at four with no disturbance along the game.
The results of the experiments sectioned with respect to the demand pattern applied are
summarized in Table 8.
Computerized |Cost [Min Inv |Max Inv [Max Amp
(44448888
IPATTERN I:
|Group 1 4958,5 |-37 340 344
Group 2 3.301,5 |-120 89 148
\Group 3 3794 +99 26 121
Group 4 1931-55 5 138
[Average I3496,3 +77,75 |137,5 [187,75
(4444128888
IPATTERN Il:
Group 5 3945,5 |-123 134 223
\Group 6 1770 |-45 31 69
\Group 7 3593,5 |-62 117 179
Group 8 2864 |-61 (71 113
[Average 3043,3 |+-72,75 |88,25 [146
188884444
IPATTERN Il:
Group 9 1556-41 (74 [98
Group 10 1000,5 |-36 28 50
[Group 11 783 +11 32 43
|Group 12 2792-64 125 158
[Average 1532,9 |-38 64,75 [87,25
144444444
IPATTERN IV:
|Group 13 793,513 28 37
Group 14 729 -12 28 33
Group 15 3263-40 156 145
Group 16 2259 |3 92 82
[Average 1761,1 |-15,5 {76 (74,25
Table 8. Results of computerized game experiments sectioned with respect to the
customer demand pattern
ANOVA tests were conducted to analyze the demand pattern effect on the variables. The
results are presented in tables 9-12.
[Total Cost
[ANOVA
ISS Dof _MSD F Ratio P Value
[SSPattern {11047884 3682628 B,06425063 [0,069189
ISSE 14421646 [12 1201804
ISST [25469530 |15 1697969
Replications
HM 2 3 4 [Average Sum
IPATTERNI #4958,5 3.301,5 3794 1931 I3496,25 13985
PATTERN Il 8945,5 1770 3593,5 2864 13043,25 12173
IPATTERN III 1556 1000,5 783 2792 532,875 16131,5
IPATTERN IV_|793,5 729 3263 2259 761,125 (7044,5
y..89334
ybar2458,375
SST = 25469530
SSPattern= 11047884
SSE= 14421646
Table 9. Anova results for total cost values
(Min Inventory
[ANOVA
ISS Dof MSD F Ratio P Value
ISSPattern |10471,5 3 8490,5 4,04989123 (0,033402
ISSE 10342,5|12 861,875
ISST 20814 [15 1387,6
Replications
M1 2 3 4 [Average Sum
PATTERN! |-37 -120 -99 -55 -77,75 +311
PATTERN Il +123 -45 -62 -61 +72,75 +291
PATTERN III |-41 -36 -11 -64 +38 +152
PATTERN IV }-13 -12 -40 3 -15,5 +62
y.816
ybar-51
SST= 20814
SSPattern= 10471,5
SSE= 10342,5
Table 10. Anova results for minimum inventory value
Max Inventot
[ANOVA
Iss Dof MSD F Ratio P Value
ISSPattern |12329,25 [3 A109,75 (0,6051574 0,624148
ISSE 81494,5 12 6791,208
ISST (93823,75 [15 6254,917
Replications
HM 2 3 4 [Average Sum
IPATTERNI [340 89 26 95 137,5 550
IPATTERN Il [134 31 117 71 88,25 353
IPATTERN Il |74 28 32 125 64,75 259
IPATTERN IV [28 28 156 92 76 304
y.11466
ybar91,625
SST= 93823,75
SSPattern= 12329,25
SSE= 81494,5
Table 11. Anova results for maximum inventory values
IMax Amplitude
[ANOVA
ISS Dof MSD F Ratio P Value
ISSPattern [33494,19 8 (11164,73 |2,10714075 |0,152727
SSE (63582,25 |12 298,521
ISST (97076,44 |15 6471,763
Replications
iM 2 3 4 [Average Sum
IPATTERNI [344 148 121 138 187,75 (751
PATTERN Il [223 69 179 113 146 [584
IPATTERN Ill [98 50 43 158 87,25 349
IPATTERN IV_[37 33 145 82 (74,25 [297
y.1981
ybar123,8125
SST = 97076,44
SSPattern= 33494,19
SSE= 63582,25
Table 12. Anova results for maximum amplitude values
Analyzing the order and inventory graphs of subjects from teams with different demand
patterns, it was seen that typical behavioral characteristics were observed regardless of the
demand structure (See Figures 9 and 10 for sample inventory graphs to 2 most different
demand patterns). However, using %10 significance level, demand pattern has a significant
effect on the cost and minimum inventory variables. The cost values and absolute minimum
inventory levels of demand patterns III and IV have a mean significantly smaller than those
of I and II. This may simply be caused by steady demand figure of 4 in demand patterns III
and IV instead of 8 in demand patterns I and II. The magnitude of the demand had a
significant role in determining the value of these parameters rather than changing the
behavioral pattern observed. Oscillation, amplification and phase lag are the common
characteristics observed in the inventories and order rates independent of the demand
pattern.
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Time Time
Figure 9. Inventory graphs of group 6 (demand pattern I)
RETAILER WHOLESALER
= 20 2
515 IN A g
END oe
2s MONK J ON)
3 = 2
1 4 7 10 13 16 19 22 25 28 31 34 37 i
Time
DISTRIBUTOR FACTORY
20 » 30
5 & 2 IN
= 10 = %
§ 4 Ar 7 8 io AN [
z z
a ° sw ee OE J
2 | 4 7 1013 16 1422 he 31 34 3 2 Deaton
3 -10 @ -10 1 4 7 10 13 16 19 2228 28 31 34 3)
D 20 D 29
Time
Figure 10. Inventory graphs of group 13 (demand pattern IV)
Analysis of Learning Effect
The final experimental analysis issue was existence of transfer of learning from the board
medium to the computer medium. Three teams played the board game with pattern
4,4,4,4,8,8,8,8,... prior to playing the computerized version with pattern 4,4,4,4,12,8,8....
Two groups of comparisons were done. The results of the replications in the computer
medium were compared both to the prior board game experiments conducted with the same
team and other computerized game results with the same customer demand pattern.
Playing the game on board had a positive effect on the score. Although second pattern was
slightly more difficult compared to the first, “Jearning’” subjects scored better with respect
to their previous performance in the board game, with a p-value of 0,081. Even though their
behaviors generated higher amplitude and maximum inventory levels, they were able to
reduce their minimum inventory levels ending up with lower cost values.
The /earning subjects performed better also compared to the same demand pattern results in
the computerized games (p-value: 0,039). Regarding total cost values, all of their results
were even better than the best performance achieved by the relevant demand pattern group,
which is a cost figure of 1770 (See Table 8). Table 13 shows the detailed results of these
learning subjects.
Performance of Learning Teams
Computerized (after board) Board
Demand pattern:4444(12)88 Demand pattern:44448888
Cost Min Inv_| Max Inv | Max Amp | Cost | Min Inv | Max Inv | Max Amp
Group 1 | 1570,5 -42 53 87 2536 -59 29 85
Group 2 |_ 1173 -29 56 83 1703 -44 36 62
Group 3 |_ 1564 -27 65 81 2590 -76 42 107
Table 13. Performance of “Learning Teams”
4. Conclusion and Discussions
In this study, a multiplayer interactive simulation game version of the “Beer Distribution
Game” was developed. Since conducting experiments is much easier in computerized
environment than on board, several computerized versions of Beer Game exist but none of
them is an exact replica of the board version. Having an exact replica has both scientific
and practical importance. We developed a computerized game completely faithful to the
board game. Several critical issues in this effort are emphasized. 3 alternative model
structures are analyzed and the one finally proposed not only mimics the board game, but
also presents the players exactly the same information as the board game does.
Using the game developed, several gaming experiments were conducted. Subjects were
selected from university students. Oscillation, amplification and phase lags are the common
characteristics in other studies about the Beer Game and these behavior patterns are also
observed in this study independent of the demand pattern used. Results of both the board
game and computerized game reveal that players lack the understanding of the structure
that involves higher order delays. Although they are instructed to take caution of the
accumulating supply line, they try to adjust their inventory levels by over-reacting as if no
delays exist between the placing of an order and its arrival. The high amplitudes of
inventory cycles are the result of this misconception.
Four different customer demand patterns were used in the experiments with the
computerized game and these experiments were compared in terms of total cost, minimum
inventory reached, maximum inventory reached and maximum amplitude variables. The
demand patterns have a significant effect on the total cost and minimum inventory. This
numerical difference can be attributed to the amplitude of the orders.
Players who played the board game scored significantly better than those who played the
computerized version with the same demand pattern. There are several possible reasons of
this fact. Firstly while playing the board game one touches the inventories, records the
inventory levels herself and since the game advances much more slowly than the
computerized version she has more time to think on her ordering strategy. In the
computerized game it is very easy to give very high orders, just slide the order bar, and this
generally results in high-amplitude fluctuations whereas in the board version one counts the
shipments one by one and realizes that placing too big orders like forty or fifty is not
convenient. All these are possible reasons for the significant score differences. In any case,
these differences have important implication for research and practice and must be further
investigated.
Another conclusion drawn upon the experiments is that players that first played the board
game before playing the computerized game performed significantly better than those of
who directly played the computerized game. These players also improved their own
performances in their second games. These results can be attached to the learning effect.
Finally, we have also constructed a supply network model in which each sector has more
than one supplier and more than one customer. This model can be used to figure out how
the network structure affects the amplification, phase lag and inventory oscillations.
Comparisons with respect to these criteria can be done between supply chain and supply
network structures. Another important future research direction would be to further analyze
the nature and sources of differences of players’ performances between the computerized
and board versions of the Beer Game.
References:
1] Barlas Yaman, Ozevin M.Giinhan. Analysis of stock management gaming experiments
and alternative ordering formulations” Systems Research & Behavioral Science, Vol. 21,
Issue 4, 2004, pp. 439-470.
[2] Giindiiz Baris, “Information sharing to reduce fluctuations in supply chains: a dynamic
modeling approach”, MS Thesis, Bogazici University Industrial Engineering Department,
2003.
[3] Sterman John D., “Modeling Managerial Behavior: Misperceptions of Feedback in a
Dynamic Decision Making Experiment”, Management Science, Vol. 35, No: 3, pp. 321-
339, March 1989
[4] Sterman J. D., “Teaching takes off - Flight Simulators for Management Education”,
OR/MS Today, October 1992, pp. 40-44
[5] System Dynamics Society, “Instructions for Running the Beer Distribution Game”
[6] Aybat N. Serhat, Daysal C. Sinem, Tan Burcu, Topaloglu Fulden, “Decision Making
Tests with Different Variations of the Stock Management Game”, The 23" International
Conference of the System Dynamics Society Proceedings
[7] Bayraktutar Ibrahim, Independent Study on Beer Game, Miami University, Ohio, 1991
[8] The Web Based Beer Game, The MIT Forum for Supply Chain Innovation Webpage,
http://beergame.mit.edu/guide.htm
