PROCRASTINATION DYNAMICS:
A STUDY OF DELAY TACTICS AND THEIR IMPLICATIONS
Wang Zhao, Khaled Gaafar
I. INTRODUCTION
II. PROCRASTINATION IN OBSERVATION
Il. PROCRASTINATION IN MODEL
IV. ANALYSIS
lidati
Structure
lia:
Behaviour
Behaviour interpretation
Scenario analysis and testin;
V. POLICY DESIGN
VI. IMPLEMENTATION AND CONCLUSIONS
REFERENCES
APPENDIX 1: List of tables
APPENDIX 2: List of figure:
APPENDIX 3: Model
Procrastination Dynamics Zhao & Gaafar
Procrastination Dynamics:
A Study of Delay Tactics and Their Implications
Wang Zhao, Khaled Gaafar
European Master in System Dynamics, University of Bergen, Norway
Abstract - In dealing with compulsory or voluntary task, a common phenomenon always experienced by students
is procrastination. Procrastination causes not only substandard quality in outcome, but also results in tiredness and
high stress levels which is to mental well-being. In this paper, p is modelled through
a system d ics perspective to und its underlying hani: behind it. The model is based on
Sterman’s (2000) “Managing Your Workload” problem, as well as the authors’ own experience with
procrastination. It capitalizes on the concepts of perception delays, utility cost-based decision- tules, and crisis
management techniques procrastinators employ, with the goal of ling such p and
therein. The paper concludes that repeated misperception of an extra utility cost for starting work results in
procrastination, that such misperception is related to workload of the task, and that physical limit holds
procrastinator from working as fast as anticipated. We then move to recommend policies to overcome the wicked
problem that touches many people’s lives adversely.
Keywords — System Dy ics, Procrastination, E ion Formation, Decision Making.
1 INTRODUCTION
Procrastination derives from the two Latin words ‘pro’ and ‘crastinus’ which translate to ‘in favour of? and
‘tomorrow’ respectively. It thus takes a form of affinity to putting off a prescribed task, or a series of tasks to a
later date. In the information age, Moore’s law dictates that every 18 months we are bombarded with more and
more alluring distractions that could impair us from consistent performance over a specific task-horizon. It is
easy to fall victims of procrastination. It has been argued that some people procrastinate due to fear of failure,
concerns about ability, excessive work pressure (Tucker-Ladd 2006), fear of success (being handed more tasks
and the resulting increased workload) without sufficient reward, or perfectionism which leads to procrastination
(Seo, 2008). This paper an I, or at least ious type mainly in the academic context.
It is assumed that those people, even procrastinating, can perceive the rewards of the tasks they are postponing,
and still willing to take action for it. However, such effort to take actions keeps failing for some reason, i.e. they
de facto do nothing until the deadline draws very close. R: such prevalent i it is worth
noting that some university counselling services distribute hl which makes it
a worthy topic of study and analysis.
Il. PROCRASTINATION IN OBSERVATION
A typical procrastination starts with undertaking a task. The task doesn’t necessarily need to be compulsory.
Although in most cases tasks are attributed by some degree of compulsion, people also procrastinate with
voluntary plans. For instance, diet, exercise, or even the mission to stop procrastination. Procrastination in tasks
with deadline is easier to identify, but this doesn’t mean there is no procrastination in continuous tasks. Participants
in both kinds of tasks could be subject to procrastination (Akerlof, 1991).
High-achievers can also be procrastinators, and not rarely so. It may be argued that procrastination pays off,
judging against i dards (O1 ie, 2004). Despite social stigma against
procrastination, the outcome can be ‘very good’ which explains why some students invest the absolute minimum
time and effort, to maximize the output, which would give a feeling of triumph over the system. The drawback of
cramming is, however, that it impairs true learning achieved by more PP to
studying (McIntyre & Munson 2008).
Procrastination Dynamics Zhao & Gaafar
Procrastinators tackle a task by simply ‘doing nothing’, or it at least it seems so from an extemal perspective as
they may be mulling over the problem to solve. But as long as the task is undone, or still not given up as in the
case of voluntary personal initiatives, the person will knowingly decide to postpone it again until the very end a
recurrent decision-making process aimed at maximizing benefit and minimizing perceived cost.
Procrastinators finally become active in doing the task when there’s no more room for maneuvering around the
deadline. The logic is quite the opposite of Parkinson’s Law (Parkinson & Osborn, 1957) by assuming that work
contracts to get done within the time left for its completion! This could involve “pulling an all-nighter” to get the
task done, compromising quality. Tasks without deadline or a supervisor may fade into the background, and are
thus more difficult to observe. This suggests a ‘turning-point’, motivated primarily by the deadline that shifts the
attitude towards working and forsaking procrastination.
From the perspective of an external observer, the two most obvious indicators of one’s progress in task completion
are ‘working hours per day’ and ‘how many tasks are left untouched’. Suppose there is a task with deadline of 6
days, a typical behaviour may be observed below:
Working hours per day Remaining tasks
Hours per day
Tasks
Working
Figure I (lefi): Procrastinators always start late, and cannot maintain a constant productivity
Figure 2 (right): Tasks get solved just before deadline.
Obviously, procrastination does harm. Not only those who will make use of procrastinators’ outcome, but also
procrastinators themselves recurrently experience high stress levels (McIntyre & Munson 2008), which generates
a strong motivation to alleviate it, if not to completely overcome it. We believe that a thorough diagnosis of the
problem root-causes is the prerequisite of taking action, and we chose system dynamics modelling for this purpose.
System dynamics is developed by Jay Forrester as a tool to understand complex systems and design policy
(Forrester, 1961). Meadows et al.(1972) see system dynamics as a useful method to help people focus more on
the connections among pieces in addition to pieces themselves. It supposes that all systems have common elements
including accumulation, feedback, and delay (Beall et al., 2011), from which growth, decay, and oscillation can
be generated (Ford & Ford, 2009). It also enables people to reproduce all these patterns by building quantitative
model, so that they could devise and test policies to mitigate the problematic behaviour. Therefore, it is a perfect
means for studying complex systems, both as a diagnostic and a prescriptive tool. It provides the platform for
integrating theory and empirical evidence to explore key leverage points for policy design.
Il. PROCRASTINATION IN MODEL
Empirical findings enable us to formalize the mental model quantitatively. Following a typical system dynamics
approach, we define variables that can be captured from a frozen frame (paused state) of the system - stocks. First,
we assume a person who usually procrastinates has nothing but one assignment composed of a number of tasks
to finish within a specific period of time. Submission after the deadline will not be accepted, and all tasks are of
the same difficulty. Assume there are multiple tasks in the assignment, ‘tasks remaining’ could certainly be one
stock, while the factor affecting it namely ‘how many tasks the person does in one day’ could not be a stock but
a flow. Moreover, given these two factors, it’s also possible to calculate how much time is still needed for all
remaining tasks.
Procrastination Dynamics Zhao & Gaafar
Remaining tasks
Task kiling Yate
remaining time needed
Figure 3: People estimate time needed for task based on “how many tasks left” (remaining tasks)
When a person works long hours they begin to experience tiredness, and this tiredness reduces the hours worked
per day as the person finds it hard to focus for long hours. The assumption is if a person works for up to 10 hours,
no effect will be observed; but once exceeding, then hours worked per day will begin to decline due to tiredness,
the more the person spends beyond that point (10 hours in this case) the more tired they will get, until completely
stopping at 18 hours. Then they will have to rest. Tiredness results in another effect: lowered quality hours. This
means that when one is tired, the time they spend on a task is not as effective as when they are less tired.
Cumulated
working hours
Ff \
Cumulative qualty hours // \
81
Effect of tinfdness on
per day
working he
worked in
the past 18 hours
Ox” accumaation
Effect of Tirédness
‘on hour quality
Figure 4: Tiredness and its implications on number of hours worked and hour quality
Normal hour quality
S
In determining how many quality hours should a person spend on the
wil task, an underestimation mechanism results in the procrastinator
hour aitnesdes always desiring to work less hours than what is needed. The method
chosen to model this is adopted from Present worth analysis used in
accounting (i.e. net present value, NPV). There is a discount rate
which determines the degree of underestimation he employs, over the
time horizon of days left as shown in Figure 5.
Figure 5: Underestimation of needed quality working hours to finish a task
Desired working hours per day The procrastinator works based on a goal seeking loop, always
wee comparing how many hours he worked with the desired
hee wkng working hours he perceives he needs to work. however, this
per day ; 5 ‘
Adjustmegh in will not exceed the maximum possible working hours per day,
working hous perday Working hours per day base which was chosen to be 18 hours. This resonates with the
xt previously explained rule of halting all work after 18 hours of
= work the previous day.
om The more the person works, the less tasks are left to finish, and
ie ttle this adjusts the hours still needed (see Figure 7), but at a delay
as previously mentioned in figures 5 and 6. Below is the main
Figure 6: Goal-seeking mechanism of working hour balancing loop that aims to accomplish the assignment.
adjustment to meet desired level
Procrastination Dynamics
Zhao & Gaafar
Femaining tasks
uty
hours sillnaded
Dayd let
4 qualty
hrs sired
co
“Killing the task, closing the gap"
Si ‘working hours per day Yorking hours per day base
wing os pet day Wang hos par yb
‘time for woking
hours per day
Task kite
The procrastinator begins to feel anxious as he
is disillusioned with his estimate of how many
hours are needed to finish the task. This anxiety
is modelled here as schedule pressure, and as it
rises it results in a compromise to get things
done.
This is accomplished through lowering the
number of hours allocated per task, thus
lowering quality of the output, but increasing
task killing rate, which reduces tasks remaining
and accordingly adjusts the perception of quality
hours still needed (see Figure 8). Stress or
anxiety of the procrastinator were not modelled
explicitly here, yet their effects are clearly
witnessed in both the structure and behaviour,
see Analysis section.
Figure 7: Goal-seeking mechanism of working to finish the assignment
erating tasks
.
tours sled
by
as ss,
but gets things done’
—
i
\
Desiet wo
Peved quality
rs atl neadet
ia
7
tours per day
TF Sele
Moc voting ~~ pressure
hows paraay~ By
P
gjime fr wstng
Figure 8: Balancing loops that aim to kill remaining tasks
Whether start to work?
Usiity cost difference
Overall utility cost of
starting tomarrow
#
Overall uiilty cost of
Days left
Salience factor
Deadline
Porcaived quality
hours silll needed
Figure 9: Decision-making mechanism on whether to
start working or keep on procrastinating
“‘Kiling the task, closing tho gap" //
oe
ff
The two loops B2 and B3 both aim to kill
remaining tasks, yet B3 has less delays and thus
short-circuits B2, as it acts faster, when schedule
pressure is high enough.
The core mechanism underlying the problem
dynamics is the decision rule upon which a
procrastinator starts working.
The decision rule is Boolean (yes-or-no) and
based on Akerlof’s (1991) utility cost model of
procrastination (see Figure 9). If the perceived
utility cost of starting to work today exceeds the
perceived utility cost of starting tomorrow, the
person will always choose to postpone the work
to the next day, i.e. to procrastinate. The utility
cost could be considered as a kind of ‘bother’ or
‘consumption of energy in a tedious way’. In
this algorithm it is a function of time left to
complete the work, perceived quality hours still
needed to complete the task, and a salience
factor.
Salience factor reflects the key idea of Akerlof (1991), and
thus plays a central role in his decision-making mechanism. It
is based on an observation: people tend to attach extra
importance (salience) to affairs closer to them, in (including
but not limited to) spatial and temporal senses. For instance,
advices from a close friend affect decision more than those
from a stranger, a misfortune happening right tomorrow
makes people feel worse than one happening 10 years later.
Akerlof termed such
behavior’, and believed that utility coat (or more precisely,
perceived utility cost) of doing a task right away hassles a
person more than utility cost of doing the same task tomorrow,
because the former one is more immediate and deserves more
concern. In equation, such ‘over-perceiving’ is modelled by
multiplying the utility cost with a salience factor — which
therefore only exists in the equation for starting today (see
Figure 10).
Procrastination Dynamics
Zhao & Gaafar
Overall utility cost of starting today
= = quality hours still needed! starting
Days left
x(Salience factor + Days left)
Overall utility cost of starting tomorrow
_ (Perestved quality hours still needed
Days left 1
Figure 10: Utility cost equations
) x(Days left - 1)
Because of the salience factor, utility cost of
starting today will always exceed that of
tomorrow. Therefore, a person
pursuing maximum overall utility will always
choose to start tomorrow ~ and this is a decision
just for today. When tomorrow comes, the same
process will happen again, and the same
decision will be made again. The more time a
procrastinator has, the less costly it appears to
start work tomorrow versus today. However,
there must be one day (always very close to the
deadline), on which even taking salience factor
into consideration, the utility cost of starting tomorrow is higher than starting today, due to drastic increase in
“work per day’ caused by decrease in ‘days left’. Then it is time for procrastinator to start working. As a further
move based on Akerlof (1991), the salience factor in this study is interpreted to be a function of the size of the
assignment, the larger it is, the more burdensome it is perceived by the person.
On a
/
| eee
X
/
ona LBS
Figure 11: Reinforcing effect of tiredness on task
killing
As the deadline draws near, the perception of the actual needed
quality hours increases as it approaches its real value rather than
the underestimated magnitude (due to the discounting
mechanism, see Figure 6 above). As soon as the work finally
gets started, a crisis management mode is entered, whereby the
procrastinator suddenly drops everything else and realizes the
immense cost of further procrastination, thus decides to work.
The last important mechanism to point out is a result of working
long hours and the fatigue ensuing. It operates to lower working
hours the more tired the person gets. As working hours are
reduced, task killing rate drops which raises the desired working
hours. This pushes the person to work for more hours, seeking
the goal of ‘desired working hours’, which in turn accumulates
more tiredness. It is thus a reinforcing loop as seen in the
aggregated diagram to the left.
Based on these observations, the story may be summarized as a conditional goal seeking behaviour aimed at
accomplishing the assignment only when the costs of further procrastination exceed the cumbersomeness of
working on the assignment. This is compounded by the fact that the procrastinator underestimates the time
sufficiency to complete the assignment, thus waits longer. Once the person starts working, if time is insufficient
he will start spending less time per task by lowering the quality of the output. Moreover, the more hours he spends
per day leads to tiredness and hence a competition arises between the reinforcing loop R1 as well as B1 against
the balancing loops B2 and B3 (see Figure 12). Exogenous inputs are coloured yellow. A stock-flow diagram
representing the full-scale model is included in the documentation
tb tis
Desired voring
hours! say
“Killing the task, closing the gap"
whethor San to work
tity east
‘ifetence “Decision making”
i
+ he
Salience factor
erceved gualty
Remaining tasks
ute sill needed Be
ae
imu doy —$——
on house! day
ust
Taek ig ate
a
incotring
Figure 12: Aggregate causal loop diagram for the proposed theory.
Procrastination Dynamics Zhao & Gaafar
Accumulated tiredness stops the person from working too many hours per day
Closing the gap of remaining tasks by working more hours per day
Closing the gap of remaining tasks by putting less hours into one task
Accumulated tiredness reduces the quality of a working hour, making an hour’s work yield less
Table 1: Explanation of CLD
IV. ANALYSIS
Can the model reproduce the reference mode of behaviour? If so, does such reproduction come from a structure
sufficiently reflecting what happened in the real world? This chapter will discuss such issues through model
analysis. It will link the beh; al of I with the structure outlined in Chapter 3. The first
question asked in analysis is the model’s validity. With building model being a continuous process, validation
was considered in-progress from the very beginning of the modelling exercise.
Structure validation
Validation is first guaranteed by deliberate structure confirmation, where only the most convincing hypothesis
would be accepted and kept in structure. Units were carefully checked for consistency. Economics-based decision
tules are introduced in this model as a module to model a procrastinator’s decision to start working. Not like in
system dynamics field, people see a broader use of concepts such as cost or utility in the economic sphere, and
system dynamics model runs into unit troubles from time to time in dealing with economic equations. Instead of
forcing a modification on the i the authors d dall ions and the units that should be there,
and made sure the output from such module to be with proper unit or to be unitless.
The model represents a clear boundary of settings: an assignment involving certain number of tasks to do, a
deadline, and an overall difficulty for all tasks based on the average experimental results. Situations where tasks
have heterogeneous difficulty are more often used to discuss order placement, or prioritization, among tasks
(Brocas & Carrillo, 2001), therefore are not included herein.
Against the settings, the individual faced by an assignment is abstracted into 3 aspects: mental perception of tasks,
ivity, and physical condition. Mental shift resulting from perception of workload triggers a procrastinator
to work, i.e. to build up productivity (Akerlof, 1991). Working causes fatigue in the physical condition and in turn
impairs productivity. Productivity affects how fast the tasks are processed, which consequently changes the
person’s perception of workload. All said structures have been made explicit in Chapter 2.
The model passed several structure tests i ing: extreme diti test, i ion error test, d
consistency test, structure verification test, boundary adequacy test, and parameter verification test.
Behaviour validation
There are basically 2 obvious ‘problematic’ patterns in the reference mode: starting to work right before the
deadline, and unstable productivity. Both features can be found in a base run of the model, regardless of whether
the procrastinator chooses to pursue a high productivity or to be reluctant to work until the very end.
Procrastination Dynamics
Zhao & Gaafar
Mindset a) Eager to finish quickly
eae TT
Mindset b) Reluctant to work fast
Figure 13: Outcomes from a base run of the model, same background settings with different mindsets.
Table 2: Parameter settings for base runs
DIFFICULTY
MINDSET
TASK AMOUNT DEADLINE
Basel | 6 tasks 7 days
Base2 | 6 tasks 7 days
Futfilment ofthis assignment
os
ar
5 os
Days
= = Eager to finish —— Reluctant
Figure 14: Assignment fulfilment between the 2 mindsets
4 hours/task
4 hours/task
Once starts, work hard immediately
Once starts, work hard gradually
If the procrastinator chose to pursue a high
productivity after initializing the task completion
process, before which no progress had been
made, there would be a fast decline in remaining tasks.
This productivity was closely linked to the
‘Adjustment Time for working hours/ day’. The
shorter the Adjustment Time, the faster he would be
able to reach the goal of desired working hours per day.
However, working hard for too long exhausted the
person’s mental faculties and lowered the quality of a
working hour, as shown in Figure 13 (a). However, by
doing this, the person could get his schedule pressure
under control, avoid using too much the loop
‘Divesting Time’, and therefore got a higher fulfilment
of the assignment.
On the other hand, a person reluctant to work fast may only exhausted in the very end, but at the same time he
had to lower his work quality to get things done, resulting in a lower overall fulfilment as a cost. But for the
purposes of this model, consequences of lower quality such as getting low grade were excluded from the scope.
Under both mindsets, the simulated person only managed to start working when close to the deadline, and not
able to manage a steady productivity.
Behaviour interpretation
A closer examination of other variables helps to give more insights into the run. Taking the reluctant procrastinator
for example, as shown below, we selected 8 important variables to interpret the dynamics of procrastination.
Procrastination Dynamics Zhao & Gaafar
Effort needed and made
Hours
yey sed sunoH
10 1s 20 25 30 as o “s so ss so 6s 72 1s so
Days
1— Normally needed quality hours (Hours) 2~ Quality hours still needed (Hours)
~~ Perceived quality hours still needed (Hours) += Difficulty, quality hours per task (hoursitasks)
-s~ Perceived difficulty (Hourstasks) —s—Hours allocated per task in real time (Hoursftasks)
“7 —Cumulsted working hours (Hours) —s—Cumulative quality hours (Hours)
Figure 15: Behaviours produced by a base run of the model, same background settings with different mindsets
Initially, as the assignment was received, there was a steady increase in normally needed quality hours (line 1),
indicating how many quality hours a person ideally needed to spend on the assignment. Because we can only get
to know the exact difficulty of a specific task (line 4) by attempting to undertake it, if we estimate the quality
hours needed to finish (line 2), it can only be calculated using an empirically ‘guessed’ difficulty, namely
“perceived difficulty” (line 5).
Human beings, students included, are usually subject to misperceptions due to which they attach less importance
to less salient matters. Modelled through a ‘net present value’ algorithm, needed quality hours were perceived
much lower by a procrastinator, than they were at the very beginning (line 3).
We assume procrastinators don’t proactively reduce their tasks’ quality, even if they tend to postpone a lot (and it
is often the overestimation of how well a task should be done that holds procrastinators from starting (Seo, 2008).
The approaching deadline ‘squeezes’ the overestimated part, thus brings the task quality down to reality,
sometimes even less). Therefore, hours allocated per task in real time (line 6) kept identical to perceived difficulty
(line 5) until it was forced to be lowered.
As time went by, the procrastinator perceived more needed quality hours (line 3), and as described before, at a
turning point, he finally started to work. If there was any difference between the actual difficulty and the difficulty
he perceived, he started to adjust his perception as soon as he started a task. This process was reflected as the goal-
seeking behaviour of line 5 to line 4. Since line 6, line 2, and line 3 all based themselves on perceived difficulty
(line 5), all of them saw an upward shift respectively.
After starting to work, cumulative working hours (line 7) started to rise, so did cumulative quality hours (line 8).
They were coincided as hours allocated per task in real time (line 6) was still identical to perceived difficulty (line
5). However, as a cost of starting at a too low productivity, schedule pressure went uncontrolled in the final stage:
even if the procrastinator worked at maximum working hours per day (which is 18 hours/day in this case), he
couldn’t finish all tasks at a normal quality. From then on, hours allocated per task in real time (line 6) parted
from perceived difficulty (line 5), resulting in a distance between cumulative quality hours (line 8) and normally
needed quality hours (line 1) when deadline was finally app d. However, the p i suffered less
from physical fatigue: cumulative quality hours (line 8) was not much lower than cumulative working hours (line
7), indicating a very small loss in efficiency due to tiredness.
Scenario analysis and testing
Model robustness decides to what extent can the model be applied. The more robust the model is, the broader
phenomenon it can be used to explain. It is worth noting that only rational conditions may be used to test extreme
condition, i.e., we cannot give a 200-hour work load to a person within a one-week deadline, given the assumptions
about difficulty, productivity and maximum hour/ day.
Procrastination Dynamics Zhao & Gaafar
in this part is carried out on both the procrastinator side and the assignment side. We assume all
procrastinators have the same physical condition and behaviour pattern toward schedule pressure, so the only 2
variables that would change across procrastinators is how much extra importance they attach to salient events, i.e.
the salience factor, and their historical perception (experience) of difficult, based on which they form the
estimation of this assignment even before they start investing time and effort in it.
Scenario 1: various workloads with constant salience factor
Scenario | is designed to test the procrastinator’s reaction to change in assignment. Salience factor is set to 2.
3 hrsits 3 hrsits 3 hrsitsk 3 hrsits
TASKS 1 tasks 3 tasks 5 tasks T tasks 9 tasks
QUALITY HOURS 3 hrs 9 hrs 15 hrs 21 hrs 27 brs
DEADLINE DAYS | 7 days 7 days 7 days 7 days 7 days
Table 3: various workloads
Table 4: Simulation results with constant salience factor and various workloads
The simulation results show that if we take salience factor as a constant, no matter how much workload a
procrastinator gets, he would start from the same time point. Explanation could be found in how the person decides
to start. The decision rule governing the procrastinator, as shown below, is to compare the utility cost for today
and for tomorrow, if there is a decrease in utility cost for tomorrow due to less workload, there should also be a
decrease in today’s, for they are calculated from the same ‘Perceived quality hours still needed’, as shown in the
equations.
On the contrary, procrastinators develop tactics to dispose of the workload. As shown in the result, the
procrastinator simply increased every day’s working hours in response to assignment with more workload, which
10
Procrastination Dynamics Zhao & Gaafar
led to obvious burnout in the last 2 runs - a huge gap between ‘working hours per day’ and ‘quality hours per day’,
indicating a lowered hour quality due to cumulative tiredness. Along with this was the considerable drop in task
quality across assignments because of schedule pressure, which in turn caused increasingly unsatisfactory overall
task fulfilment, as shown in the last column.
Scenario 2: same workload with various salience factor
Scenario 2 is designed to test if the model can reproduce behavior patterns of people with different procrastination
levels, the model’s sensitivity to the salience factor which is the critical feature that distinguishes
procrastinators from the others. Akerlof (1991) used a salience factor of 2 in his discussion, and referred to it as
‘a small salience cost of beginning a project’. In this scenario, we first assumed salience factor to be constant and
test how change in workload would influence the behaviour; then we tested how, given a certain assignment,
would different salience factor influence the behaviour. In both tests, we assumed the person knew the difficulty
of assi from the very begi to elimi: the influence of misperception of difficulty.
Taking assignment 4 from scenario 1.1 as the base run (difficulty = 3hrs/tsk, tasks = 7) and salience factor from
0 to 4, we got the following runs:
Salience
factor
1
Salience
factor =
Salience
factor =
3
Salience
factor =
4
Table 5: Simulation results with various salience factor and constant workload
The simulation results show that it is the salience factor that is a determinant of when to start. With salience factor
equal to 0 or 1, the person showed no implication in procrastination, he starts working from the very beginning.
This is because with a too small salience factor, utility cost for starting today is always smaller than the increase
in total utility cost for starting one day later, so the procrastination option will not seem attractive. Via iteration,
the critical value for salience factor is around 1.5, regardless of the deadline and the workload, if we accept the
assumption that the daily disutility is proportional to the square of working hours in that day. This observation
also implies a possible leverage point for policy: can salience factor be reduced intentionally? Policy 2 in the next
chapter will discuss more on this.
Procrastination Dynamics Zhao & Gaafar
Scenario 2 compensates flaws in robustness that scenario 1 alone could implies: as our experience, we don’t
procrastinate on everything, as shown in scenario 1’s result. A new question is, are the two variables studied above
respectively, namely assignment and salience factor, independent? Commonly, we accept inclination to
procrastinate as an aspect of one’s personality configuration, but this doesn’t explain procrastinator’s ‘selective
procrastination’. In fact, procrastinators often p by doing hing else (‘side-tasks’), and these ‘side-
tasks’ used by them to escape from the ‘main-task’ must indicate a smaller salience factor - otherwise it would
not have been prioritized over the ‘main-task’. It creates room for further quantitative research on the such links,
especially when it comes to a certain industry or a certain group of people, where quantification of difficulty and
task amount could be more viable.
Scenario 3: limiting maximum working houi
Setting a run (difficulty = 3hrs/tsk, tasks = 7, salience factor = 2, maximum working hours per day = | 8hrs/day)
as base run, and reducing the maximum working hours from 18 hours/day to 12 (run 2.1), and finally to 9 working
hours/ day (run 2.2), we got the following results:
Table 6: Simulation results, Base run vs. Run 2.1 vs. Run 2.2
working hours per day a schedule pressure
— = _] nt 7 —_
In all scenarios, the procrastinator started at the same time, since the parameters governing his decision rule were
not affected by how many hours he can work/ day, rather by the time left, utility cost, and tasks remaining.
The maximum working hours’ limit did affect the quality of the output, however, since loop B3: "Haste makes
waste, but gets things done" activated to kill tasks, faster than the original loop B2 due to the time constraint
placed on the procrastinator. Yet the effects of this loop in run 2.2 were more prominent than in the base run. Run
2.2 delivered the worst quality of work.
The results above confirm the aforementioned hypothesis, that work began at the same time, with the working
hours being capped, loop B2 played caused a reduction in quality hours per task, reflected in the graph of run 2.2
falling short of both the base run and run 2.1. The key driver behind loop B2 is schedule pressure, confirmed by
the graph above. Run 2.2 experienced the highest peak due to the large disparity between desired working hours
per day, and maximum working hours per day.
Considering the implications of runs 2.1 and 2.2, it does not come as a surprise that overall fulfillment of the
assignment was the lowest for run 2.2. This measure compares cumulative quality hours actually spent on the
assignment to the normally required working hours (calculated from actual difficulty of the assignment and
number of tasks required).
The base run p ip the assi; with an 84% quality, meaning that based on average
standards he would not get the maximum grade he would have fulfilled had he started earlier. This is debatable of
course if the procrastinator was especially talented, or well informed in the topic of the assignment; and thus this
quality measure assumes that the procrastinator’s abilities, and the difficulty measure (number of quality hours
required per task) are both reflective of each other.
Run 2.1 achieved a 73% quality, and finally run 2.2 achieved a plummeting 65%. In real life a ‘successful’
procrastinator balances several factors, namely his abilities, the maximum number of hours he is willing to invest
once he starts, and the grade he desires for the Yet the ‘not so I' procrastinator would be
aptly represented by run 2.1 and 2.2.
The results make intuitive sense because if you start late, but not willing to go the extra mile sacrificing some
sleep time or other activities, the quality of your output will suffer, and so would your grades.
Procrastination Dynamics Zhao & Gaafar
V. POLICY DESIGN
Analysis of unfavorable implications from procrastination gives us sufficient ground to talk about what we can
do about it. Even in cases where p i ly give out ptable output as long as getting some
“side-task’ done as a fé ible by-product of p i they still experience both mental strain and physical
exhaustion. Observing the refé mode of behavior (as shown in Figure 16), if we assume a person can work
for 8 hours with full quality each day, the area of At+B+D would be the workload that he could have normally
done within the deadline, while B+D reflects the required quality hours for the assignment. Procrastination, from
a perspective of mere behavior, is to transfer a part of work from D to C, while using D for something else. Our
wishful thinking of the ideal case is to use only B and D for the work, without occupying C.
Figure 16: Procrastination as a type of time arrangement with high concentration in the end
However, such ‘optimal arrangement of time’ couldn’t simply be achieved by ‘ordering the procrastinator to do
so’. All discussions above have shown that such a behavior of pattern has an origin rooted deeply in
procrastinator’s underlying system of making decisi As long asap i is asked to do some task and
has a period of ‘free time” "to work on it, he or she will automatically produce such pattern. It may be argued that
an of strict discipline could the to pro inate, but such external intervention
is not always available, and living under long-lasting surveillance may y bring considerable unfavorable side-effects.
Policy 1: Splitting up the task
A reasonable policy suggestion could be ‘to break down the task into smaller ones. Since procrastinators show a
better performance (both in overall fulfillment and in tiredness) when they are faced by a smaller assignment (as
shown in Table 2 in Chapter IV - Analysis, the smaller a task is, the less likely its quality will be lowered in the
end), if we can divide a larger assignment into 2 or more smaller ones, it is le to predict p i
will do better in each and thus show a more favorable overall fulfillment. A policy scenario is thus designed to
test whether “chopping large assignment up” will make a difference to the overall fulfillment.
Taking assignment 4 from scenario 1.1 as the base run (difficulty = 3hrs/tsk, tasks = 7), a constant salience factor
of 2, and splitting up the task into 2 smaller equal tasks (scenario 3.1), and another time unequally (scenario 3.2),
yielding the following results:
working hours per day quality hours per task schedule pressure
igure 17: Scenario 3 results
These scenarios explores what would happen if a pi i did not fund lly change his perception of
utility, yet took action by placing an interim deadline on himself, once fairly, and a second time with a more
spaced-out attitude towards the deadline, meaning that the first deadline was a smaller bit of the total workload.
This notion has been explored thoroughly by Ariely and Wertenbroch (2002) where they conducted field studies
to determine if interim deadlines helped improve performance. One of their findings was that suboptimal splitting
of tasks yielded lower performance than evenly spaced deadlines; it is thus assumed that scenario 3.1 is an external
deadline, while scenario 3.2 is one internally set by the procrastinator, suboptimally.
Procrastination Dynamics Zhao & Gaafar
This model agrees with their results, as breaking up the task reduces the maximum schedule pressure incurred
throughout the assignment. When the task is split equally the overall performance is better than when adopting a
more lax approach to the interim deadline. Leaving more work to be completed before the 2" deadline, as opposed
to fair splitting, leads to B3 activating to finish the task before the 2™ deadline, lowering quality of output. This
is shown in figure above comparing the 2 scenarios. The person had to work for longer hours during the last 2
days, leading to less hours spent on each task due to higher schedule pressure. This resulted in an overall lower
quality of the assignment.
Policy 2: Incentive factor and di: ing rate adj
It has been outlined that the salience factor is the main reason a procrastinator delays the start of work, yet what
would happen if a counterweight was placed? An incentive factor which depicts the rewards of starting today?
A new factor was added to the equation of utility cost of starting tomorrow as follows:
Perceived quality hours still needed
Overall utility cost of starting tomorrow = 1
a e * Days left
x (Days left~ 1+ Incentive factor)
Results showed that it is not enough, because of the discounting in determining the perceived quality hours needed.
This means that to overcome procrastination one not only needs to incentivize, but also to thoroughly assess the
task requirements beforehand in order to start strong and this has prominent policy implications as will be
discussed in the following section.
The graph below shows the results of adding an incentive factor of 3, as well as reducing the discount rate to 0.1.
This means that the Perceived quality hours still needed will be more in line with the actual Quality hours still
needed.
Less hours are worked towards the deadline, quality is maintained throughout, there is minimal schedule pressure,
and finally the outcome is of higher quality than the base run.
working hours per day quality hours per task schedule pressure overall fulfillment of assignment
Figure 18: Scenario 4 results vs. Base Run
VI. IMPLEMENTATION AND CONCLUSIONS
As di d before, 'cl up' would be a useful policy, but a policy can be effective only with
proper enforcement, which is hardly what we can expect from a procrastinator. We couldn't expect a procrastinator
to be 'sel ive’ when assi; them equally d tasks. The main force that drives a
procrastinator to work is a nearer drawing deadline, and a deadline can only be a deadline if there is some penalty
upon missing it. In other words, what a procrastinator fears is not the deadline itself, but the consequence of failing
to meet it. Such consequence often comes from those who supervise the procrastinator. Supervisors’ active action
in the process of procrastination will make both parties better off.
This “Shifting burden to intervention” (Braun, 2002) means to rely on external help to solve the problem rather
than making change inside the system. It is usually referred to as a bad policy, with negative long-term
implications. However, before judging a policy to be bad, one needs to define the boundary of the system in
question, in order to tell ‘external’ from ‘internal’. Procrastination, in the first glance, happens only to the
procrastinators, having nothing to do with others, so p i are often d to ‘change th ves”
But since low-quality works would not do any good to their ultimate users, stakeholders of this i issue should
include the supervisors of the work, or other students involved in the same task. Policy based on interpersonal
dynamics therefore can take place.
Procrastination Dynamics Zhao & Gaafar
Promising to a group of people a certain progress before a specified time can create a positive pressure, which can
be used to counter the extra utility cost of starting to work right now. Thus the self-esteem of the procrastinator
would be improved upon better productivity, which would drive a procrastinator to start early. This is also
effective when it comes to tasks without deadlines (like term projects), in such conditions to get enrolled in a
group and discipline oneself with the group’s schedule is considerably useful. Supervisors could also set micro-
deadlines, halfway through the assignment, to slice a ‘huge’ procrastination into two smaller ones to guarantee an
acceptable progress, as discussed in one of the policies.
Moreover, to make a ‘one-time’ decision is always easier than to regulate oneself for a long time. For
procrastinators, if they can choose to do a task in a way other than doing alone, it’s highly suggested to choose so.
Similar tactics include to set fixed ‘time point’ in one’s daily life. For instance, if you choose to attend a lecture
next morning, it’s less likely you will stay up until very late tonight.
This paper aimed to explore the drivers underlying procrastinating behavior, and pointed out to the key leverage
areas to improve performance. It utilized System Dynamics as a tool for analysis and policy design. What the
authors conclude is that procrastination is a systemic problem affecting a multiple people, rather than a flaw of
one's moral character; misperceived extra importance attached to salient matters is also an important factor
constituting the stability of our world. Generally speaking, it is the connection with people that gives us a better-
founded reflection of the world and eli all possible misp are d to reach
out to people surrounding them, to solve the problem systemically, : and to Tead a systematically better life.
Procrastination Dynamics Zhao & Gaafar
133
14.
REFERENCES
Akerlof, G. A. (1991). P ination and i The ican Economic Review, 81(2), 1-19.
Ariely, D., & Wer h, K. (2002). P ion, deadlii and performance: Self-control by
precommitment. Psychological science, 13(3), 219-224.
Beall, A., Fiedler, F., Boll, J., & Cosens, B. (2011). Sustainable water resource management and
participatory system dynamics. Case study: Developing the Palouse basin participatory model.
Sustainability, 3(5), 720-742.
Braun, W. (2002). The system archetypes. System, 2002, 27.
Brocas, I., & Carrillo, J. D. (2001). Rush and procrastination under hyperbolic discounting and
interdependent activities. Journal of Risk and Uncertainty, 22(2), 141-164.
Ford, A., & Ford, F. A. (1999). Modeling the environment: an introduction to system dynamics models of
environmental systems. Island press.
Forrester, J. W. (1997). Industrial Dynamics. Journal of the Operational Research Society, 48(10), 1037-
1041.
McIntyre, S. H., & Munson, J. M. (2008). Exploring cramming: Student behaviors, beliefs, and learning
retention in the principles of marketing course. Journal of Marketing Education, 30(3), 226-243.
Meadows, Donella H; Meadows, Dennis L; Randers, Jorgen; Behrens III, William W (1972). The Limits
to Growth; A Report for the Club of Rome's Project on the Predicament of Mankind. New York: Universe
Books.
Onwuegbuzie, A. J. (2004). Academic procrastination and statistics anxiety. Assessment & Evaluation in
Higher Education, 29(1), 3-19.
Parkinson, C. N., & Osborn, R. (1957). Parkinson's Law, and Other Studies in Administration: And Other
Studies in Administration. Houghton Mifflin.
Seo, E. H. (2008). Self-efficacy as a mediator in the relationship between self-oriented perfectionism and
academic procrastination. Social Behavior and Personality: an international journal, 36(6), 753-764.
Sterman, J. D. (2000). Business dynamics: systems thinking and modeling for a complex world
Tucker-Ladd, C. (2006). Psychological self-help,(Chapter 4: Behaviour motivation and self-control)
viewed 2 March 2009.
Procrastination Dynamics Zhao & Gaafar
APPENDIX 1: List of tables
Table 1: Explanation of CLD 7
Table 2: Parameter settings for base runs
Table 3: various workloads
Table 4: Simulation results with constant salience factor and various workloads
Table 5: Simulation results with various salience factor and constant workload.
Table 6: Simulation 2 results, Base run vs. SC 2.1 vs. SC 2.2
APPENDIX 2: List of figures
Figure | (left): Procrastinators always start late, and cannot maintain a constant productivity............ 3
Figure 2 (right): Tasks get solved just before deadline.
Figure 3: People estimate time needed for task based on “how many tasks left” (remaining tasks).
Figure 4: Tiredness and its implications on number of hours worked and hour quality...
Figure 5: Underestimation of needed quality working hours to finish a task
Figure 6: Goal-seeking mechanism of working hour adjustment to meet desired level
Figure 7: Goal-seeking mechanism of working to finish the assignment
Figure 8: Balancing loops that aim to kill remaining tasks
Figure 9: Decision-making mechanism on whether to start working or keep on procrastinating.......... 5
Figure 10: Utility cost equations 6
Figure 11: Reinforcing effect of tiredness on task killing.
Figure 12: Aggregate causal loop diagram for the proposed theory. 6
Figure 13: Outcomes from a base run of the model, same background settings with different mindsets.
8
Figure 144: Assignment fulfilment between the 2 mind: 8
Figure 15: Behaviours produced by a base run of the model, same background settings with different
mindsets
Figure 16: Procrastination as a type of time arrangement with high concentration in the end
Figure 17: Scenario 3 result:
Figure 18: Scenario 4 results vs. Base Run
Procrastination Dynamics Zhao & Gaafar
APPENDIX 3: Model documentation
Formulation and comments: Units
‘Tasks and Assignment
Remaining tasks(t) = Re tasks(t- dt) + - i *dt=0.001 Tasks
The stock of tasks to do, declines as there is a Task killing rate, and arises from Assignment input. Initially there is no task, but initial
introduced to avoid zero d. mn.
‘Assignment input = PULSE(7, 1,200) Tasks/Day
Inflow of the stock, an exogenous parameter, reflecting th
ignment, which comprises several tasks. The step function ensures the
inflow only lasts for 1 day.
= Quality hours per. per taskin real time Tasks/Day
Outflow of the stock, decided by daily working hours and how many hours the person would allocate into a task, whi d by the influence
of anxiety from the reference hours allocated per task.
“Difficulty, quality hours per task" =3 Hours/Task
An exogenous parameter, calibrating the difficulty of the assignment by how many quality hours a single task needs (e.g. how many hours the
professor wants the student to allocate to a task). Itis presumed that all tasks in one assignment are of the same difficulty. Quality hours
working hour with full outcome.
Reference hours allocated per task = "Difficulty, quality hours per task" Hours/Task
Itis assumed that people are d
ig tasks in full qual
hey will spend as many hours on one task as they are required to spend (e.g. by the
professor). Therefore, reference hours allocated per task equals to difficulty.
Hours allocated per task in real time = Reference hours.
Hours/Task
task
When schedule pressure level is high, people tend to lower the quality of their tasks in hand to meet the deadline on ime, the real
quality hours they put into one task will be subject toa modification by schedule pressure, represented by a norm:
Normally needed quality hours(t) = Normally ity hours(t- dt) + ity hours input -
earance ity hours for next assi )*dt=0.001 Hours
The stock of quality hours normally needed by the remaining tasks. It arises as assignment being placed, and will not decline until the entire
is finished. Quality pent in the assignment are counted elsewhere. The stock is
zero division.
Normally it input = Assig input*Dit ity hours per task”
‘Aco-flow of Assignment input, indicating that incoming assignment (tasks) will lead to the increase of needed quality hours.
converting rate.
earance of normally needed quality hours for next assignment = IF(Iffinished=0) THEN 0 ELSE (10000) Hours /day
When one assignment is done (Iffinished = 1), this stock will be evacuated quickly (10000 ho
's/day) to get ready for next assignment. This
mechanism is designed to simulate consecutive assignments in one single run.
Difficulty Perception
Historically perceived difficulty = 3 Hours/task
Reflecting the overall difficulty the person perceived from p nents, used to
difficulty.
= Perceived dil = dt) + (Adj ived difficulty) *dt = Historically perceived difficulty Hours/task
Ittakes time for people to perceive how difficult this current assignment is. A first order information delay is therefore introduced to represent this
process and the delay therein. Only when the person has started with the assignment can he or she really know how difficul
person will rely on his previous experience to form expectation.
Ad in perceived difficulty = ("Difficulty, quality hours per task"-Perceived difficulty)/Adj time for perceived difficulty*If
Hours/tasks/Days
started
‘The adjustment part for the above-menti
ned perceiving process. Only when the person has started with the assignment can he or she really know
how difficult itis. A global indicator If started is therefor
introduced to control the beginning time.
Adj time for perceived difficulty = (1/12) iN)
Procrastination Dynamics Zhao & Gaafar
Formulation and comments: Units
Time for people to perceive the assignment's difficulty. it usually doesn't take a long time, soa relatively small number (1/24 day, or 1 hour) is
assigned.
Global Indicators
If finished = IF(Remaining tasks>0.15)THEN 0 ELSE 1 Unitless
Aglobal indicator, elicited from Remaining task, indicating where the current assignment has been finished. 0.15 is introduced instead of 0 to avoid
thenumerical long-tail effect.
Ifstarted = IF(If to trigger >0)THEN(1)ELSE(0) Unitless
icited from the block representing mechani cating whether the person has started with the assignment.
The blockis explained blow.
Mechanism to start working
Deadline = 0+STEP(7, 1) Days
Aspecific date (counting from the begi
n) on which the assignment should be turned in.
Days left = MAX(0.01, (Deadline-TIME)) Days
Dil
ference between current date and dead!
ne. The max function ensures that Days left remains non-negative regardless of the current date.
Quality hours still needed = Remaining tasks *Perceived difficulty Hours
Calculates how many hours will be used to finish the r
mai
ng tasks. This variable calibrates ‘how much work the person should have been able to
perceive/ take in to consideration, without n
= ity hours stil is e/ (1+ Dis ays left-1)),
sperception.
Hours
Quality hours still needed)
Calibrates the person's perception of the above-mentioned ‘Quality hours needed’. Human being tend to attach more weight to salient event. An
assignment with a deadline of 7 days will be perceived as a much smaller one in the very beginning, and the perceived weight will rise as time
passes by. A formula used in accounting to calculate present value from a future value is used here to figure out how much work the procrastinator
feels he or she has as total
Discount rate = 1 Unitless
rrowed from accounting, ing the extent of mii person has when perceiving a future event.
Salience factor = 2 Unitless
factor calibrating how much more importance a person will attach to a salient event. From Akerlof (1991). In the model, Salience factor is linked
to task amount by a linear function, as an alternative assumption that a person inclination to i faced
= (Percei it il jence factor*1+(
Unitless
quality hours still needed/Days left)*2*Days left
From Akerlof(1991), procrastinators attach more importance to salient events. When comparing utility costs of
starting work today or tomorrow, while non-procrastinators choose to start early, procrastinators, because of an
additional utility cost attached to today, tend to start later.
Incentive factor = 3
This is the factor that increases the cost of starting tomorrow, such that it acts as an incentive against procrastination.
ility cost. i = (Perceived qualit i L.01)-1))*2*(MAX(Days left,
Unitless
L01)-1+ Incentive factor)
Ibid,
Utility cost difference =
Calculate the difference between the above 2 utility costs.
If to trigger = IF(Utility cost difference<0)THEN(1)ELSE(0) Unitless
If the utility cost of starting tomorrow finally exceeds the utility cost of starting today, it will trigger the procrastinator to start wor
Iever triggered = Ifever triggered(t) = IFever triggered(t- dt) + (If to trigger) *dt = 0 Unitless
Once triggered to start wor ill keep worki ‘This stocked maintains the triggered status.
Productivity Adjustment
Desired working hours per day = Perceh it i Hours /days
Having started to work, the person wants to solve all the tasks in the remaining days. We use even distribution here because in
relatively short
period, it's acceptable to assumesuch. If the period is longer, algorithm for calculating annuity in accounting could be adapted here.
Procrastination Dynamics Zhao & Gaafar
Formulation and comments: Units
Ad time for working hours per day = 0.1 Days
Once starting to work, i. getting his or her hands around the work, the person will adjust his productivit ; because of no
form salience factor.
Max working hours per day = 18 Hours/days
Maximum working hours a person can have in one single day.
we i per day base<Max working hours, ired working
: Hours /days /days
hours per i j time E(O)
As long as working hours per day (base) hasn't reached maximum of 18 hours per day, it will be adjusted toward the desired working hours per day.
Working hours per day base(t) = Working hours per day base(t- dt) + (Adjustment in working hours per day) *dt Hours /days
Working hours per day is represented by a stock, since it takes time to change. It is ‘base’ because a stock cannot turn to 0 immediately after all tasks
finished,
Schedule pressure = Desired working hours per day/Max working hours per day*(1-If finished) Unitless
sh all the tasks. If a person feels he or she cannot finish everything ever
Pressure coming from not being able to
hours in all the rest days, schedule pressure will be over one.
Effect of schedule pressure on hours allocated per task = GRAPH(Schedule pressure) Unitless
When schedule pressure reaches a certain level, the person wi quality of the tasks to get thing: done by reducing
quality hours per task.
‘Working Hours per Day
Qumulative working hours(t) = Cumulative working hours(t- dt) + (Working hours per day - Qlearance of cumulative
working hours for next assignment) * dt = 0.001 Mours
Stock orking hours up until from workin; p (which is the action of production) and gets quickly evacuated
only after the assignment is finished. Initial value set to 0.001 to avoid zero di
earance ive working assignment = is THEN 0 ELSE (10000) Hours/days
When one assignment is done (Iffinished = 1), the stock of cumulative working hours will be evacuated quickly (10000 hours/day) to get ready for
next assignment. This mechanism is designed to simulate consecutive assignments in one single run.
Working hours per day = Working hours per day base*(1-If finished) Effect oftiredness on working hours per day Hours/days
Working hours per day observed from external, taking the effect of tiredness into account. Introduction of If finished guaranteed it will drop to zero
rightafter all tasks are finished.
Tiredness / Labor Burnout
Working hours in the past 18 hours(t) = Working hours in the past 18 hours(t- dt) + (Tiredness accumulation - Tiredness
Hours
elimination) *dt = 0
The stock of working hours in the past 18 hours. It is assumed that people's level of tiredness is based on how many hours they have worked in the
past 18 hours. Too many working hours will affect working hours per day (forced rest from physi ition) and hour quality ( one
hour's working).
TH ion = Worki y Hours /days
Working itself builds up tiredness.
Tiredness elimination = DELAYN(Tiredness accumulation, 0.75, 60, 0) Horus /days
Working hours happening more than 18 hours ago will be subtracted from the stock of tiredness. This is done by an outflow which is 18 hours (0.75
day) high order delay of the inflow. High order makes it an exact delayed reproduction of the inflow (a translation delay).
Effect of Ti r quality (Workin in the past 18 hours) Unitless
Tiredness influences working hour's outcome. If there are more than 7 working hours in the past 18 hours, hour quality starts to drop. And hour
quality will be dramatically lowerif there are more than 13.
Effect of tiredness on working hours per day = GRAPH(Working hours in the past 18 hours/18) Unitless
Tiredness influences decision on working hours per day. Ifthere are more than 7 working hours in the past 18 hours, physical condition will stop
theperson from putting as many hours into tasks as before, ie, a forced rest.
Quality Hours
‘hours(t- dt) it ‘per day - Clearance ive quality
‘hours(0)
Hours
hours for next assignment) * dt = 0
20
Procrastination Dynamics Zhao & Gaafar
Formulation and comments Units
The stock of accumulated quality hours spent on tasks up until now. It raises from quality hours spent per day, and only gets quickly evacuated after
the assignment is finished. Initially itis 0.
Quality hours per day = Normal hour quality *Btfect of Tiredness on hour quality*Working hours per day Hours /day
Inflow of the stock accumulated quality hours. When there is not much tiredness, a working hour isa quali However, when
tiredness is built up to a high level, quality hour is subject to a modification, therefore lower than a working hour.
Normal hour quality = 1 Unitless
When there is not much accumulated
redness, a working hour is a quality hour.
Qearance of cumulative quality hours for next assignment = IF(If finished=0) THEN 0 ELSE (10000) Hours /day
When one assignment
done (If finished = 1), the stock of cumulative quality hours will be evacuated quickly (10000 hours /day) to get ready for
next assignment. This mechanism is designed to sit
sal time = MAX( fs it ;, 0.0001, it 3
Unitless
0001)
Fulfillment, or overall quality of this assignment is calculated by the ratio between Normally needed quality hours (required by the assignment) and
Cumulative quality hours (spent by the person). The ratio will be lower than 1 only when the person decided to lower his or her quality when faced
by high anxiety.
21
