Supplementary files are available for this work. For more information about accessing
these files, follow the link from the Table of Contents to "Reading the Supplementary Files".
Simulations for Planning Dresdner Bank’s E-day
Jiirgen Strohhecker
Business School for Banking and Finance (HfB)
SonnemannstraBe 9-11
D-60314 Frankfurt am Main
Germany
Telephone: +49 69 154008-110
E-Mail: strohhecker@hfb.de
Confronted with the approaching introduction of euro coins and notes, Dresdner
Bank’s branches had to consider that the cash related transactions between
17" December 2001 and 28" Fe ebruary 2002 would rise much above the normal level.
On top of the regular business, they had to cope with an unknown amount of exchange
transactions of Deutschmark into euro. To avoid chaotic situations in the branches and
high extra costs, the branches had to prepare themselves and had to decide on a couple
of measures available. The paper presents how four different scenarios on customer
behaviour are developed, and how these scenarios are linked with a queuing simulation
model which was able to show the impact of different assumptions on the situation in
the branches during the changeover period. Simulation and analysis results showed that
Dresdner Bank’s branches were facing some challenges during changeover period.
Absolute chaos on broad front was however pretty unlikely.
Key Words: Euro, Queuing Simulation, Scenario Technique, Planning, Decision
Making, Bank Management
1 The challenge of introducing euro banknotes and coins on 1° January 2002
Since Ist January 2002 the euro is the official means of payment in Germany as well as
in 11 other States of the European Union. Despite a partly euro sceptical opinion of the
German people throughout 2001, the introduction of euro banknotes and coins on
1“ January 2002 was a great success (European Commission, 2002). The acceptance of
the new money was high and by the mid of January 2002 almost nobody tried to pay
with German marks anymore although they could have done until 28" February
(European Commission, 2002).1
The smoothness of the changeover period was not an obvious task. Changing all the
circulating coins and bank notes in 12 European countries at the same time was one of
the biggest challenges the organizations involved had ever faced. 14.5 billions bank
notes had to be printed — if piled up, a tower with a height of at least 1.200 km would
result. 50 billions coins had to be stroked — enough to load more than 8.000 forty-ton
lorries (Deutsche Bundesbank, 2001). Two third of this tremendous amount of money
had to be distributed to millions of bank branches, post office counters, wholesalers and
retailers, shops and agencies by 31" December 2001.2 All these actions had to be taken
1 In Germany the so-called “dual circulation period“ ran from Ist January to 28th February 2002.
2 1/3 was needed as reserve stock.
so that 300 million European could welcome the new year 2002 and the new notes and
coins simultaneously. A lot of planning and preparation was necessary for all the
organizations involved to ensure a smooth changeover process. As one of the biggest
private banks in Germany, Dresdner Bank AG started a large-scale project at the
beginning of 2000. One part of this project was to help the branches to plan some
measures suitable to cope with a great rush expected for the last days of December 2001
and the first weeks of 2002. Having delivered the euro coins and notes to the branches —
a process the European Central Bank (ECB) called frontloading and started in Germany
on 1“ September 2001 — a lot of work was done, but the most challenging part of the
changeover process for the branches was still to come.
Dresdner Bank alone had in over 800 branches 900 automatic cash safes and 1,200 cash
dispensers. All these had to be filled with euro notes in time. Approximately 2,250 cash
desks needed to be provided with euro coins. And 1.5 million euro starter kits with
coins worth 20 Deutschmark (DM) had to be distributed to customers starting on
17" December 2001. Planning all these activities was not an easy task due to a
tremendous amount of detail complexity. Uncertainties were however relatively low.
Conversely, the planning of measures for the branches revealed to be very complex. Due
to high uncertainties, lack of data and some dynamic complexity it turned out to be very
difficult to forecast the impact of the introduction of euro coins and banknotes on a
branch’s business from 17" December 2001 until 28" February 2002.
Basically it was not necessary to change DM into euro explicitly in a bank’s branch as
trade and industry had committed themselves to accept DM for everyday buying and
give euros as change (Deutsche Bundesbank, 2001). The most optimistic scenario
therefore was: nothing happens at all, same procedures and business as last year. This
idealistic view was however very unlikely to become reality. Nobody in the project team
was so optimistic to vote for the ideal scenario. Everybody thought of reasons for
customers to visit a branch, especially for older customers who are used to come to a
branch for updating their savings book. It seemed to be very unlikely that this long
established habit would suddenly change when the euro was introduced. On the
contrary, the possibility of changing DM into euro at the same time could have been
even a stronger incentive to visit a branch. Another common argument was that some
customers would remember that they still had foreign notes and coins like for example
Franc or Lira that they would not be able to spend any more. People would come into a
branch and change the money before it would be impossible to do so. A third argument
was the following: if the euro was to be quickly accepted everywhere, there could be a
lot of people who would have too much German marks left and who would not want to
spend them in shops anymore. They would then be forced to visit their bank’s branch to
get rid off them. And last but not least, some people would not be satisfied with all the
information provided through the media and would want to ask the cashier personally.
Despite all the uncertainties, the project team’s members were convinced that cash
transactions and workload in branches would rise during the changeover period.
Therefore measures had to be planned as the bank managers did not want to see long
queues, long waiting times, and a lot of angry customers. They feared a strong negative
impact on Dresdner Bank’s image and, as a consequence, a damage in future sales. On
the other hand the additional costs caused by issuing euro banknotes and coins should
have been minimized and the sale of other bank products should not have suffered from
chaos in the branches. What could be done? During the project a considerable number
of ideas and measures were collected. The following section gives a brief and systematic
overview of the suggestions.
2 Possible Actions for Dresdner Bank Branches
Contrary to the first indications, it appeared that a Dresdner Bank’s branch would have
to cope with challenges during the changeover period. Of course almost everybody
thought of opening extra cash desks or extending the opening times e.g. in the morning
or evening or over the weekend. However these kinds of actions could not be more as a
last resort. Surely they would have had an effect, but they simultaneously would have
been very expensive and really difficult to implement.
Installation of extra counters for example was likely to fail in many branches because of
missing free space in the counter hall. If there were no space restrictions, then the
automatic cash safe could have become the bottleneck. Usually one safe is able to
provide cash for two or three counters maximum. If the limit were reached, a new cash
safe would have to be installed. This, however, would have been so time consuming and
expensive, that lots of severe reasons would be needed to allow its implementation.
While it did not seem to make sense to extend the number of regular branch counters,
the installation of additional counters for special tasks, e.g. the giving out of euro starter
kits, was worth thinking about. These specialized counters with limited service offers
would be able to extend service capacity in branches where a great rush was expected.
Nevertheless, the installation and operation of specialized counters was relatively costly
as well. Therefore it seemed to be reasonable to consider other measures that were not
so cost-intensive.
Before trying to extend the capacity by installing new counters, branches should make
sure that the existing ones would always be on duty. Counters that were not normally
used had to be opened. For that, enough employees would have been made available to
prevent the counter from being closed during necessary breaks. For taking the load off
the cashiers a back office could have been installed which would have been able to do
preparatory work as well as special things such as fanning out the banknotes or handling
big payments.
Maximization of the available capacity as discussed above was one important task in
preparing Dresdner Bank’s branches for the DM-euro changeover. Trying to prevent the
customers from coming into a branch in the most critical days would have been,
however, even better. For reaching this goal the suggestion was made to address and
inform in small branches customers individually in November and December 2001
while handling their bank transactions. In large and more anonymous branches posters
could be displayed. Intensive marketing for home banking, credit or bank cards and
other cashless payment systems were discussed as promising additional measures. As
additional measure, it was also suggested to fix dates for sales talks to make time and
capacity planning easier and help to achieve the sales targets.
Customers that would come into a branch despite all the measures discussed above
should be guided as well as possible. This could be done by putting up additional
direction signs or installing an information counter or providing specialized service staff
walking around. Offering waiting customers tea or coffee as well as cakes and pastries
could help to ensure a good atmosphere. Table 1 summarises again all the measures
discussed above.
Categories | Measures Practicability | Effect on
of Measures Costs
Guiding Optimisation of direction signs simple very little
customers 7 F 7
Installation of an information counter simple medium
Service staff in the counter hall simple medium
Offering tea or coffee and cakes and pastries simple little
Reducing the | Informing and influencing customers simple little
need of
capacity Intensified marketing for home banking simple little
Intensified recommendation of cashless payment simple little
Fixed appointments simple little
Increasing Installation of a back office simple medium
capacity 7 F . a 7 F
Use additional cashiers medium-difficult | medium to high
Opening normally not used counters (incl. cashiers) | simple medium to high
Expanding opening times (incl. cashiers) medium-difficult | medium to high
Installation of special cash desks for special difficult medium to high
services (incl. employees)
Installation of additional counters (incl. automatic very difficult very high
cash safe and cashiers)
Table 1: Possible measures for a bank’s branch during the dual circulation period
Taking into account that the objectives customer satisfaction, image safeguarding and
costs minimization are pretty much incompatible, it was necessary to select carefully
which measure was appropriate for which branch. The prerequisite for a rational
decision however was information on the expected seriousness of the situation between
17" December 2001 and 28" February 2002. The estimations available, however,
seemed to be of low reliability and certainty. Therefore the project team decided to
gather additional information and use simulation models for improved forecasts.
Especially two areas for further information improvement were identified:
e On the one hand, information should be made available on the actual use of cash
transaction capacity and on additional resources that could be used.
e¢ On the other hand, scenarios should be developed showing when how many
customers will probably come to a branch and try to change cash — in addition to
the normal business.
To make the additional information available Dresdner Bank’s accounting database was
queried and two simulation models were developed. The first simulation model
supported the development of the scenarios of customer behaviour (see following
section 3). Based on these scenarios the second simulation model — a queuing
simulation model — was used to determine on a day-by-day basis the consequences for a
specific branch (see sections 4 and 5). Variables of interest were for example the
percentage of capacity used, the length of the waiting line, or the amount of critical days
i.e. days with high overload. For each branch a report was created that brought the
different pieces of information together and served as a basis for improved decision
making.
3 Scenarios of Customer Behaviour
To deal with uncertainties connected with the forecast of customer behaviour the project
team decided to work with four different scenarios:
¢ Scenario A was based on the idealistic, but unrealistic assumption that no change
compared with the previous year will occur. Although everybody believed
scenario A to be completely improbable to happen, it was important as a starting
point for the development of the other scenarios (B to D).
¢ Scenario B was regarded as being optimistic.
¢ Scenario C assumed that several problems would occur.
e Scenario D was the worst-case scenario where almost everything would go wrong.
With these four scenarios the uncertainty about the future development was not hidden
but structured and therefore for all people involved less frightening (Ringland, 1998).
Because it was necessary to support the decision on the appropriate measures for each
Dresdner Bank’s branch individually, branch specific scenarios also had to be
developed. Considering the fact, that Dresdner Bank had over 800 branches in Germany,
it was clear, that this could not be done manually. Automated routines had therefore to
be developed to specify the scenarios.
Basis for scenario A were the actual cash transaction data collected between
18" December 2000 and 23 February 2001. The number of transactions was counted
on a daily basis for three customer groups separately: private customers (PK), corporate
customers (FI) and small enterprises (GE). Additionally eight transactions types were
distinguished:
e KKEZ: current account pay in
e KKAZ: current account pay out
e SPEZ: savings account book pay in
¢ SPAZ: savings account book pay out
¢ SPN: updated print of a savings account book
¢ SOAK: buying foreign currencies
¢ SOVK: selling foreign currencies
e HGA: hand over of packed coins
The reason for the disaggregation of the cash transactions was the belief that there were
significant differences in the transaction times between the categories.? The result of the
data collection effort is illustrated in Figure 1. It shows as an example a very small part
of the whole picture: the amount of a branch’s cash transactions during one single day
(arbitrarily chosen from December 2000).
4 Although the differences in the transaction times later actually turned out to be significantly different,
the impact on the weighted aggregated distribution of transaction times was quite small (see Figure 14 on
p. 16). The disaggregation nevertheless proved to be useful because of its ability to increase the project
team members’ confidence in the model.
y mGE
100 y Fl
aPkK
2 80
S
g 60
2 40
5
F 20
0
R RF GF GS S$ 8 8 &
No oR N 8 = FB R
Figure 1: A branch’s transaction dataset for a single day
To create Scenario A the data collected from 8" December 2000 to 23" February 2001
was then mapped to the changeover period. For example, the number of transactions
during Monday, 18" December 2001, was equated with the data from Monday,
17" December 2000. Besides that, estimations for two transaction types that were not
documented in the IT systems, had to be added. The one transaction type concerned was
direct exchange i.e. the customer gives the cashier 50 DM and gets back 25,56 €; the
other type was the customer’s wish to have access to his safe-deposit box.4
Scenario A was — as already pointed out — believed to be unrealistic. It was however
very important to give the experts the possibility to validate the queuing simulation
model by comparing the output with their last year’s experience. And it also was the
starting point for the development of the scenarios B to D. B, C, and D changed -
compared with A - the following parameters:
¢ the cumulated number of cash transactions between 17 December 2001 and
28" February 2002
e the distribution of the cash transactions over the changeover period
e the composition of the transactions regarding customer groups and transaction
types
A euro specific new task for the cashiers without any equivalent in 2000/2001 was the
distribution of the starter kits.5 All in all, Dresdner Bank’s branches had to find a taker
for 1.5 millions of such kits. Because everybody in the project team was convinced that
customers demand would be large enough to sell them without great problems, no
differentiation between the scenarios was made. Therefore all scenarios had the same
distribution of the transactions over time assuming that the starter kits would be sold out
by end of December 2001 (see Figure 2).
4 Abbreviations for the additional transaction types: KSF = transactions involving customer needs to go to
their safe-deposit box; ZZW = direct change of marks into euro.
5 Abbreviation: SK = selling euro starter kits.
®
3
3
@ 20%
2
£ 15% 4
g
3
5 10% 4
©
S
£ 5% |
5
2
& 0% 4
\ “ N “ \ \ fh Ag
_) \) \) S _) \) \) S
“ “ “
S ) S)
LF FF SH
S LP PP PH & MW PH
Figure 2: Distribution of euro starter kits sales
While it seemed to be relatively easy to plan the additional workload caused by the sale
of euro starter kits, it was far more difficult to predict customers’ behaviour in January
and February 2002. In a brainstorming session held in October 2000 a broad range of
factors were identified that were thought to be able to influence the customers’ wishes
and needs to come to a Dresdner Bank’s branch. Figure 3 shows the result of the
brainstorming as a policy function diagram (Morecroft, 1994).
Amount of Money
Hoarded by People Holiday Plans
Peoples‘ State
of Knowledge about the
Changeover Process
DM-€-Change
in Foreign Countries
Customers‘
Desire to Change
DM into €ina
Bank Branch
Sub-Frontloading
of Sales Outlets Technical Problems
with Cash Dispensers
Weather
Technical Problems
End of the Dual with Vending Machines
Circulation Period Curiosity
about the €
Figure 3: Policy function diagram for the peoples’ desire to change DM into euro
Most of the factors depicted in Figure 3 were seen as exogenous inputs, what in a
System Dynamics terminology means, that they are not part of feedback loops.
(Forrester, 1961). Nevertheless they were believed to have a more or less strong effect
on the exchange dynamics. Quantification, however, turned out to be quite difficult and
the team members mental models were not fully congruent. Therefore a small
simulation model of the generic exchange process was built to get a rough idea of the
dynamics. Figure 4 shows the main stocks and flows as well as the main feedback loops.
Probability to Receive
Number of Transactions DM Instead of € as
in an Hour —— “a Change
Customers Receiving or Finding DM + Probability of Finding
Number of DM Cash at Home
Customers per ”
Branch R1 BS
DM Reappearence
Never Ending Story
Customers Having (Customers Having}
DM Cash € Cash
Customers Changing
pM into € Available Transaction
+o ¥. é Capacity
Curiosity DM er, Customer -
‘ wa Capacity
+ Customers ey
to Change aa
Average
B2 Ee Waiting Transaction Time
Time per Customer
Customers’
Willingness Avoiding Queues
eo
toWait -
oe a Perceived and ra
Communicated Average
Waiting Time
Figure 4: Model supporting scenario development®
The balancing feedback loop B1 describes the basic exchange process. Customers
having DM coins and notes become willing to change their cash into euros, go to their
branch and perform the transaction moving themselves into the stock of customers that
have only euro coins and notes left. This basic loop — named “DM Withdrawal" — was
supposed to dominate at least in the long run. Finally, the values for all involved
variables would be zero by nature as with the end of the dual circulation period, DM
would not be accepted as a means of payment anymore. However, some limiting factors
and loops had to be considered. Limited customer servicing capacity is on the one hand
able to constrain the flow of customers changing DM into euro.” The resulting queues
on the other hand bring the avoiding-queues loop (B2) into life.
However, the model’s main idea was to take into consideration that the process of
changing DM into euro was not irreversible: Customers were thought to receive or find
DM coins and notes once more after having been in a branch and changed their DM
cash into euro. Consequently Figure 4 shows a backflow of customers finding or
receiving DM to the stock of customers having DM cash.8 This backflow creates a
positive feedback (R1) loop that is marked with thick arrows in Figure 4 and labelled
6 For further information on the meaning of the symbols and the modeling approach used in Figure 4 refer
to Sterman (2000).
7 The rate equation uses the MIN-function to express this limitation: Customers Changing DM into € =
MIN (Customers Willing to Change , Customer Servicing Capacity).
8 The equation is: Customers Receiving or Finding DM = Customers Having € Cash * Number of
Transactions in an Hour * Probability to Receive DM Instead of € as Change + Customers Having € Cash
* Probability of Finding DM Cash at Home
“Never Ending Story”. There was no lack of reasons why this could have happened. In
the brainstorming meeting for example were the following arguments listed:
¢ problems with the frontloading (branches) and sub-frontloading (shops)
e badly informed small businesses
© temporary rejection of the euro through the people
e technical problems with vending machines
e technical problems with cash dispensers
The base run portrayed in Figure 5 was generated using the parameter values listed in
Table 3 and displayed in Figure 30 in appendix A.
2,000
1,000
0 6 12 18 24 30 36 42
Day
Customers Having DM Cash : BaseRun ———*+——+—+—+—_ Customer
Customers Having € Cash : BaseRun ———2-—2-22-2-_ Customer
80
40
0 ‘ A
0 6 12 18 24 30 36 42
Day
Customers Changing DM into € : BaseRun —*——*+—+—__ Customer/Hour
Customers Willing to Change : BaseRun -2——2—2——_ Customer/Hour
Figure 5: Base run dynamics
The base run dynamics during the first 18 days are determined by the balancing
feedback loop B1 dominating in these days; the more customers however have changed
all their DM coins and notes into euro, the weaker becomes BI and the more the
reinforcing loop R1 comes into action. After some 18 days, a temporary equilibrium is
reached — unfortunately far away from the desired one with all DM coins and notes
withdrawn from circulation. The final state, in which everybody use exclusively euro
cash, is only achieved at the end of the dual circulation period where DM acceptance
draws to an end. DM coins and notes eventually become useless for people and have to
be changed, which causes once more higher workload than normal in the branches
during the last days of February.
° The backflow of customers into the level “Customers Having DM Cash” introduces not only the
reinforcing feedback loop R1, but at the same time the balancing feedback loop B3.
The lower time chart of Figure 5 shows the effect of limiting customer servicing
capacity. In the very first day more customers want to change their cash than could be
serviced. Queues are certain to occur during this first day. Because of the short time
period with overstrained capacity, however, the “Avoiding Queues” loop is weak.
Running some simulations with varying probabilities that customers receive DM instead
of € as change when shopping confirmed the assumption that the “Never Ending Story”
loop could highly endanger the whole changeover process. The line marked 2 in Figure
6 shows what everybody in the team feared: high workload for the cashiers throughout
the changeover period with peaks at the beginning and at the end.
75
50
25
0 ——- rs $
0 6 12 18 24 30 36 42
Day
Customers Changing DM into € : BaseRun —*——*+—+—__ Customer/Hour
Customers Changing DM into € : PConstHigh —-2——-2—2—_ Customer/Hour
Customers Changing DM into € : PConstZero —-*———3_ Customer/Hour
Figure 6: Impact of variations in the probability of receiving DM instead of euro
The other variable that turned out to be highly sensitive was curiosity. In absence of
curiosity — an only theoretical scenario — it was assumed that the customers would come
equally distributed into the branch to change their cash. As shown in Figure 7 this
behaviour however would result in increasing workload with a peak at the end of the
dual circulation period due to the never ending story loop. On the other hand the higher
curiosity was assumed to be at the beginning, the more customers would come to the
bank’s branches in the first few days of 2002 causing a period of permanent rush.
75
50
25
0 at
0 6 12 18 24 30 36 42
Day
Customers Changing DM into € : BaseRun —*——+—+——_ Customer/Hour
Customers Changing DM into € : HighCuriosity —~—2-——2—-_ Customer/Hour
Customers Changing DM into € : NoCuriosity —-*--—-s8_ Customer/Hour
Figure 7: Impact of variations in curiosity
Because not all the factors that were identified in the brainstorming session (shown in
Figure 3) had been included in the model, the scenarios of customer behaviour were not
directly based upon the simulation output. Instead, a group of experts was asked to give
their estimations having to their disposition a description of the three scenario
environments and the simulation results. What they had to estimate was firstly the
percentage of cumulated transactions on top of 2001’s numbers, secondly the
distribution of theses additional transactions over the two-month time span and thirdly
the probability for a scenario becoming reality. The following scenario descriptions
were given to the experts, each of them representing a specific setting of factors found
in the brainstorming session.
e In scenario B very little problems will occur in all the areas relevant for putting
euro banknotes and coins into circulation. The sub-frontloading will be widely
used and well-done and therefore big shops as well as small shops will have
enough euro cash for change. The cash-transporting companies will be well
prepared and able to cope with the challenges imposed to them. Consequently
supplying the bank branches and shops with euro will take place without
significant problems and removing the DM cash will be done just as easily. As a
result the probability that customers would receive DM after having got rid off all
their coins and notes will be very low. The public will be well informed and
understand that it will be no problem to pay with DM in January and February.
ECB, Bundesbank, government and all public and private banks will have made a
lot of publicity about the new currency with the result that the euro will be well
accepted by the people and everybody will be pretty curious about the new coins
and notes. Besides that, the advertising campaigns during 2001, to reduce the
amount of money hoarded by private individuals, will be successful as well. The
amount of DM coins and notes that will have to be changed will therefore be
relatively low. Even for the DM circulating abroad, hardly anything will flow back
to Germany, as numerous places to change the money will have been installed. All
cashless payment systems will work smoothly, so there will be no need to pay by
cash. Hardly any problems will occur with the other technical systems i.e. cash
dispensers, vending machines etc.
e In scenario C several difficulties will occur. However, these problems will not be
really serious. As a result of too much bureaucracy sub-frontloading will be well
accepted only by large shops and trade companies with a network of branches. A
significant percentage of small and medium stores therefore will try to collect
their euro cash change at the bank’s branches just when they will need it (that is
1° or 2"! January 2002). The probability to get once more DM cash will be
consequently higher. Furthermore, the public is assumed to be less well informed,
more sceptical and more interested in personal information through bank clerks.
¢ Scenario D is the worst-case scenario. Problems will arise all along the line.
Compared to C the sub-frontloading will be even worse. A lot of stores will not
have enough euro cash and therefore will be forced to give DM coins and notes as
change. The situation will be even made worse by the people that will be badly
informed. A feeling of insecurity and anxiety will be wide spread. Furthermore,
the advertising campaigns during 2001 to reduce the amount of money hoarded by
private individuals will be an almost complete failure. Customers will bring huge
amounts of coins to the branches in January and February 2002. The haulage firms
will be overstressed and badly performing their tasks due to some spectacular
robberies precautions, which will slow down all the processes and increase the
bottlenecks.
Final estimation of the scenario parameters was done in a workshop in April 2001.
Although each expert had of course his own opinion, the discussion ended with a
consensus. The joint estimation was:
1. Plus 40 % in cumulated transaction for scenario B, plus 60 % for scenario C and
plus 150 % for scenario D (seen in relation to scenario A).
2. A distribution of the additional transactions over the two-month time span as
shown in Figure 8.
3. A probability of 45 % that scenarios B or C will become reality and a probability
of only 10 % for scenario D.
9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
—e— Szenario B
—— Szenario C
—s— Szenario D
02.01.02
07.01.02
10.01.02
15.01.02
18.01.02
23.01.02
28.01.02
31.01.02
05.02.02
08.02.02
12.02.02
18.02.02
21.02.02
26.02.02
01.03.02
Figure 8: Distribution of additional transactions during the changeover period
Another workshop was used to discuss changes in the mixture of transactions due to the
specific needs of customers during the exchange period. In this workshop was, among
others, for example the following argument discussed. Because 12 national currencies
would vanish the need for changing Deutschmark into foreign currencies should go
down. As a result the percentage of this transaction type had to be reduced for scenarios
B, C and D compared with scenario A. This kind of analysis and estimation was done
much more deeply. However, because of only relatively small differences in the
transaction time distributions for the 12 transaction types, it later turned out, that the
effect of changes in the transaction mixture had very little impact on the simulation
results. Therefore it does not seem to make sense to go here further into detail.
The result of the scenario development was ultimately an hypothesis, which defined
when and how many additional transactions will be required by customers in a specific
bank branch during the changeover period. Figure 9 and Figure 10 give an example for
the private customer’s transaction mix for two different days.
120 mw Additional transactions in
scenario B
100.
B Basis (Scenario A)
KKEZ KKAZ SPEZ SPAZ SPN SOAK SOVK HGA KSF ZZW SK
Figure 9: Private Customers’ transaction mixture for a day end of December
450 w Additional transactions in _|
400 scenario B
350 @ Basis (SCenario A)
300
250
200.
150.
100.
50
0.
KKEZ KKAZ SPEZ SPAZ SPN SOAK SOVK HGA KSF ZZW SK
Figure 10: Private Customers transaction mixture for a day in early January
To show the consequences of each of the four scenarios, the queuing simulation model
described in the next section was used.
4 The Queuing Simulation Model for Dresdner Bank’s Branches
The cashier’s regular business in a bank branch was not hard to describe and also
relatively easy to model. Figure 11 illustrates the processes.
During the business hours customers enter the branch if they need to perform a
transaction. They come into the counter hall that serves as waiting room and provides an
overview over the counters availability. If all the counters are occupied, customers
usually join the waiting line and wait until it is their turn. If a counter is or becomes
available the customer steps in and asks the cashier for performing the intended
transaction. When the service is finished, which might take a short or long time
depending on the type of transaction, the customer steps back and leaves the branch.
Branch
Se @e
&
Se e
Potential Customers
Figure 11: Business processes related to cash transactions in a bank’s branch
Translating Figure 11 and the description given above in a system dynamics stock and
flow diagram leads to Figure 12. The stock ‘Potential customers of the branch’ is
initialised with the estimated amount of customers who want to come to a branch on a
specific day for carrying out at least one cash transaction. This initial value is derived
from one of the scenarios A to D described in section 3.
Potential Customers Customer ata
customers of waiting in
the branch counter hall counter
Customers rane walking Customer leaving a
entering the toa ae counter
branch “4
Initial value for as
i Transaction time
customers of Ne
the branch
<Branch open>
Probability distribution
conn "Sea for transaction time
open> ready>
Figure 12: Stock and flow diagram of cash transaction processes in a bank’s branch
The stock ‘Potential customers of the branch’ is decreased by an outflow — customers
that enter the branch. Entries are modelled as a random variable, the distribution of
which can be set by a lookup table. The project team decided though, that for all initial
simulations of the four scenarios the distribution is assumed to be uniform. The reason
for this simplification was that a tremendous amount of work would have to be carried
out to determine the real distribution for each branch and workday individually. The
branch manager however was offered the possibility to order new simulations by
providing more realistic data if he was not satisfied with the assumption of a uniform
distribution.
After having entered the branch, customers are waiting in the counter hall forming a
queuing line until a counter becomes available for them. Therefore not an ordinary level
but Vensim’s QUEUE FIFO level was used in the model to represent the customers
waiting in the counter hall (Vensim Reference Manual, 2000). The service process at the
branch’s counters has very discrete characteristics: only one customer can be served at
one counter at the same time and the counter is occupied as long as the customer is
being served. To model this structure adequately a subscript variable ‘Counter’ was
introduced and subscripts were used for the variables ‘Customers walking to a counter’,
“Customers at a counter’ and ‘Customers leaving a counter’. Structurally this means that
there is an array of flows draining the level ‘Customers waiting in counter hall’ and each
flow is feeding a separate level representing the customers being served at the different
counters (see Figure 13). Due to the discrete characteristic of the structure all the
subscripted variables can have either the value 0 or 1.
ivew 4 TZ
Customers x Customers ze =a)
waitin
in counter: hall fas atcounter| [7 ay
Customer Customer leaving
walking counter 1
to counter 1
Figure 13: What subscripting means structurally
To allocate the counters available to the waiting customers, Vensim’s ALLOCATE
INTEGER function is used (Vensim Reference Manual, 2000). This function guarantees
that exactly one customer is walking to a counter if it becomes available. How long a
customer stays at a counter is determined by the transaction time. The customer is not
leaving the counter until his transaction is finished. Due to the discrete perspective
chosen the customers leaving a counter are modelled using Vensim’s fixed delay
function DELAY MATERIAL. Delay time is set equal to transaction time that may vary
depending on the type of transaction and the group the customer belongs to. Therefore
transaction time is again modelled as a random variable. As in the case of customers’
entries the probability distribution of the transaction time can be set using a lookup table
(Vensim Reference Manual, 2000).
To parameterise the model for some demo simulations the following data of a randomly
selected Dresdner Bank’s branch are used.
¢ Opening hours: 8.30AM to 12.30 PM and 2 PM to 5 PM
e¢ Number of counters open: 2
e Equal priority for both counters (necessary for allocation)
e Initial values for potential customers of the branch: 137 for scenario A, 198 for
scenario B, 222 for scenario C and 330 for scenario D. These values are computed
from the scenario data of one day as shown in Table 2.
¢ A uniform distribution for the random variable ‘Customers entering a branch’
¢ Scenario specific distributions for the random variable ‘Transaction time’ as
shown in Figure 14.
Sc. CG* |KKEZ KKAZ SPEZ SPAZ_ SPNSOAK SOVK HGA KSF ZZW_ SK| 51 22
A FI 11 3 1 0 0 (0) 0 1 1 9 0} 26
A GE 10 4 1 0 0 0 1) 1 1 8 0} 25
A PK 15 28 5 12 14 3 3 1 1 4 0} 86137
B FI 15 4 1 0 0 (0) (0) 1 1 13 0 35
B GE 13 5 1 0 0 i) 0 1 1 12 0} 33
B PK 24 38 6 16 21 5 3 4 1 6 9g} 130 198
c FI 16 5 1 0 0 0 0 1 1 15 0} 39
c GE 15 6 1 0 i) i) 0 1 1 16 0} 40
c PK 27 48 6 18 17 5 3 1 1 8 9} 143 222
D FI 27 8 1 0 0 (0) 0 1 1 26 0} 64
D GE 24 10 1 0 i) i) 0 1 1 23 0} 60
D PK 38 81 5 25 18 9 6 1 1 13 9] 206 330
customer group
Table 2: One day’s transaction profile of a randomly selected branch
The probability distributions for the random variable ‘Transaction time’ shown in
Figure 14 are the result of an aggregation process. The starting points of the aggregation
are the distributions of transaction time for each customer group and transaction type.
These 33 distributions (11 types of transaction and 3 customer groups) were estimated
based on available data and the experience of cashiers. Figure 15 shows for example
two curves for the transaction types KKEZ, ZZW, and SK for private customers. To get
the weighted and aggregated curves shown in Figure 14, the numbers in the matrix of
Table 2 have to be first expressed as percentages and then the resulting matrix has to be
multiplied with the matrix lying behind Figure 15. Because the mixture of transaction in
a branch varies from day to day, the distribution for the random variable transaction
time is valid only for one single day and has therefore to be recomputed every day.
50%
Se. A
—Scen.
40% ——Scen. C []
—Scen. D
2 30% |
ee}
o
a2
g 20% / ia
10%
. oo
05115225 335 445 555 665 775 8 85 9 95 10
transaction time [minute]
Figure 14: Scenario specific distributions for the variable ‘Transaction time’
30.0%
= ZQWIsk _|
—4—KKEZ
25.0%
20.0%
ity
15.0% +
10.0%
son | 7
0.0% oral
05 115 2 25 3 35 4 45 5 55 6 65 7 7.5
transaction time [minutes]
probabil
Figure 15: Probability distribution for two types of transaction (private customers)
The Figures 16 to 19 show the results of the simulation when the model is initialised
with the parameters for scenario A and simulated once with one random sample for each
of the two random variables.
As it should be customers are entering the branch pretty equally distributed over the
opening hours (Figure 16).
|
til
9 10 1 12 13 14 15 16 17 18
Time
°
J
Because the number of customers wanting to do transactions in the branch is relatively
low, no bottleneck occurs. Figure 17 shows that at no point in time two or more
customers have to wait in the branch simultaneously. All the customers entering the
branch could be served immediately.
1 ih |
LT
8 9 10 1 12 13 14 15 16 17 18
Time
Figure 16: Customers entering the branch
Figure 17: Customers waiting in counter hall
Figure 18 demonstrates that there are only very few situations during the day when the
second counter is needed for serving customers. It is then not astonishing that the
average service capacity of the two counters is used only up to about 50 % (Figure 19).
2
8 9 10 1 12 13 14 15 16 17 18
Time
Figure 18: Customers being served
0.6
0.45
0.3
8 9 10 11 12 13 14 15 16 17 18
Time
Figure 19: Average service capacity of counters used
To get an idea of the two random variables’ impact on model behaviour, a sensitivity
simulation is done. The only parameter changed is the random number seed variable that
is needed to initialise the random number generator. Using 500 different random se-
quences as input for the variables ‘Customers entering a branch’ and ‘Transaction time’
the behaviour over time of the variable ‘Average service capacity of counters used’
varies as shown in Figure 20. The results came up to the project team’s expectations.
Average service capacity of counters used 50% 75 05% 1007
0.8
0.6
0.4
0.2
°3 30 18.00
Time
Figure 20: Sensitivity graph as illustration of the influence of the random variables!
But how will the branch’s situation be when a bottleneck occurs? To answer this
question the model is run with the parameter input for scenario D. Customers are now
entering the branch in rapid succession, and very soon, huge queues develop. Figure 21
shows that by the time the branch is closing for lunch break, 50 customers are waiting in
the counter hall. It takes the whole lunch break to serve them and to empty the branch.
The situation during the afternoon is not much better. %4 of an hour overtime has to be
done to fulfil the customers’ demand for cash transactions.
10 The simulations results are displayed as confidence bounds. These are computed at each point in time
by ordering and sampling all the simulation runs. Thus, for example, for a confidence bound of 50 %
(yellow in Figure 20), 1/4 of the runs will have a value bigger than the top of the confidence bound and
1/4 will have a value lower than the bottom.
60
40
20
8 9 10 11 12 13 14 15 16 17 18
Time
Figure 21: Customers waiting in counter hall in scenario D
One might argue that no customer will be willing to wait for almost 1% hours to get
some notes and coins changed. Therefore two further outflows from the level
“Customers waiting in counter hall’ were added to the model (Figure 22). Some
customers might be willing to come back to the branch sometime later that day. These
customers flow back into the stock of potential customers of the branch. Others might
not be willing to make once more an attempt to perform the desired transaction. Perhaps
these customers will try to change their money some other day, or they may never come
back again — for the one day’s time horizon of the model, they flow beyond the
boundaries of the model.
Percentage of customers
leaving counter hall without 4
beeing served
A 7
Customers leaving
counter hall without
é a”
beeing sened Customers not willing Average waiting
“——* to come back later time
+ Probability
Percentage of distribution for
customers wiling 4 Customers willing to come transaction time
tocome back —» back later that day
later that day
Transaction time
Potential Customers
nba Customer at a
pues Pe = ain an
Customers Customer Customer
ae entering the walking to a ] leaving a
Initial value for branch counter + . counter
potential t + *_Counter free
customers of <Branch open>
the branch <Counter open> —<Counter ready>
Figure 22: Stock and flow diagram of the enhanced queue simulation model
Due to the structural enhancement of the model, two more parameters had to be
estimated: the percentage of customers willing to come back later that day and the
customers’ willingness to wait in counter hall. The values for both parameters were first
estimated by the project team and then discussed again in a workshop with experts. As a
result the percentage of customers willing to come back later that day was estimated to
be 4. And the curve shown in Figure 23 was accepted as input for the lookup table
function relating the percentage of customers leaving the counter hall to the average
perceived waiting time. In words Figure 23 means, that 95 % of the customers accept a
waiting time of 2 minutes, 10 % of 5 minutes and so on. Everybody however would
leave the branch, if the perceived waiting time was more than 14 minutes.
100% oo
80%
60%
40% a
20%
0% |__.—__*
0 2 4 6 8 10 12 14
Customers leaving the branch due to percieved waiting time [minutes]
Figure 23: Customer’s willingness to wait in a branch
The structural changes described above lead to a different behaviour of the model. As
indicated by Figure 24 the queues are dramatically reduced. The reason however is not
better service and more capacity, but customers leaving the counter hall because of long
waiting lines. Due to this behaviour there is a tremendous difference in the number of
customers served comparing the two model’s outputs as shown in Figure 25.
8
6
4
2
0
8 9 10 1 12 13 14 15 16 17 18
Time
Figure 24: Customers waiting in counter hall in scenario D (enhanced model)
400
300
first model
enhanced model
8 9 10 1 12 13 14 15 16 17 18
Time
Figure 25: Comparison of the cumulated number of customers served in scenario D
The queuing simulation models were together with their assumptions, simplifications,
and results presented and discussed several times during the project. Several validation
tests were carried out (Sterman, 2000). Finally, everybody involved in the process was
convinced that the structure as well as the behaviour of the models looked reasonable
and appropriate to support the decisions outlined in section 2.
Because the model described above was suited to simulate one day of one Dresdner
Bank branch, 50 simulations were necessary to cover the whole changeover period for
one branch from 17" December 2001 to 28" February 2002. To gain one branch’s
results for all four scenarios A to D, 200 simulations had to be performed. All in all
about 160,000 simulations had to be carried out to provide all the 800 Dresdner Bank
branches with simulation based decision support information.
Each one of these 160,000 simulations had to be initialised with its own specific set of
parameters stored in a large Microsoft Access database. To obtain direct access to this
database and to manage this substantial amount of simulations, a user interface was
programmed using Delphi and the model was rewritten in Object Pascal. The model was
again validated and finally, around Easter 2001, the simulation program could start.
5 Simulation and Simulation Output
Because of the stochastic elements in the model, one simulation per day and per branch
was not sufficient. A single simulation of a stochastic model is no more than a kind of
behaviour snapshot based on only one sequence of random numbers (Pidd, 1998).
Decisions that are taken based upon such a snapshot are pretty likely to be wrong. The
reason why they are likely to be wrong is that no distinction is made between the effects
of the sampling variation and those of the system configuration (Pidd, 1998). For more
valid insights in the system’s behaviour, the distribution of the output variables has to
be determined and closely observed. To gain this information, a stochastic simulation
model has to be simulated repeatedly — how often depends on the precision of the results
wished (Steinhausen, 1994). Based on some tests and making a compromise between
precision and simulation time, in this case 50 repetitions were considered necessary.
Nevertheless, at least 8 million simulations were required to provide all the output data
compulsory for decision support. Estimated simulation time on 800 MHz Pentium III
computers was all in all about 800 hours. Using a computer pool of 15 machines, the
simulations were done over two weekends.
To judge whether the situation in a specific Dresdner Bank’s branch was critical or not,
the project team decided to make the following information available:
e Cumulated transactions successfully performed
¢ Cumulated transactions that could not have been fulfilled
¢ Cumulated service minutes done
e Average waiting time per customer
¢ Maximum length of queue in counter hall
Using the information given above, a service index was additionally computed
according to the following equation:
cumulated transactions performed
cumulated transactions wanted by customers
service index =
So, the service index measures a branch’s ability to serve its customers. Another
interesting information could be derived, the counter capacity used. It could be
computed as follows:
cumulated servide minutes done ,
‘opening minutes * counters
counter capacity used =
For each branch an eight pages report was designed showing the relevant parameters,
the simulation results for all the scenarios A to D, and a quick overview over the
branch’s situation. This report was printed in a pdf document and distributed to the
seven regional project teams in the middle of the year 2001. Members of these seven
teams had the job to distribute the reports to the single branches and to discuss the
simulation output and the measures that should be taken with them. To train the member
of the regional project teams a regular project meeting and a workshop was used.
Additionally a hot line was installed to provide support in the case of questions and the
possibility to request for specific simulations based on different assumptions.
In addition to the branch-specific reports and more addressed to the euro 2002 project
central office and the board of directors a rough clustering of Dresdner Bank branches
was elaborated. Looking through the reports, three types of branches could be identified:
e Type | branches showed no bottlenecks even in scenario D. They were completely
uncritical. The counter capacity used was permanently below 50%, average
waiting time per customer is low and the maximum queue length in the counter
hall is short (Figure 26). Special cost-intensive measures for branches of type 1
therefore were regarded as unnecessary.
100% 100
90% counter capacity used —---— 90
80% + miongest queue 180 @
3 s
2 70% 70 I
$ 2a
2 60% 6028
3 2
B 50% fLs0Z5
§ 38
& 40% 40 2s
S =.
2 30% 30° «8
° £
20% 20 2
10% 40
0% 0
17/12/01
20/12/01
27/12/01
14/01/02
17/01/02
22/01/02
25/01/02
30/01/02
04/02/02
07/02/02
12/02/02
15/02/02
20/02/02
25/02/02
28/02/02
ay
ge
ss
35
28
Figure 26: Type 1 branch (= uncritical)
e Branches of type 2 were faced with several days of great rush throughout the
scenarios B to D. Especially at the beginning of January and at the end of February
counter capacity used
counter capacity used
2002 the counter capacity was highly used. The results were long queues and a lot
of customers leaving the branches without being served (Figure 27). So, a
combination of several, not too cost-intensive measures were thought to be
sufficient for type 2 branches.
Type 3 branches were facing severe difficulties during the period where euro coins
and notes were put into circulation. Figure 28 shows that cashiers had almost no
time for recovery throughout the whole changeover period. Overstrained
employees were the rule. For this type of branch the euro introduction was feared
to cause chaos. Therefore it was regarded as absolutely necessary to prepare an
action plan to cope with the challenges.
100% 100
90% + counter capacity used
80%
70%
60%
50%
40%
30%
20%
10%
0%
miongest queue
a
o
longest queue
[number of cash transactions]
ses
aaa
rES&
Sak
04/01/02
09/01/02
14/01/02
17/01/02
22/01/02
25/01/02
30/01/02
04/02/02
07/02/02
12/02/02
15/02/02
20/02/02
25/02/02
28/02/02
Figure 27: Type 2 branch (= some really critical days)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
longest queue
[number of cash transactions]
17/12/01
20/12/01
27/12/01
04/01/02
09/01/02
14/01/02
17/01/02
22/01/02
25/01/02
30/01/02
04/02/02
07/02/02
12/02/02
15/02/02
20/02/02
25/02/02
28/02/02
Figure 28: Type 3 branch (= very critical situation)
As a result of clustering, 95 of the 822 Dresdner Bank branches were identified as
belonging to type 1 and were regarded as mostly uncritical. Only 32 branches were
discovered as being highly critical i.e. that meant these branches had to expect more
than 15 days with high workload. The overwhelming majority of branches — 695 exactly
— were classified as type 2 branches. Therefore the simulation showed that the branches
would have to deal with some critical days, but far from getting into severe troubles.
An even more detailed picture was the result of a further analysis and classification
based on single days. In this analysis a workday in a branch was regarded as critical if
the counter capacity used — based on the mean of all simulations — was greater or equal
to 75 %. Workdays between 50 % and 75 % used capacity were categorized as medium-
critical, and workdays below 50 % were seen as uncritical. Considering Dresdner Bank
as a whole with 50 workdays between 17" December 2001 and 28" February 2002 and
822 branches, Figure 29 shows the result of the clustering efforts: scenario B for
example is accompanied by 3.355 (or 8,2 %) critical days, 4.931 (or 12,0 %) medium-
critical days and 32.814 (or 79,8 %) uncritical days.
100,0%
80,0%
60,0%
40,0%
20,0%
uncritical
0,0% medium-critical
critical
Scenario @
Figure 29: Clustering of workdays during changeover period
Simulation and analysis results showed that Dresdner Bank’s branches were facing
some challenges during changeover period. Absolute chaos on broad front was however
pretty unlikely. An adequate mixture of measures put together for each branch
individually could be sufficient for preventing severe troubles.
6 Conclusions
As stated in the very beginning, the changeover to the euro in Germany as a whole was a
success story. The same is true for the Dresdner Bank. Although it was not completely
possible to avoid queues — especially in the first days of 2002 — the exchange process
went off smoothly. No severe technical problems occurred. Peter Timmerscheidt,
member of Dresdner Bank’s euro 2002 project team, pointed out: “I was very surprised
that everything proceeded so fast, although the German people allegedly love their
mark. The big pragmatism of the citizens was surprising for me too” (Dresdner Bank,
2002).
The simulation based branch reports have certainly not been the single crucial factor
producing this success story. However, they have been valued as an important piece of a
jigsaw by most of the members of the central and regional project teams involved in this
subject. The development of scenarios of customer behaviour, the gathering of branch
specific data and the simulation of the critical 50 days were seen as an important means
for improved, fact-based discussions and argumentation.
References
Deutsche Bundesbank (Ed.): Gemeinsames Konzept fiir die Inverkehrgabe von Euro-
Bargeld in der Bundesrepublik Deutschland, Frankfurt am Main: without
publisher, 2001 (pdf document downloadable through http://www.bundes-
bank.de/euro/inhalt.htm, 18.07.2001).
Dresdner Bank (Ed.): Dresdner Banker, Issue 229, March, 2002.
European Commission: Communication from the European Commission to the Euro-
pean Council. Review of the introduction of euro notes and coins (6 March
2002), 2002, (pdf document downloadable through http://europa.eu.int/
comm/economy_finance/publications/euro_related/2002/com0306_en.pdf).
Forrester, Jay W.: Industrial Dynamics, Cambridge: M.LT Press, 1961.
Morecroft, John D.W.: Executive Knowledge, Models, And Learning, in: Morecroft,
John/Sterman, John D.: Modeling for Learning Organizations, Portland:
Productivity Press, 1994.
Pidd, Michael: Computer Simulation in Management Science, 4th ed., Chichester:
Wiley, 1998.
Ringland, Gill: Scenario Planning: Managing for the Future, Chichester et al.: John
Wiley & Sons, 1998
Steinhausen, Detlef: Simulationstechniken, Miinchen/Wien: Oldenburg, 1994.
Sterman, John D.: Business Dynamics: Systems Thinking and Modeling for a Complex
World, Boston et al.: Irwin McGraw-Hill, 2000
Ventana Systems, Inc.: Vensim® Reference Manual, Harvard: without publisher, 2000
Appendix
For the base run displayed by Figure 5 (p. 9) the following parameter values were used:
Parameter Value | Unit Source
Available Transaction Capacity 120 [Minutes/Hour] Maximum Value!!
Average Transaction Time 1.95 [Minutes/Customer] | Data/Expert interv.
Number of a Branch's Customers 1780 | [Customer] Average value
Branch Workdays During the Dual Circulation 42 [Days] Average value
Period
Hours of Business per Day 8 [Hours/Day] Average value
Number of Transactions in an Hour 0.25 [Transactions/Hour] | Estimation
Perception Delay 24 [Hours] Estimation
Table 3: Base run parameter values
The probability of finding DM cash, the probability to receive DM instead of € as
change and the curiosity were thought to be time dependent parameters. They were
therefore modelled using lookup table functions. The parameters used for the base run
were the results of an estimation process.
0,06
—Probability to Receive DM
0,04 instead of € as Change —4
[Dmni/Transaction]
0,02
0 A n n
0,01
0,008 Probability of Finding _|
DM Cash [Dmnl/Hour]
0,006
0,004
0,002
0 fl fl n f f n
16
5 12 Curiousity [Dmnl] —
£8
=|
24
0 n n n n n n
0 6 12 18 24 30 36 42
Day
Figure 30: Base run values for the time dependent parameters
11 A typical Dresdner Bank branch has two cash desks that can be used maximally 60 minutes per hour to
service customers. The total available transaction capacity therefore is 120 minutes per hours assuming
that the two cash desks are permanently staffed.
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