CAPACITY ADJ USTMENT INA SERVICE FACILITY WITH
REACTIVE CUSTOMERS AND DELAYS: SIMULATION AND
EXPERIMENTAL ANALYSIS.
Carlos Arturo Delgado Alvarez
HEC, School of Business and Economics, University of Lausanne
Dorigny, 1015-Lausanne, Switzerland
441 21 692 34 67
E-mail: carlos.delgado@ unil.ch
Ann van Ackere
HEC, School of Business and Economics, University of Lausanne
Dorigny, 1015-Lausanne, Switzerland
E-mail: ann.vanackere@ unil.ch
Erik R. Larsen
Institute of Management University of Lugano
6904, Lugano, Switzerland
E-mail: erik.larsen@ usi.ch
Santiago Arango
Complexity Center Ceiba, Faculty of Mines, Universidad Nacional de Colombia
Medellin, Colombia
E-mail: saarango@ unal.edu.co
ABSTRACT
In this paper, we apply system dynamics to model a queuing system wherein the
manager of a service facility adjusts capacity based on his perception of the queue size; while
potential and current customers react to the managers’ decisions. Current customers update
their perception based on their own experience and decide whether to remain patronizing the
facility, whereas potential customers estimate their expected waiting time through word of
mouth and decide whether to join the facility or not. We simulate the model and analyze the
evolution of the backlog of work and the available service capacity. Based on this analysis we
propose two altemative decision rules to maximize the manager’s cumulative profits. Then,
we illustrate how we have developed an experiment to collect information about the way
human subjects taking on the role of a manager in a lab environment face a situation in which
they must adjust the capacity of a service facility.
KEYWORDS: Queuing system, capacity adjustment management, system dynamics,
experimental economics, adaptive expectations
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
INTRODUCTION
Most typical research in queuing problems has been focused on the optimization of
performance measures and the equilibrium analysis of a queuing system. Traditionally,
analytical modeling and simulation have been the approaches used to deal with queuing
problems. Most simulation models are stochastic and some more recent models are
deterministic (van Ackere, Haxholdt, & Larsen, 2010).
The analytical approach describes mathematically the operating characteristics of the
system in terms of the performance measures, usually in "steady state" (Albright & Winston,
2009). This method is useful for low-complexity problems whose analytical solution is not
difficult to find. For complex problems, a simulation approach is preferable as it enables
modeling the problem in a more realistic way, with fewer simplifying assumptions (Albright
& Winston, 2009).
We consider those queuing systems in which customers decide whether or not to join a
facility for service based on their perception of waiting time, while managers decide to adjust
capacity based on their perception of the backlog of work (i.e. the number of customers
waiting for service). The analysis of queuing problems could be aimed at either optimizing
performance measures to improve the operating characteristics of a system or understanding
how the manager and customers interact with the system to achieve their objectives. In the
real world, queuing is a dynamic problem whose complexity, intensity and effects on the
system change over time. Still, some problems may be modeled using the assumptions of
classical queuing theory (Rapoport, Stein, Parco, & Seale, 2004). Considering the complexity
of queuing problems, which is due to a set of interactive and dynamic decisions by the agents
(ie. customers and the manager) who take part in the system, we will focus on studying the
behavioral aspects of queuing problems.
Haxholdt, Larsen, & van Ackere (2003) and van Ackere, Haxholdt, & Larsen, (2006);
van Ackere et al., (2010) have applied deterministic simulation methodologies for studying
behavioral aspects of a queuing system. Other authors have included cost allocation as a
control for system congestion (queue size) (e.g. Dewan and Mendelson 1990). In this way,
customers’ decisions on whether or not to join the system are influenced by such costs.
Likewise, those decisions can be based on steady-state (e.g. Dewan and Mendelson 1990). or
be state-dependent (e.g. van Ackere 1995). The seminal papers on this subject are Naor
(1969) and Y echiali (1971). Other authors have included dynamic feedback processes to build
perceptions of the behavior of the queue (van Ackere et al., 2006) and/or of demand (van
Ackere et al. 2010), which influence the decisions of customers and managers. A more
detailed discussion of the state of the art on behavioral aspects in queuing theory can be found
in (van Ackere et al., 2010).
We propose two methodological approaches to achieve our goals. Firstly, we use
system dynamics to learn about the macro-dynamics of customers and the manager interacting
in a service facility. Specifically we analyze how the available service capacity and the queue
evolve and how the delay structure affects the manager's decision. We also want to assess
how the manager adjusts capacity based on the evolution of the backlog of work (i.e. the
number of customers waiting for service). Haxholdt et al. (2003) and van Ackere et al. (2006
and 2010) applied system dynamics to tackled similar problems. System dynamics is useful
for problems, which do not require much detail. That is, those which can be modeled at a high
level of abstraction. This kind of problems is usually situated at the macro or strategic level
(e.g. marketplace & competition, population dynamics and ecosystem) (Borshchev &
Filippov, 2004)
Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
Next we apply experimental economics (Smith, 1982) to capture information about how
subjects playing the role of a manager in a lab environment, decide when and by how much to
adjust the capacity of a service facility. We use the system dynamics based simulation model
as a computational platform to perform the experiment. For more details about how system
dynamics models have been used to carry out laboratory experiments, see (Arango,
Castaneda, & Olaya, 2011). Experimental economics is a methodology that based on
collecting data from human subjects to study their behavior in a controlled economic
environment (Friedman & Sunder, 1994).
This paper is organized as follows: Firstly, we discuss the dynamic hypothesis of the
problem proposed initially by van Ackere et al. (2010) and explain why we modify the model.
Then, we analyze the model behavior of the base case. In the following section, we introduce
two alternative strategies to manage the capacity adjustment of the service facility. We
determine the optimal parameters for these strategies and analyze the resulting system
behavior. We also perform a sensitivity analysis to the parameter values. Finally, we present
the experimental laboratory and discuss the collected results.
A SERVICE FACILITY MANAGEMENT MODEL
In this section, we analyze the dynamic hypothesis of the queuing model proposed by
van Ackere et al. (2010). This model captures the relationship between customers and
manager (referred to as the service provider) as agents who interact in a service system. The
causal loop diagram of Figure 1 portrays the feedback structure of these two actors in the
system. The model consists of two sectors: the customers’ behavior is to the left and that of
the manager to the right. Both sectors are connected by the queue, whose evolution
determines the dynamics of these actors in the system. Customers decide whether to use the
facility based on their estimate of waiting time, while the manager decides to adjust the
service capacity based on the queue length. Examples of this kind of system include a garage
where customers take their car for maintenance, and workers or students who daily patronize
a restaurant to have lunch. In both examples, customers are free to use or not the facility for
service and the manager is motivated to encourage customers to use his facility by adjusting
its service capacity.
a Service
=, fe, % nN
r
¥ Cc Capacity
Capacity
Potential Customer Customers Current Customers 1g? %
Expected Waiting time Satisfaction Capacity aa _ Retirement
Cc “Sc, 01 Desired Pai: =
_ Service ~ Capacity Reduction Loop
Potential Customers Loop *
Capacity
Figure 1. Feedback loop structure for a customers-facility queuing system
Two groups of customers are assumed: current and potential customers. The former
make up the customer base of the facility; they periodically patronize it as long as they are
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
satisfied. They consider being satisfied when their expected waiting time is less than the
market reference, which they find acceptable. The second group represents those customers
who the manager envisages as potentially attractive to the business. They can be either former
customers, who left due to dissatisfaction, or new customers who require the service and look
for a facility. They decide whether or not to join the facility depending on their expected
waiting time, which they also compare to the market reference.
Customers form their perception of waiting time (Wi) each period using adaptive
expectations (Nerlove, 1958), as shown in Equation 1:
W, =9*W.4 +09) Wis (1)
where @ is called the coefficient of expectations (Nerlove, 1958) and 1/@may be
considered as the time taken by customers to adapt their expectations. Current customers
adjust their expectation based on their last experience (W,), while potential customers rely on
word of mouth. The decision of joining a facility for service based on its reputation often
requires more time than when we base this decision on our own experience. Thus, we assume
that the time required by potential customers to adapt their expectations is longer than or
equal to that of the current customers.
While the current customers’ perception determines their loyalty to the facility, the
potential customers’ perception defines if they will join the customer base. The lower the
waiting time perceived by current customers, the more loyal they are, whereas the higher the
perceived waiting time, the more customers will leave the customer base. Regarding potential
customers, the lower their expected waiting time, the more will become new customers for the
facility. The rates at which new customers join the customer base and current customers leave
it are modeled using nonlinear functions of the satisfaction level. van Ackere et al. (2010)
discuss some alternatives to model these functions.
To summarize the customers’ dynamics: longer queues bring about higher waiting times
for current customers and increased perceptions of waiting time for potential customers,
implying that the level of satisfaction with the facility’s service of both customer groups
decreases. Consequently, over time this reduction in customers’ satisfaction leads current
customers to leave the facility and discourages new customers from joining it in the future.
Thus, the number of customers waiting for service will decrease until the waiting time tends
to acceptable levels compared to the market reference and the customers’ perception
stabilizes. These dynamics are described by the two balancing loops to the left in Figure 1.
As far as the service provider (the right side of Figure 1) is concerned, van Ackere et al.
(2010) model the type of service systems where the capacity adjustment involves an
implementation time. For instance, hiring new employees requires new training, laying off
staff may imply a notice period, acquiring new IT systems takes time, among others.
However, the authors represent this time in the model using an information delay (Sterman,
2000); after the manager estimates the required capacity, any needed adjustment is
implemented gradually. This is a simplified view of the delay structure. In a system dynamics
context, this kind of delays is better modeled through material delays, which capture the real
physical flow of the capacity (Sterman, 2000). Once the adjustment decision has been made,
its implementation process does not materialize immediately. We deviate from van Ackere et
al. (2010) by incorporating this material delay structure in the model, as the stock and flow
Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
diagram of Figure 2 illustrates. In this way, we can model how the manager accounts for his
previous decisions, which have not yet taken effect, to make his next decision.
Capacity i. Capacity
Delivery ae Retirement
Delay Delay
(Capacity on] % 7 Senvice Capacity to \ :
a al mee
Capacity Order Capacity Cepaciy Decision to be Retired | Capacity
Orders Delivery cay YA __, Retirement
il + +
Future a
te Sewice
Capacity
Desired
Service
Capacity
Figure 2. System dynamics representation for the capacity adjustment management of a
service facility.
The capacity adjustment process is depicted in Figure 2 by capacity orders and the
decision to retire capacity, which determine the available service capacity. Starting from the
left, the manager decides how fast and how much to adjust capacity based on his desired
service capacity and the future capacity. The latter is explained below and depends on his
previous decisions. He estimates the desired service capacity based on his perception of the
average queue length and a market reference for the waiting time ( tr). Like the customers,
the manager forms this perception by applying adaptive expectations. He updates his expected
average queue length based on the most recent observation of the queue (Q,.). This expected
average queue length (EQ,) is given by:
EQ, =8* Qi4 +0 -A)* EQ. 4 (2)
where (is the coefficient of expectations for the manager and 1/f may be interpreted as
the time required by the manager to adapt his perception. Then, the desired service capacity of
the manager is determined as follows:
pe, =Fae (3)
The longer the queue the greater the desired service capacity and the larger the capacity
orders (c.f Figure 1). After the manager decides how much capacity to add (c.f. capacity
orders in Figure 2), these orders accumulate as capacity on order (CO) until they are available
for delivery (c.f. capacity delivery delay in Figure 2). Some examples of this kind of delayed
process in capacity acquisition include construction of new buildings, purchase of new
equipment and hiring staff. Once the capacity order is fulfilled, the service capacity (SC) will
be increased by the capacity delivery. The greater the service capacity, the higher the service
5
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
rate and thus fewer customers waiting. In this way, a third balancing loop (c.f. capacity
acquisition loop in Figure 1) results from the dynamics between the manager and customers.
The decision of adjusting capacity may also imply removing capacity. When this
occurs, the capacity, which the manager decides to withdraw, will be designated as capacity to
be retired (CbR). This capacity remains available to the customer during the capacity
retirement delay (e.g. end a lease on a building, notice period for staff, etc). Hence, the
currently available service capacity at the facility at time t is given by,
ASC; =SC; + CbR; (4)
After the delay involved in the capacity retirement, the available service capacity will
decrease due to this retirement, as shown in Figure 1, and the number of customers in the
queue will thus increase. This effect yields the fourth balancing loop in the system. This loop
describes the behavior caused by the decisions of capacity reduction.
Finally, the capacity that will be available once all the manager's decisions have been
implemented, i.e. the future capacity, is given by,
FSC; =CO; + SC; (5)
Then, Equations (4) implies that FSC; equals
FSC; =ASC;+CO;- CbR: (6)
To summarize the manager’s dynamics: longer queues increase his desired service
capacity. The higher this desired service capacity, the more capacity the manager orders or the
less he removes. Over time, the capacity orders will increase the available service capacity,
while the capacity retirement will decrease it. Consequently, the higher (the lower) the
available service capacity the lower (the higher) the number of customers queuing. Like the
customers’ dynamics, the two balancing loops, which describe the manager’s behavior, may
lead to stabilizing his perception over time. Thus, we are interested in studying how the
manager analyzes the customers’ behavior in order to adjust capacity and how the multiple
delays involved in the system affect his decisions.
MODEL BEHAVIOR
Before trying out some alternative policies or strategies to model the manager’s
decisions and discussing descriptively some experimental results, we analyze the typical
behavior of the system occurring when one of the equilibrium conditions is modified. The
model is initially set under the equilibrium conditions, which are described in Table 1. Then
we illustrate the impact on the system behavior of increasing the size of the initial customer
base from 175 to 200. The other initial values remain as shown in Table 1. We simulate the
model for 100 time units using a simulation step of 0.0625 time units.
Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
State Variables Equilibrium Unit
Value
Customer base 175 People
Queue 50 People
Average queue 50 People
Capacity on order 0 People / Time
Service capacity 25 People / Time
Capacity to be retired 0 People / Time
Perceived waiting time of current customer 2 Time unit
Perceived waiting time of potential customers 2 Time unit
Exogenous Variables Value Unit
Visit per time unit 0.15 1/ Time unit
Market reference waiting time ( %r) 2 Time unit
Delays Value Unit
Time to perceive queue length (1 / B) 4 Time unit
Capacity delivery delay 4 Time unit
Capacity retirement delay 2 Time unit
Perception time of current customers (1 / @) 2 Time unit
Perception time of potential customers (1 / ¢) 4 Time unit
Table 1. Initial conditions of equilibrium
Figure 3 illustrates the evolution of the available service capacity and the number of
customers waiting for service. We can observe that the manager adjusts the service capacity
by imitating the evolution of the queue (i.e. the backlog of work). In this sense, he is trying to
keep the average waiting time close to the market reference and while keeping the utilization
rate close to 1, as shown in Figure 4. The lags involved in the manager and customer
dynamics in addition to the manager’s reaction result in the oscillating phenomenon and a
certain decreasing tendency, as shown in Figure 3. Next, we go into more detail of the causes
of this pattern.
An increase in the customer base will raise the arrival rate. Considering that the service
capacity remains constant due to the lags involved in the capacity adjustment process and the
formation of perceptions by the manager, more customers will wait for service. As the queue
increases, the manager adjusts gradually his desired service capacity. According to Figure 1,
the higher the desired service capacity, the larger the capacity orders. However, the capacity is
delivered after 4 periods. The average waiting time therefore increases initially as plotted in
Figure 4, affecting the perception of current customers and the expected waiting time of
potential customers. When the perception of waiting time exceeds the market reference (2
time units), the customer base starts to decrease because more current customers are
dissatisfied and fewer potential customers wish to join the facility. Hence, when the
manager’s decisions to add capacity start to materialize, the backlog of work (i.e. the queue)
7
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
is falling. Consequently, the available service capacity reaches its peak at about the time the
queue is reaching its nadir. Moreover, the manager reacts again to this behavior of the
customers, but on this occasion by reducing his available service capacity to avoid having idle
capacity. Neither manager nor customers consider the delays inherent in the reaction of each
other. Hence, the backlog soars because of the manager’s decision. Thus, despite the manager
trying to adjust the service capacity by imitating the evolution of the queue, the multiple
delays in the system bring about a fluctuating pattern as illustrated in figure 3.
—— Available Service Capacity (Customers / Time unit)
---- Queue (Customers)
Figure 3. Illustrative behavior of the available service capacity and queue length
100
5.0 12
45 f +
et Ae” i oy
35 1 | 1 mt an fos \| | \
3.0 : Ht) U VV
Pos | i a 06
Ae | PY Py ty f
215 i a a | 04
10 \ \ wat
02
05
0.0 0.0
0 2% 40. 60 8 100 0 2 4 6 80
Time Time
a) b)
Figure 4. Illustrative behavior of (a) the average waiting time and (b) the utilization rate.
We have explained the model and illustrated a typical case where the manager reacts to
customers’ dynamics. In the next section, we propose other alternative decision rules to
enable the manager to adjust capacity more effectively. These rules are based on the
manager's perception of the backlog of work. Two alternative ways to form this perception
based on the evolution of the queue are introduced. The decision mules consider both the
required capacity adjustment and the speed at which this adjustment is carried out.
Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
ALTERNATIVE DECISION RULES
The aim of the manager is to maintain sufficient available service capacity (ASC,) in his
facility in order to satisfy the customers. He thus decides whether to adjust the service
capacity and at what time to do so. We propose a heuristic to determine the required capacity
adjustment (RC At) by incorporating the speed at which the manager decides to adjust it. Let a
be the service provider's speed to adjust capacity, i.e. how fast he decides to either add or
reduce capacity. We defined above that the capacity adjustment decisions depend on the
future service capacity (FSC,), and the desired capacity (DC,). Thus, including @ in this
definition, we may state RCA, as follows:
RCA, =a* (DC, —FSC;), (7)
where @ must be nonnegative and less than 1. This adjustment involves either an
increase in capacity (when DC; - FSC; >0), a decrease in capacity (when DC; - FSC; <0), or
leaving capacity unchanged (when DC; - FSC; = 0). Taking into account that the capacity
delivery delay may be different from the capacity retirement delay (c.f. Figure 2), we assume
that the speed to either add or remove capacity can also be different. In this sense, the
parameter ais determined as follows:
oa, if DC, -FSC, <0
a=o . (8)
Aa if DC, —FSC, >=0
where DC; and FSC; are as defined in Equation 3 and 6. Consider now that the manager
does not necessarily keep in mind all his previous decisions, some of which are still in the
process of execution. Thus, the future service capacity (FSC;), which the manager perceives,
would be modeled as:
FSC; =ASC;+y* (CO;- CbRi) (9)
where yrepresents the proportion of the capacity adjustment that has not yet been
implemented, which the manager takes into account. Replacing a DC; and FSC; using
Equations 8, 3 and 9, respectively, in Equation 7, the decision of how much to adjust capacity
each period is determined by
RCA, =a* B* Qi eS -ASC, —y* (CO, “bn (10)
MR
s.t.
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
oa if BP Qa HA“ PIEQ asc, ye (CO, —CbR,) <0
ano pos MeO ay
Ac? if FP FU“ AEO4 asc, -# (CO, —CbR,) >=0
MR
We propose a second manner to estimate DC;. Instead of using adaptive expectations,
the manager may simply consider the most recent backlog, i.e. customers waiting for service
(Q,), to estimate demand. That is, he looks at his current order book to decide how much
capacity is required. Such an attitude is meaningful in situations where capacity can be
adjusted fairly cheaply and quickly, e.g. by using temporary staff. In this case Equations 10
and 11 become:
RCA, mati ase, -y* (CO; “chk (12)
Tr
s.t.
ra if St -asc, -# 0, —CbR,) <0
a=9 0. (13)
ee? if —' —asc, —y* (CO, —CbR,) >=0
TR
Optimal Strategies
Our objective is to find optimal values for the parameters az @2z 8 and y which
determine the above two strategies, to maximize the manager’s cumulative profits over 100
time units. In order to calculate this profit we introduce a fixed cost and revenue resulting
from providing the service. The equations 10 to 13 are nonlinear and thus complicated to
optimize analytically. Thus, we apply simulation optimization (Keloharju & Wolstenholme,
1989; Moxnes, 2005) in order to find the optimal parameter values.
We use the optimizer toolkit of Vensim where the cumulative profits are set as the
payoff function. The optimal parameter values we obtain are given in Table 2. According to
this table, the second strategy, i.e. when the manager forms his perception based on the most
recent value of the backlog, reaches the best payoff (2’151 compared to 2’059 for strategy 1).
This occurs because when using strategy 2 the manager makes decisions a bit more
aggressively than when using strategy 1, as shown figure 5. Hence, the manager reaches
higher profits when he relies on the most recent information about the customers’ behavior,
ie. Q;. The optimal value of A (i.e. the coefficient of expectations), which equals 1 (see table
2), for strategy 1 strengthens the above remark. A coefficient of expectation equal to 1 means
that the manager updates his expectation by using only the most recent information regarding
the backlog. That is, the manager does not account for the past. In that case, Q;,.; is the latest
information about the backlog the manager has to update his perception, EQ, at time unit t.
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Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
Maximum
Strategy |Alpha1|Alpha2| Beta |Gamma Payoff Value
A daptive
expectations 1.00 0.00 1.00 0.40 1'950
Most _recent/
value of the) 1.00 | 0.00 | NA | 0.37 2071
backlog
Table 2. Optimal values of the parameters which define each strategy
Strategy 1 Strategy 2
0 20 40 60 80 100 0 20 40 60 80 100
Time Time
(a) (b)
Figure 5. Evolution of the queue (i.e. backlog) and the available service capacity for the two
capacity adjustment strategies with the optimal parameter values.
Figure 5 shows the behavior of the two parts of the system (customers and the manager)
for both strategies. Their optimal behaviors are similar. Like in the base case, when the
manager applies either of these two strategies, the backlog grows at the beginning of the
simulation and the manager reacts by increasing capacity. However, as he bases his decisions
on the most recent information about the backlog, he notices quickly that the backlog goes
down. Thus, his decision to increase capacity becomes less aggressive resulting in the
utilization rate gradually increasing back to 1 (see Figure 6). Consequently, the manager’s
decisions encourage current customers to remain loyal which in tum encourages the manager
to keep the available service capacity constant. The manager’s behavior brings about current
customers being satisfied and thus inducing potential customers to patronize the facility
through word of mouth. New customers joining the customer base imply that the arrival rate
steeply increases. The manager responds by slowly increasing the available service capacity,
which quickly reduces the queue. From this point onwards, an oscillating phenomenon starts
to emerge. This oscillating pattern differs from that of the base case in that it grows
exponentially over time.
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C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
Strategy 1 Strategy 2
12 12
1.0 f 1 1.0
2
# os = £ 08 a \ |
§ 06 0.6
: 04 04
0.2 0.2
0.0 0.0 T T T r 1
0 20 40 60 80 100 0 20 40 60 80 100
Time Time
(a) (b)
Figure 6. Evolution of the utilization rate for the two capacity adjustment strategies set up
with the optimal parameter values.
Sensitivity analysis
We perform a sensitivity analysis to understand the impact of the different parameters,
which define the alternative strategies, on the model behavior. In particular, we analyze the
effect of a change in the values of these parameters on the manager’s cumulative profits and
the evolution of the queue.
First we illustrate the case in which we change @o(i.e. the speed at which the manager
removes capacity). We select this parameter because it has the strongest impact. Figure 7
illustrates how changing the value of azin both strategies affects the evolution of the queue
and the manager’s cumulative profits. We can observe that changes in these two variables
emerge after about 27 time units, particularly, when az is large (e.g. 0.5 or 1.0), ie. when the
manager quickly removes capacity. For instance, using both strategies with azequal to 1.0 the
cumulative profits decrease about 70% compared to the optimal value, while the backlog
decreases by about 98% for strategy 1 and 94% for strategy 2. Likewise, the higher the
parameter, the more the backlog oscillates.
Changes in the other parameters have small impacts on the evolution of the cumulative
profits and the queue. As far as @ (i.e. the speed at which the manager add capacity) is
concemed, for very small values (e.g. 0.0 and 0.1) the manager’s cumulative profits and the
queue are slightly reduced using both strategies. Regarding the speed at which the manager
updates his perception in Strategy 1, i.e. 8 varying this parameter results in similar effects as
changing a Finally, by trying different values of ywe found that they do not have any
significant impact.
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Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
2500 + Cumulative Profit (Score) Queue
2000 4 .
g Py,
3 1s00 | . F
Fw 4 ce /
fs} 8
500 + ee
0
0 20 40 60 80 100 +08
Time
a)
2500 4 Cumulative Profit (Score)
2000 4 /
i ;
He 1500 + e /
i 1000 5 a Z \
° ——
500 + rf a
0 LAA, LCRA
0 20 40-60 80 100 M0560 8 who
tine Time
c) d)
seek a2=0 ----a2=0.1 ——o2=05 ---a2=10
Figure 7. The cumulative profits and queue length when strategies 1 (Figs a and b) and 2
(Figs c and d) are simulated for selected values of a2, keeping values of 04, B, and yconstant
as shown in Table 2.
A SERVICE FACILITY MANAGEMENT EXPERIMENT
We use the model described above as a computational platform to implement a
laboratory experiment (c.f. Smith, 1982). The objective behind this experiment is to collect
experimental information to assess how human subjects taking on the role of a manager face a
situation in which they must adjust the capacity of a service facility. We also want to analyze
how they use the available information to make capacity adjustment decisions. The subjects
have information about the behavior of both the facility and the customers. Regarding the
facility, they know the past and current available service capacity and utilization rate. As for
customers, subjects know the past and current backlog (i.e. the number of customers waiting
for service).
Experimental Protocol
We design this experiment based on the protocol for experimental economics (e.g.
Smith, 1982; Friedman and Sunder 1994). We recruited undergraduate and master students in
Finance, Management and Economics from the University of Lausanne. They were invited to
13
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
participate in an experiment designed to study decision making in a service industry, through
which they could earn up to 80 Swiss Francs. We received about 400 replies and selected 187
subjects following the principle of “first come, first served” in order to perform six
experimental treatments. Each treatment had at least 30 participants. Subjects were allocated
across eleven experimental sessions; each involved around 16 subjects and lasted, on average
90 minutes. Two facilitators supervised each session. The task of the subjects was to use a
computer based interface, which portrayed the service capacity adjustment problem of a
garage, to decide each period how much capacity to add or remove. They had to perform this
task for 100 experimental periods.
This experiment was conducted in the informatics laboratories of the School of
Business and Economics. Upon arrival at the laboratory, the subjects were allocated to a PC
and separated from their neighbor by another PC. Communication between the subjects was
forbidden. Once they were seated, we gave them written instructions and a consent form,
which they had to sign before starting the experiment. Then, a short introduction to the
experiment was presented to them. The instructions were quite simple and provided subjects
with a short explanation of the system that they had to manage in the experiment and all the
information, which they had available to carry out their task. We present the instructions and
the interface used to run the experiment in the appendix of this paper.
We gave the subjects the payoff scale through which they eamed their reward
depending on their performance in the experiment. Performance was measured based on the
cumulative profits that subjects had at the end of the experiment, i.e. at the period 100 or
when the available service capacity reached 0, If that happened before than the period 100.
Experimental Treatments
In addition to the base case, we have designed other five experimental treatments to
understand how the manager adjusts the capacity of an industry service. These five treatments
are divided in two groups to study the effect of different factors. The first group is composed
of four treatments and its objective is to analyze how the delay structure, inherent to the
system, affects how the manager decides to adjust capacity. This delay structure includes the
delays the manager knows (i.e. the implicit lags in capacity adjustment), and those which are
unknown to him (i.e. the time required by potential and current customers to update their
perceptions). The last group has a single treatment, which includes a cost to add or remove
capacity. Table 3 summarizes the conditions of each treatment.
Current | Potential | Timeto | Timeto | Cost per
Treatment | customers | customers | increase | decrease | unit change
Delay Delay capacity | capacity | in capacity
Base Case 4 2 4 2
A 10 Z 4 2
B 6 4 4 2,
c 4 2 8 4
D 4 2 2 1
E 4 2 4 2 1
Table 3. Treatment conditions.
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29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
EXPERIMENTAL RESULTS
All subjects overreact to the initial increase of the backlog. This sudden rise is
independent of subjects’ decisions since it depends on the initial conditions. Thus, we can
interpret this first reaction of the subjects as a learning process in which they are trying to
adapt to the system behavior. In other words, we can call this initial period a transition period.
Recall that we observed a similar pattern of the backlog in the simulation results.
From this point onwards, we identify three groups of subjects, whose decisions result in
similar behavioral patterns. Figure 8 illustrates the evolution of the backlog and the available
service capacity of two typical subjects of each group. The first group is composed of those
subjects who overreact strongly to the initial overshoot of the backlog and then they make
many small decisions to gradually adjust capacity over time (e.g. Subjects 5 and 11). Most of
these decisions concem capacity addition. Consequently, the garage’s available service
capacity for this kind of managers presents an exponential increase over time. A fter the initial
transition, the available service capacity and the queue behave in the same way. Thus, we can
consider that these subjects quickly learn to manage the system to achieve sustainable growth.
The subjects in this group achieved the higher scores of the experiment.
The second group (e.g. Subjects 12 and 18) represents those subjects who, after their
slight overreaction to the initial backlog, make fewer but more aggressive capacity adjustment
decisions than the subjects of the first group. Moreover, they continue to overreact to the
evolution of the backlog over time. This behavior results in an oscillating pattern for both the
backlog and the available service capacity: they increase exponentially, but more slowly than
for the first group. These two groups, despite achieving quite different behavioral patterns
compared to the two optimal strategies discussed before, attain similar total profits.
The last group includes subjects who, even after the transition period, continue to
overreact significantly to the evolution of the backlog (e.g. Subjects 3 and 30). Although in
some cases the backlog evolves as when simulating the optimal strategies (see Figure 5), the
subjects did not capture the customers’ behavior. We can consider that these subjects were
unable to handle the delay structure inherent to the system. They performed poorly, achieving
the lower payoffs, and occasionally finding themselves with zero service capacity before the
end of the experiment.
15
C.A. Delgado, A. van Ackere, E.R. Larsen, and S.
Subject 5 : Score = 2'551
0 20 40 60
Time
80 100
Subject 12 : Score = 2'207
40
Time
60 80 100
Subject 3 : Score = 719
Customers or
Customers / Time unit
Arango, 2011
Subject 11: Score = 2'407
40 60
Time
80 100
Subject 18 : Score = 2'212
Customers or
Customers / Time uni!
40
Time
60 80 100
Subject 30: Score = 651
Customers / Time unit
100
_ ~~ Queue
—A vailable Service Capacity
Figure 8. Experimental results for six typical subjects.
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29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
Treatment Results
The outcomes of the treatments were compared using the Wilcoxon Rank-Sum test or
Mann-Whitney U test. Table 4 shows the corresponding p-values. Using a 0.05 significance
level, these p-values enable us to interpret that the cumulative profits achieved in treatments C
(i.e., slow adjustment) and D (i.e., fast adjustment) are, on average, significantly different
compared to the cumulative profits achieved in the other treatments. By looking at the box
plots in Figure 9 we can get an idea of such a difference as the mean cumulative profits of
treatments C and D are either above or below the mean cumulative profits of the other
treatments, supporting the remark inferred from the Wilcoxon Rank-Sum tests. We can also
observe that the variability in treatment D is less compared to that of the other treatments. In
addition, the distributions of treatments A, C, D and E are reasonably more symmetric than
those of treatment B and the base case.
Col Mean -
Treatment | Treatment | Treatment | Treatment
Row Mean Basecase
A B Cc D
P-Values
Treatment A 0.2805
Treatment B 0.9035 0.1772
Treatment C 0.0008 0.0029) 0.0000}
Treatment D 0.0002) 0.0000 0.0003} 0.0000)
Treatment E 0.2871 0.7562 0.2310 0.0003} 0.0000}
Table 4. P-values of the Wilcoxon Rank-Sum test for the cumulative profits
°
84
m
—
l-_ = ma —-
* = ° ”
Bo °
a
Boy e
fo} ° e
3 |
gle
OT BASE A B G D E
Figure 9. Box plots for the cumulative profits by treatment
CONCLUSIONS AND FURTHER WORK
In this paper, we have applied a system dynamics model to study how the manager of a
service facility adjusts capacity based on his perception of the queue length, whereas potential
17
C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
and current customers react to the managers’ decisions. While current customers update their
perception based on their own experience and decide whether to stay in the customer base,
potential customers update their perception through word of mouth and decide whether to join
the customer base. We have simulated the model and analyzed the evolution of the backlog of
work and the available service capacity. Based on this analysis we have proposed two
alternative decision rules to maximize the manager's cumulative profits. Then, we have
illustrated how we developed an experiment to collect information about how human subjects
taking on the role of a manager in a lab environment face a situation in which they must
adjust the capacity of a service facility.
Simulating this queuing model showed that when the manager tries to adjust the service
capacity by imitating the evolution of the queue (i.e. the backlog of work), the multiple delays
in the system bring about an oscillatory phenomenon. Optimizing the parameters, which set
the alternative strategies, we found that the manager reaches higher profits when he relies on
the most recent information about the customers’ behavior, i.e. the most recent backlog. The
sensitivity analysis enables to conclude that changes in the speed at which the manager
removes capacity have a strong impact on the evolution of the available service capacity and
the backlog. Varying the other parameters results in small impacts on the evolution of these
two variables.
As far as the experiment is concerned, we identify three groups of subjects, whose
decisions bring about similar behavioral patterns. The first group included the subjects who
overreact strongly to the initial sudden increase of the backlog and make many small
decisions to gradually adjust capacity over time. The second group represented the subjects
who, after overreact to the initial backlog slightly, they make fewer but more aggressive
capacity adjustment decisions than the subject of the first group. The last group included
subjects who even, after the transition period, overreact significantly to the backlog. The two
first groups, despite quite different behavioral patterns compared to the two optimal strategies
discussed, achieved similar total profits.
The next step will be estimate a decision rule which adjusts to collecting data from
Subjects. Extensions include incorporating prices to manager’ decisions, i.e. a unit cost for
each unit of capacity which the manager decides to add or remove. An interesting approach
would be to conduct another experiment wherein another group of human subjects will
assume the role of customers.
REFERENCES
Albright, S. C., & Winston, W. L. (2009). Management Science Modeling (Revised 3r., p.
992). South Western Cengage Learning.
Arango, S., Castaneda, J., & Olaya, Y. (2011). Laboratory Experiments and System
Dynamics. Medellin.
Borshchev, A., & Filippov, A. (2004). From system dynamics and discrete event to practical
agent based modeling: reasons, techniques, tools. The 22nd International Conference of
the System Dynamics Society. Oxford.
Dewan, S., & Mendelson, H. (1990). User Delay Costs and Internal Pricing for a Service
Facility. Management Science, 36(12), 1502-1517.
Friedman, D., & Sunder, S. (1994). Experimental methods: a primer for economists (1st ed.).
Cambridge: Cambridge University Press.
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Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
Haxholdt, C., Larsen, E. R., & van Ackere, A. (2003). Mode Locking and Chaos in a
Deterministic Queueing Model with Feedback. Management Science, 49(6), 816-830.
Keloharju, R., & Wolstenholme, E. F. (1989). A Case Study in System Dynamics
Optimization. Journal of the Operational Research Society, 40(3), 221-230.
doi:10.1057/palgrave.jors.0400303
Moxnes, E. (2005). Policy sensitivity analysis: simple versus complex fishery models. System
Dynamics Review, 21(2), 123-145. doi:10.1002/sdr.311
Naor, P. (1969). The Regulation of Queue Size by Levying Tolls. Econometrica, 37(1), 15-
24.
Nerlove, M. (1958). Expectations and Cobweb Phenomena. The Quarterly Journal of
Economics, 72(2), 227-240.
Rapoport, A., Stein, W. E., Parco, J. E., & Seale, D. A. (2004). Equilibrium play in single-
server queues with endogenously determined arrival times. Journal of Economic
Behavior & Organization, 55(1), 67-91. doi:10.1016/.jebo.2003.07.003
Smith, V. L. (1982). Microeconomic Systems as an Experimental Science. The American
Economic Review, 72(5), 923-955.
Sterman, J. D. (2000). Business Dynamics: Systems thinking and modeling for a complex
world (p. 982). Chicago, IL: Irwin-McGraw Hill.
van Ackere, A. (1995). Capacity management: Pricing strategy, performance and the role of
information. International Journal of Production Economics, 40(1), 89-100.
van Ackere, A., Haxholdt, C., & Larsen, E. R. (2006). Long-term and short-term customer
reaction: a two-stage queueing approach. System Dynamics Review, 22(4), 349-369.
van Ackere, A., Haxholdt, C., & Larsen, E. R. (2010). Dynamic Capacity Adjustments with
Reactive Customers. Management. Lausanne.
Yechiali, U. (1971). On optimal balking rules and toll in the GI/M/1 queuing process.
Operations Research, 19(2), 349-370.
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C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
APPENDIX
A. Computer Interface
ae aaa (Tea The Queue Experiment
Service capacity
Your decisions (change in service capacity)
o 5 10 1520
Backlog
Time Reverue Capacity costs | Profitper period | Cumulative raft
4 928 $125 5 fo
1 2 a 6 a ‘00
Time= 1
sackiog 20
| Simulate one period | Capacity utilisation 1
B. Subjects’ Instructions (Base case)
Instructions for the participants
NOTE: PLEASE DO NOT TOUCH THE COMPUTER BEFORE BEING ASKED TO
DO SO
Welcome to the experiment on decision making in a service industry. The instructions
for this experiment are quite simple. If you follow them carefully and make good decisions,
you may earn a certain amount of money. The money will be paid to you, in cash, at the end
of the experiment. Y ou are free to halt the experiment at any time without notice. If you do
not pursue the experiment until the end, you will not receive any payment. The University of
Lausanne has provided funds to support this experiment. If you have any questions before or
during the experiment, please raise your hand and someone will come to assist you.
We assure you that the data we collect during the course of this experiment will be held
in strict confidence. Anonymity is guaranteed; information will not be reported in any manner
or form that allows associating names with individual players.
Description of Experiment
This experiment has been designed to study how managers adjust service capacity in a
service facility. Below is a short explanation of the system that you will have to manage in the
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Proceedings of the
29th International Conference of the System Dynamics Society.
Washington D.C., July 24 to 28, 2011
experiment. It is a relative simple system and you only have to make two decisions each time
period (increasing capacity and/or decreasing capacity).
The situation
You are the manager of a large garage, which repairs and maintains cars. Y ou have an
existing customer base as well as many potential customers who currently are not using your
services, but might consider doing so in the future. Both groups are sensitive to the waiting
time.
Waiting time: is the average time between the moment a customer calls your garage to
make an appointment and the time the car has been serviced. This depends on two factors,
how many other customers have made reservations previously (i.e. how long is the queue) and
the service capacity of the garage (i.e. how many cars can on average be serviced per time
period). Due to planning constraints, this waiting time cannot be less than one month.
Customers: These customers use your garage on average every twice a year. They
evaluate the expected waiting time (which is based on (an average of) the last few times they
have used your garage) and compare this expected waiting time to the time they consider
acceptable (the average for the industry, which is 2 months: the elapsed time between the
moment a customer calls, and the moment he can pick up his car after servicing averages 2
months). If they are satisfied (i.e. the expected waiting time is comparable to or better than the
average for the industry) they will remain your customer and retum again to use your garage.
If they consider that the waiting time is too long compared to the industry average they will
switch to another garage.
Potential customers: These are people who might become customers if they consider
that your waiting time is attractive (i.e. less than the industry average). However, given that
they are currently not among your customers, they only hear about the waiting time at your
place through word of mouth. Consequently, their estimate of the waiting time at your place is
based on less recent information than the estimate of your current customers. Note: the
number of potential customers is unlimited.
Service Capacity: This is the number of cars the garage can service on average in one
month. You, as the manager, control the service capacity of the garage, i.e. you have the
possibility to increase and/or decrease capacity. However, this cannot be done
instantaneously: it takes 4 months to increase capacity (e.g. ordering more tools, hiring
people, acquiring more buildings etc) and 2 months to decrease capacity (end a lease on a
building, lay off people, etc). Note: If at some point your decisions result in a service capacity
equal to zero (0), the garage will be closed and the experiment is ended.
Your Task
As the manager, you make decisions regarding any change in capacity for the garage
each month. To help you make these decisions you have information about the number of
customers currently waiting for service or whose car is currently being serviced (referred to as
the queue), profit, the current capacity of the garage, and the capacity utilization rate. You
goal is to maximize the total profit over 100 months.
Cost and revenue information:
Profits [E$/month] = Revenue - Cost
Revenue [E$/month]
= number of customers served [cars/month]* A verage Price per Customer [E$/car]
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C.A. Delgado, A. van Ackere, E.R. Larsen, and S. Arango, 2011
Average Price perCustomer =1 $/car
Cost [E$/month]
= Service capacity [units]* Unit cost of service capacity [E$/unit/month]
Unit cost of service capacity = 0.5 $/unit/month
Interface
In front of the computer, you will have the interface where all interactions will take
place. The information is the same as what we have provided in these instructions. Please ask
the facilitator to have a trial run to test out the software.
Payment
At the end of the experiment, you will receive a cash reward. This will consist of a
guaranteed participation fee of 20CHF, plus a bonus which will depend on the total profit you
have achieved. This bonus will vary between 0 and 60CHF. If you do not pursue the
experiment until the end, you will not receive any payment.
You will be asked to complete and sign a receipt with your name, email address, and
student ID number. Thereafter, you can collect your payment. We will be happy to answer
any questions you may have conceming this experiment.
If you want to participate in this experiment, please sign the consent form on your desk.
This form must be signed before the start of the experiment
If you have no further questions, please ask the experiment facilitator to begin. Good
luck and enjoy the experiment.
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