The 34" International Conference of the System Dynamics Society
17-21 July, 2016; Delft University of Technology, Delft, Netherlands
The Shifting the Burden Archetype:
A Workforce and Task Backlog Management Game
Seniha Zeynep Giiran and Hakan Yasarcan
Industrial Engineering Department
Bogazici University
Bebek — Istanbul 34342 — Turkey
szeynepguran@gmail.com
hakan.yasarcan@boun.edu.tr
Abstract
We first develop a workforce and task backlog management model based on the
shifting the burden archetype. The model involves the corresponding solution archetype in
addition to the problem archetype. Secondly, we develop a game based on the model.
Finally, we present an experimental design in this paper. We plan to randomly assign the
participants into three separate test groups. The first group will be guided towards the
problem archetype. The second group will be guided towards the solution archetype. The
third group will be guided towards a balanced approach that consists of both the problem
and solution archetypes. We expect that the participants who will be guided towards using
the solution archetype will improve their performances while the participants who will be
guided towards using the problem archetype will have a deterioration in their
performances. In a follow-up paper, we plan to summarize the results that will be obtained
from the experiment. The motivation for this study is to demonstrate the long term benefits
of systems thinking and system dynamics in decision making. We hope that such a
demonstration will promote systems thinking and system dynamics and increase the
willingness of the decision makers in applying high leverage policies.
Keywords: Decision making game; problem archetype; shifting the burden; solution
archetype; systems archetypes; systems thinking; task backlog; workforce management.
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -1-
Seniha Zeynep Giiran and Hakan Yasarcan
1. Introduction
System dynamics (SD) is a simulation based approach for modeling, analyzing, and
improving complex dynamic systems consisting of accumulation processes, feedback
loops, delays, and nonlinear relationships (Barlas, 2002; Barlas and Yasarcan, 2006;
Forrester, 1961; Sterman, 2000; Yasarcan, 2010 and 2011). Jay W. Forrester established
SD towards end of 1950’s. After that, many books had been written describing models that
are constructed using the SD methodology. Some of these publications such as Industrial
Dynamics, Urban Dynamics, and World Dynamics attracted the attention of academia and
business world in the 1970’s. Limits to Growth (1972) is another book that describes an SD
model and discusses its dynamics. The book is about economic and population growth of
the world under finite resources. It created a strong debate and became the subject of many
studies. As a result of the continuing attention on the issue, the updated versions of the
book are published several times, the last one being in 2004.
Systems Thinking (ST) became popular after the publication of Peter Senge’s
bestseller book, The Fifth Discipline: The Art and Practice of the Learning Organization,
in 1990 (Papucar-Caceres A., 2008; William D. Miller, 2012). Both ST and SD aim to
address complex systemic dynamic feedback problems. The main difference between the
two is that the product of an ST study is a conceptual model; however, the product of an
SD study is an operational simulation model that is analyzed mostly numerically and
sometimes analytically (Sterman, 2002). Thus, ST overlaps only with the conceptual phase
of SD (Forrester, 1994).
The span of applications of SD and ST includes Supply Chain Management, Project
Management, Diffusion Processes, Commodity Cycles, and System Archetypes, but not
limited by them.
System archetypes — balancing process with delay, limits to growth, shifting the
burden, eroding goals, escalation, success to successful, tragedy of the commons, fixes that
fail, and growth and underinvestment — aim to give insight to the managers about the
existing dynamic problems in their organizations so that they can understand and solve
those persistent problems that are systemic in nature (Senge, 1990). A system archetype
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -2-
Seniha Zeynep Giiran and Hakan Yasarcan
encompasses both the problem archetype and the solution archetype of the related problem.
The problem archetype involves the non-systemic solution to the problem that creates
unintended consequences, whereas the solution archetype involves the systemic solution
that aims to minimize the unintended consequences that appear in the long term (Senge,
1990; Wolstenholme, E.F, 2003; Wolstenholme, E.F, 2004).
Although SD has an extensive application area and there are many influential and
highly cited publications resulting from SD studies, the field is perceived as stagnating
(Forrester, 2007; Barlas, 2007). “At present, with system dynamics on a rather aimless
plateau, the field seems to be catching its breath. The field is pursuing practices of the last
many decades, but there is little evidence of a strong reach into new territory.” Forrester
(2007). Some of the important factors that are listed by the experts as an explanation for
the stagnation are lack of education, inadequate system dynamics tools, neglecting the
importance of implementation phase of system dynamics projects, and lack of intense
debate (Forrester,1994; Richardson 1996; GréBler 2007).
Kim and Senge (1994) stated that the penetration of ST in main stream management
practice is much lower than the recognition of “interdependency and change” (i.e.,
dynamic complexity) by managers. One of the reasons for the stagnation in and the low
penetration of SD/ST can be explained by the reluctance of the decision makers in
applying high leverage policies as they usually imply a worse before better results
(Sterman, 2001).
It is suggested in the literature that knowing systems thinking and its conceptual tools
such as system archetypes and casual loops give a framework to the decision maker. There
are studies indicating that having a mental model of the underlying structure of a dynamic
problem improves performances of the decision makers in dealing with that problem
(Senge, 1990; ). Some studies are based on teaching system dynamics. System archetypes
were also taught as a part of one such training program ( Schwaninger, 2003 ). However,
no performance data was collected in those studies (Cavaleri and Sterman, 1997).
Therefore, there is a gap in the literature.
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -3-
Seniha Zeynep Giiran and Hakan Yasarcan
Aiming to fill in the aforementioned gap, we first develop a workforce and task
backlog management model based on the shifting the burden archetype. The model
involves the corresponding solution archetype in addition to the problem archetype.
Secondly, we develop a game based on the model. Finally, we present an experimental
design in this paper. We plan to randomly assign the participants into three separate test
groups. The first group will be guided towards the problem archetype. The second group
will be guided towards the solution archetype. The third group will be guided towards a
balanced approach that consists of both the problem and solution archetypes. We expect
that the participants who will be guided towards using the solution archetype will improve
their performances while the participants who will be guided towards using the problem
archetype will have a deterioration in their performances. In a follow-up paper, we plan to
summarize the results that will be obtained from the experiment. The motivation for this
study is to demonstrate the long term benefits of systems thinking and system dynamics in
decision making. We hope that such a demonstration will promote systems thinking and
system dynamics and increase the willingness of the decision makers in applying high
leverage policies.
2. Workforce and Task Backlog Management Model
Kunsch et all. (2007) created quantitative SD models of real-life cases, which can be
explained by Senge’s archetypes. One of the selected archetypes is shifting the burden. In
Kunsch et all.’s business case, there is a company aiming to meet the demand of their
customers (see Figure 4 in Kunsch et all., 2007). A decision maker can take two actions in
order to satisfy the customer demand: “hiring external experts” or “training experts”.
Hiring external experts is quick, but it is comparatively more expensive. The other option,
training experts, takes time, but it is comparatively cheaper. In this model, hiring external
experts activates the feedback loop for the problem archetype as it represents the short term
solution; on the other hand, training experts activates the feedback loop for the solution
archetype as it represents the long term systemic solution. Inspired by Kunsch et all.’s
case, we constructed a detailed model of workforce and task backlog management. There
are four main sub-structures of the model: Task completion structure; internal expert
structure; external structure; and cost structure. These structures are explained in the
following sub-sections and the corresponding equations are given in the appendix.
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -4-
Seniha Zeynep Giiran and Hakan Yasarcan
2.1. Task Completion Structure
Capacity in regard to internal experts is called as internal processing capacity
whereas capacity in regard to external experts is called as external processing capacity.
Note that our model is a discrete time model. Hence, all variables are updated every
simulated week. Tasks arrive weekly; we assume tasks are normally distributed with a
mean of 1000 and a variance of 40,000. If the task arrival rate is greater than total
processing capacity, backlog level increases. On the other hand, if the total processing
capacity is greater than the task arrival rate, backlog level decreases. Note that backlog
level cannot be less than zero. Accordingly, if backlog is zero and the total processing
capacity is greater than the task arrival rate, idle capacity occurs. Task completion structure
is presented in Figure 1.
oe Task Completion Structure 8
intemal processing
= ‘Accumulated total processing ‘Accumulated total
pacity t minus 1 propessing capacity
“s . Pon
Extemal processing capacity va
O— oe Acura toa
Weekly capacity “Task Completion tasks processed ide capacity
Rate’ ‘t minus
“Accumulated total
task processed
Backlog of tasks
Backlog of tasks’
—)
Tine to 1]
process
Seed
Stdev of task arval rate
Figure 1. Task Completion Structure
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game Se
Seniha Zeynep Giiran and Hakan Yasarcan
2.2. Internal Expert Structure
Trainee Hiring Decisions is one of the three variables controlled by the decision
maker (i.e., participant). Trainees joins the workforce (i.e., enter Internal Experts stock)
after completing a four week training program. Trainees are required to get a ten hour one-
to-one training from the internal experts each week for four weeks. Internal experts work
40 hours per week. However, they can dedicate at most half of their weekly working hours
(i.e., 20 hours) for one-to-one training. Thus, each internal expert can at most train 2
trainees per week. If the trainees are more than two times of the internal experts, they need
to wait in the corresponding trainee stock until they receive the required training. The
trainees that are in the fourth week of the training program have priority in receiving the
required training. In other words, internal experts first train the trainee who is closer to
become an internal expert, and train the others if there is enough time left.
Internal Expert Firing Decision is another variable controlled by the decision maker.
There is a cost of firing an internal expert. Internal experts may choose to quit themselves,
but they are not paid in that case. Note that we assume there is a special agreement
between the trainees and the company. According to this bi-directional (reciprocal)
agreement, trainees cannot be fired and they cannot quit.
Internal expert structure is presented in the Figure 2.
Figure 2. Internal Expert Structure
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -6-
Seniha Zeynep Giiran and Hakan Yasarcan
2.3. External Expert Structure
External Expert Hiring Decision is another variable controlled by the decision maker.
Different than internal experts, an external expert is hired only one week. Accordingly,
external experts are flushed out from the corresponding stock. External expert structure is
presented in the Figure 3.
08 &) Extemal Expert Structure 8
Total weekly
manhours of EE tm1
Productivity of EE
Total Extemal Decision
External processing capacity
Figure 3. External Expert Structure
Unit cost of
firing an expert
‘Accumulated
cost of IE at t
Last 5 week avarage cost
Figure 4. Cost Structure
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -7-
Seniha Zeynep Giiran and Hakan Yasarcan
2.4. Cost Structure
There are four cost items in the model. These are; backlog cost, internal expert cost,
external expert cost, and firing cost. The cost structure of our model is presented in the
Figure 4. Note that total cost is the main performance variable.
3. Workforce and Task Backlog Management Game
We developed a game based on the structure presented in the previous section. The
decisions are entered either using sliders or by entering values. Current workforce levels,
current task backlog levels, and accumulated and weekly costs are reported. The game lasts
for 20 simulated weeks. The game surface is presented in Figure 5.
Week [=n]
NEXT WEEK DECISION ines ‘COSTINDICATORS
oS —-
(sro J ous] GD) [a
(etiam
a = = aa a Qi
ee ae 2 == eI Barat Fay
Figure 5. Game surface
4. Experimental Design
There are three treatment groups. Every group receives 4 games. The structure of the
four games is exactly the same, but a different seed is used for each game to generate Task
Arrival Rate. Thus, first, second, third, and fourth games slightly differ from each other,
but they are essentially the same. Every treatment group plays the same exact game with
the same exact seed. Thus, for example, game 3 of treatment group | and treatment group
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -8-
Seniha Zeynep Giiran and Hakan Yasarcan
3 is exactly the same. The only difference between the three groups is the hint that they
receive before the last game. The aim of these hints is to guide participants either to the
suggested solution archetype, to the problem archetype, or to a balanced version of these
two archetypes. These hints are:
There are different ad and disad ges of preferring internal experts or
external experts. It takes at least 4 weeks to train an internal expert. Whereas,
external experts are hired for the following week. Therefore, from the point of
earliness in starting to work, using external experts is more beneficial. On the other
hand, the cost of an internal expert is just one sixth of the cost of an external expert.
Therefore, from the point of salary payments, using internal experts is more
advantages. We suggest that internal and external experts should be used aiming to
balance these two advantages. We expect you to play this last game in the light of
this hint.
Although, it seems that training an internal expert takes a long time, it provides
significant advantages in decreasing costs in long term. After the trained internal
experts join the service activities, they will help you save money by eliminating the
need for the external experts. We expect you to play this last game in the light of
this hint.
Although, it seems that working with the external experts is costly, it is cheaper
than hiring and training internal experts in the long term. During the four week
training period, internal experts spend a significant amount of their time in training
activities, which causes an increase in the backlog and, thus, backlog cost.
Moreover, trainees do not contribute to the activities that reduce the backlog during
their training period. Whereas, external experts are hired for the following week
and by working full time in service activities, they prevent the accumulation of
backlog. Besides, you hire external experts for only a week. Therefore, when
backlog is very low, you are not supposed to bear unnecessary workforce costs. On
the other hand, only a small fraction of internal experts quit each week. Thus, you
are supposed to fire internal experts when it is necessary, which creates a total cost
of four week salary of the fired internal experts. For these reasons, using external
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -9-
Seniha Zeynep Giiran and Hakan Yasarcan
experts is advantageous in the long term. We expect you to play this last game in
the light of this hint.
5. Conclusions
In this study, we presented a workforce and task backlog management model and a
game based on this model. We also described an experimental design. This paper presents
a part of the study in which we aim to demonstrate the long term benefits of systems
thinking and system dynamics in decision making. We hope that such a demonstration will
promote systems thinking and system dynamics and increase the willingness of the
decision makers in applying high leverage policies.
Acknowledgements
This research is supported by a Marie Curie International Reintegration Grant
within the 7th European Community Framework Programme (grant agreement number:
PIRGO7-GA-2010-268272) and also by Bogazici University Research Fund (grant no:
6924-13A03P1).
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -10-
Seniha Zeynep Giiran and Hakan Yasarcan
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The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -12-
Seniha Zeynep Giiran and Hakan Yasarcan
: Model Equations
Accumulated _total_processing_capacity_t_minus_1'(t) = Accumulated_total_processing_capacity_"t_minus_1'(t- dt) + (Total_processing_capactty) * at
INIT Accumulated_total_processing_capacty_‘tminus_1'
INFLOWS:
4» Total_processing_capacity = External_processing_capacity + Internal_processing_capacity
\ccumulated._total_tasks_processed_t_minus‘(t- dt) + (‘Task_Completion_Rate’) * at
INIT Accumulated total tasks_processed_'t minust"
INFLOWS:
‘#0 "Task_Completion_Rate’ = Task completion_rate
7 Backiogs(t) = Backlogs(t- at) + (Backlog_inflow - Backlog_outfiow) * at
INIT Backlogs = 0
INFLOWS:
42 Backlog_inflow = Backlog_of_tasks'
‘OUTFLOWS:
420 Backlog_outfiow = Backlogs
a Backlog_cost(t) = pactloa:coatt: att) + (Weekly_backlog_cost) * dt
INIT Backlog cost
INFIOWS
4» Weekly backlog cost= Unit_backlog_cost_of_a_task*Backlog_of_tasks'
Backlog_of_tasks_'t_minus_1(t) = Backlog_of_tasks_tminus_1'(t- dt) + (Task_arrival_rate - Task_completion_rate) * dt
INIT Backlog_of_tasks_"L_minus_1'=0
INFLOWS:
40 Task_artival_rate = MIN(2*Mean_task_arrival_rate,MAX(0,NORMAL(Mean_task_arrival_rate,Stdev_ot_task_arrival_rate, Seed)))
OUTFLOWS:
‘#0 Task_completion_rate = MIN(Max_tasks_to_be_processed, Total_processing_capacity)
External_Experts(t) = External_Experts(t - at) + (Current_week's_external_experts - Enc_of_the_week) * dt
INIT External_Experts = 0
INFLOWS
‘#00 Curtent_week’s_external_experts = Hiring_external_expert_decision
OUTFLOWS:
‘#0 End_of_the_week = External_Experts
[Gl External_expert_cost(t) = External_expert_cost(t- dt) + (Weekly total_cost_of_EE) * dt
INIT External_expert_cost = 0
INFLOWS:
40 Weekly total_cost_of_EE = Weekly cost_of_an_EE"Hiring_external_expert_decision
[Gi Fires_experts(t) = Fires_experts(t- t) + (frng_rate_input- firing_rate_output)* dt
INFLOWS:
42 firing_rate_input = Firing_internal_experts
‘OUTFLOWS:
4 firing_rate_output= Fires_experts
(Gl Firing_costt = Firing_cost(t- dt) + (Weekly_firing_cost) * dt
INIT Firing_cost= 0
INFLOWS:
+40» Weekly_firing_cost = Unit_cost_of_fring_an_expert*Firing_intemal_experts
Internal_experts(t) = Internal_experts(t- a) + (Internal_experts_Inflow - Interal_experts_outfiow) * at
INIT internal_experts = 10
INFLOWS:
+0 Intemal_experts_inflow = Internal_experts’
‘OUTFLOWS:
40 Internal_experts_outfiow
[7 Intetnal_experts_'t_minus_1'()
Internal_experts
Intermal_experts_‘t_minus_1'(t- at) + (Training_completion_rate - Quiting_rate_of_IE - Firing_internal_experts) * dt
10
INIT Internal_experts_'t_minus_1
INFLOWS:
4». Training_completion_rate = Training_coverage_ration_for_4_tm 1*Normal_training_completion_rate
‘OUTFLOWS:
ce Quiting_rate_of_IE = Quiting_fraction_of_IE*internal_experts_'t_minus_1
‘4 Firing_internal_experts = MIN(Firing_decision, Internal_experts_'t_minus_1'/Time_to_fire_an_expert - Quiting_rate_of_IE)
Internal_expert_costt) = Internal_expert_costtt- dt) + (Weekly_total_cost_of_IE) * dt
INIT Intermal_expert_cost = 0
INFLOWS:
4» Weekly_total_cost_of_IE = Weekly_cost_of_an_IE*Intermal_experts’
[Gl Joining_the_workforce(t) = Joining_the_workforce(t- at) + (Noname_2- Noname_3)* dt
INIT Joining_the_workforce = 0
INFLOWS:
4» Noname_2 = Training_completion_rate
‘OUTFLOWS:
4 Noname_3 = Joining_the_workforce
2 Qutted_experts(t) = Quiie_exports(t- a) +(quting_rate_Input- quling_rate_ cute) * dt
INIT Quited_experts = 0
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -1B-
Seniha Zeynep Giiran and Hakan Yasarcan
INFLOWS:
458 quiting_rate_input = Quiting_rate_of_1E
‘OUTFLOWS:
cad aula rate output = Quited_experts
Report for Report for_week(t- dt) + (Report for_week’- Flush_out) * ot
Int Report or week = 0
INFLOWS:
42 Report for_week’ = Time+1
‘OUTFLOWS:
42 Flush_out = Report for
i Total Pane o Lcost(t- a ota cost_nflow - total_cost_outflow) * dt
INIT Total_c
INFLOWS
0 total_cost_inflow= Total_cost’
‘OUTFLOWS:
a Saal conta Total_c
Total_trainees(t) = Total_trainees(t- Pat) + (total ‘rainees_inflow - total_trainees_outtiow) *
INIT Total traiwees “Trainees, 11 minus. "Trainees 2 "minus. PrTrainess, 3. t on ‘'Trainees_4_‘tminus_1
INFLOWS
‘6. total_trainees_inflow = Total_trainees'
OUTFLOWS:
‘ total_trainees_outflow = Total_trainees
i Trainees 5 1(t) = Trainees_1_'t_minus_1\(t- dt) + (Hiring_trainee_decision - Stage_1_completion_rate) * dt
INIT Trainees_1_‘t_minus_1
Note
Hiring_trainee_decision = 0
ourFLows
2» Stage_1_completion_rate = Training_coverage_ratio_for_others_tm1*Normal_Stage_1_completion_rate
inees_2_'t_minus_1(t- dt) + (Stage_1_completion_rate - Stage_2_completion_ate) * dt
42» Stage_1_completion_rate = Training_coverage_ratio_for_others_tm‘*Normal_Stage_1_completion_rate
OUTFLOWS:
‘e Stage_2_completion_rate = Training_coverage_ratio_for_others_tm1*Normal_Stage_2_completion_rate
Gi Trainees: {_minus_1"(t~ at) + (Stage_2_completion_rate - Stage__Completion_Rate) * ct
INFLOWS:
46 Stage_2_completion_rate = Training coverage_ratio_for_others_tm1*Normal_Stage_2_completion_rate
OUTFLOWS:
4% Stage_2_Completion_Rate = Training _coverage_ratio_for_others_tm1*Normal_Stage_3_completion_rate
Trainees_4_'t_minus_1'¢) = Trainees_4_'t_minus_1'(t- dt) + (Stage_3_Completton_Rate - Training_completion_rate) * dt
INIT Trainees_4_'t_minus_1
INFLOWS:
4» Stage_3_Completion_Rate = Training_coverage_ratio_for_others_tm1*Normal_Stage_3_completion_rate
‘OUTFLOWS:
“@» Training_completion_rate = Training_coverage_ration_for_4_tm1*Normal_training_completion_rate
1g cost
external_expert L cose Week total_cost_of_EE
Weekly_tiring_cost+Firing_cos
Accumulated total_idle_capacity = Accumulated total |yooesshe_ capac /-Accumulated_total_task_processed
‘Accumulated_total_processing_capacity = Accumulated_total_processing_capacity_t_minus_1'+Total_processing_capacity
Accumulated _total_task_processed = Accumulated_total_tasks_processed_t_minust'+Task_Completion_Rate’
Accumulated _cost_of_IE_at_t- Weebly _total_cost_of_E+internal_expert_cost
Backlog_of_tasks' = Backlog of tasks ‘t_minus_1'+Task_arrival_rate-Task_completion_rate
F (Accumulated _total_processing_capacity= 0)
Capacity_Usage
THEN O
ELSE Accumulated_total_task_processed/Accumulated_total_processing_capacity
External_processing_capacity = Productivity_of_EE*Total_weekly_manhours_of_E&_tm1
Firing_decision = 0
Hiring_external_expert_decision = 0
Internal_experts' = Internal_experts_'t_minus_1'+Training_completion_rate-Quiting_rate_of_IE-
Internal_processing_capacity = Productivity_of_|E*Manhours_dedicatec| for_task_processing
Last_§_week_avarage_cost = IF TIME= 20
°
ie}
ie}
°
ie}
O°
°
ie)
ie}
ing_intemal_experts
000000
THEN
MEAN (HISTORY (Weekly_cost, 15), HISTORY (Weekly_cost, 16), HISTORY(Weekly_cost, 17), HISTORY(Weekly_cost, 18), HISTORY(Weekiy_cost,19);
ELSEO
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -14-
Seniha Zeynep Giiran and Hakan Yasarcan
© Longterm_cost = IF TIME= 20
THEN
MEAN (HISTORY (Weekly_cost 10), HISTORY (Weekly_cost, 11), HISTORY(Weekly_cost, 12), HISTORY(Weekly_cost, 13), HISTORY(Weekiy_cost,14),
ELSEO
Manhours_dedicated_for_task_processing = Total_manhours_of_IE - Manhours_dedicated_for_training
Manhours_dedicated_for_training =
MIN((Total_manhours_of_IE"Max_f pecten _of_time_for_training),(Manhours_needed__to_train__trainee__fot_one_week"Total_trainees'))
Manhours_dedicated_for_training tm
MIN(CTotal_manhours_of_IE_tm1"0 3 (Manhours_needed_t 1 {rain_a_trainee_for_one_week*Total_trainees_tm1))
Manhours_needed_to_train_a_trainee__for_one_week =
Max_fraction_of_time_for_training = 1
3 to_be_processed = (Backlog_of_tasks_‘t_minus_1'+Task_arrival_rate)/Time_to_process_a_task
Mean_task_arrival_rate = 1000
Normal_Stage_1 onel rate = Trainees_1_1
n_rate
Oo 00
minus_1'/one_week
Normal_Stage S24 "yone_week
Norinal_ Stage_3, compton rate “{minus_1one_week
Normal_training_completion_rate = Trainees_4_'t_minus_t/one_week
‘one_week= 1
Produstivity_of_E
Productivity_of IE=1
Quiting_traction_of JE = 0.05
ed= 1
stage4_manhours_need_tm1 = Trainees_4_'t_minus_1'*Manhours_neeced_to_train_a_trainee_for_one_week
00
Manhours_dedicated_for_training/Total_manhours_of_1&)100
Time_to_process_a_task= 1
Total_cost' = Accumulated_backlog_cost at t 1 cost_of_ EE at 1 1 fring cost_at 1 |_cost_of IE att
Total_External_Decision
HISTORY (Hiring_external_expert_decision,0)+HISTORY(Hiring_external_expert_decision,1)+HISTORY(Hiring_external_expert_decision,2)}+HIS
TORY(Hiring_external_expert_decision,3)+HISTORY(Hiring_external_expert_decision.4)+HISTORY(Hiring_external_expert_decision,5)*HISTO
RY(Hiring_external_expert_decision,6)+HISTORY(Hiring_external_expert_decision,7)+HISTORY (Hiring_external_expert_decision,8)+HISTORY(
Hiring_external_expert_decision,9)+HISTORY(Hiring_external_expert_decision,10)+HISTORY(Hiring_external_expert_decision,11)+HISTORY(
Hiring_external_expert_decision, 12)+HISTORY Hiring_external_expert_decision, 13}+HISTORY(Hiring_external_expert_decision,14)+HISTORY(
Hiring_external_expert_decision, 15)+HISTORY(Hiring_external_expert_decision, 16)+HISTORY(Hiring_external_expert_decision,17)+HISTORY(
Hiring_external_expert_ sec elol 12) ASTORTD etna caper 9e0, 0)
Total_internal_decision = | trainee_deci |_trainee_decision, |_trainee_decision,
2)+HISTORY(Hiring_trainee_< oe SsHISTORYEHiing ‘rainee ee 4)+HISTORY(Hiring_trainee_decision,
5)+HISTORY(Hiring_trainee_deci |trainee_d | trainee_decision,
SUSTOR Ee trainee, aedtee 9)+HISTORY Hiring_trainee, decision, 10)+HISTORY(Hiring_trainee_decision,
\9_trainee_decision, | trainee_decision, 1 \g_trainee_decision,
toerronveia frainee_decision, 15)+HISTORY(Hiring_trainee_decision, 16)+HISTORY(Hiring_trainee_decision,
inee_decision, |_trainee_decision, 19)
Tora |_manhours_of_IE = Weekly_working_hours*Internal_experts’
Total_manhours_of_IE_tm1 = Weekly_working_hours*internal_experts_t_minus_1’
Total_trainees’ = Deeds aallieeGlcaney
Total_trainees_tmt = Trainees_1_' is_t'+Trainees_2 1_minus_1'+Trainees_3° t_minus_1'+Trainees_4_%_minus_
Total_weekly_manhours_of_EE. im "weet working_hours*Hiring_external_expert_decision
Trainees = Trainees_1_1_minus_1'+Hiring_trainee_decision-Stage_1_completion_rate
Trainees2 = Trainees_2_t_minus_1'+Stage_1_completion_rate-Stage_2_completion_rate
Trainees3 = Trainees_3 ° {_minus_1'+Stage_2_completion_rate-Stage_3_Completion_Rate
Trainees4 = Trainees_4_1_minus_1'+Stage_3_Completion_Rate-Training_completion_rate
Training_coverage_ration_for_4_tm1 =IF (stage4_manhours_need_tm1=0 OR
(Manhours_dedicated_for_training_tm1-stage4_manhours_need_tm1) >0)
THEN 1
ELSE Manhours_dedicated_for_training_tm1/stage4_manhours_need_tm1
Training_coverage_ratio_for_others_tm1 = IF (Total_trainees_tm1 -Trainees_4_t_minus_1
THEN 1
CN00000000NDN00NN000N0N0
©
°
ee Se
re)
(IF Training_coverage_ration_for_4_tm1<1
THENO
ELSE (Manhours_dedicated_for_training_tm1- stage4_manhours_need_tm1)/((Total_trainees_tm1 - Trainees_4_t_minus_1')
*Manhours_needed_to_train_a_trainee_for_one_week))
Unit_backlog_cost_of_a_task=10
Unit_cost_of_firing_an_expert =
Weekly_capacity_usage = IF Total_processing_capacity=0
THEN 1 ELSE
(Task_Completion_Rate/Total_processing_capacity)*100
Weekly_cost = IF TIME= 0 THEN 0 ELSE Weekly_backlog_cost+Weekly_firing_cost+Weekly_total_cost_of_EE*Weekly_total_cost_of_lE
Weekly_cost_of_an_EE = 3000
Weekly_cost_of_an_IE = 500
Weekly _working_hours = 40
000
0000
The Shifting the Burden Archetype: A Workforce and Task Backlog Management Game -15-
Seniha Zeynep Giiran and Hakan Yasarcan
