Understanding the Implementation Dynamics of a
Technology Intervention Project
Jayendran Venkateswaran’, Kelsey Werner*, Chetan S. Solanki", and Gautam N. Yadama*
“Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
jayendran@iitb.ac.in, chetanss@iitb.ac.in
#Boston College School of Social Work, Chestnut Hill, MA 02467, U.S.A
Kelsey.werner@bc.edu, yad bc.edu
Abstract
This paper presents preliminary work on modeling and understanding the
implementation dynamics of a large-scale solar technology intervention project in rural
India. The model focuses on project implementation rather than the intervention’s
impact. The project aimed to provide solar lamps to a million school students by
assembling the technology locally at assembly-distribution centers spread across rural
India. This involved recruiting and training local people, regular supply of components
to local centers, assembly of lamps at required quality, awareness campaigning, demand
generation, sales, and diffusion/ uptake of the product in communities. These diverse
elements were brought together in a cohesive system dynamics model to explore
implementation. Three feedback loops - continuous quality improvement, demand
stimulation and work fatigue - are identified and their roles in the dynamics of the
project are discussed. An aggregate causal loop diagram is presented, based on which a
detailed system dynamics simulation model was developed. The model is calibrated to
project implementation data and used to discuss emerging dynamics. The contribution
of the paper is in bringing together elements of supply & production, new product
diffusion and project management dynamics, which can be also be used for
understanding the roll-out dynamics of other large scale technology intervention
projects.
INTRODUCTION
Around the world, several large-scale technology intervention projects are being
carried out in the areas of health care, energy, water, sanitation, etc. Most of the
publications about such projects are, rightly so, on the impact of such interventions on
the community, and the sustainability of the intervention. However, there is a lack of
literature on the dynamics of project implementation and the associated insights.
One such intervention, discussed in this paper, is the dissemination (sales) of one
million solar study lamps to as many school students in rural India within limited
project duration (Sawal et al., 2015). The management of a project of this scale is quite
challenging due to its spread across various geographical locations. Since the project
involves the sale of new products in the rural community, its uptake may be akin to a
new product diffusion process. Further, the inventory operations and processes play a
critical role in ensuring that the lamps reach the intended beneficiaries. Thus, a system
dynamic model that effectively captures the dynamics of the implementation must
include aspects of projects dynamics, new product diffusion and production-inventory
dynamics.
Project management has been well-studied using system dynamics, starting with
Cooper (1980). A variety of work has followed on the core project dynamics model, its
extensions and applications in a variety of areas (Lyneis and Ford, 2007). However,
most of the literature focuses on construction project management (Love et al., 2002;
Han et al., 2013) or software project management. The basic structure of these project
dynamics models include the rework cycle (Sterman, 2000), consisting of four stocks or
levels: Work to be Done, Work Done, Undiscovered Rework, and Know Rework. This
framework is readily amenable for projects with standard processes and work content
divisions such as construction or design projects with a specific deliverables.
The diffusion of new products in markets is well studied in literature, primarily based
on Bass models (Bass, 1969) and its extensions (Ho et al. , 2002; Mahajan et al., 1990;
Peres et al., 2010). These models typically assume infinite supply (Peres et al., 2010),
though there are recent papers that look at the effect of supply constraints and supply
uncertainties on the diffusion dynamics (Ho et al., 2002; Kumar and Swaminathan,
2003; Negahban and Smith, 2016). Also, in the classical Bass model (Bass, 1969) and
most of its extensions (Peres et al., 2010) the coefficient of innovation and coefficient of
imitation that drives the adoptions are assumed to be exogenous constant parameters.
However, the Bass family of models does provide a fundamental modeling construct to
help understand diffusion dynamics.
The applications of system dynamics methodology to supply chains and production-
inventory systems are aplenty, with the foundations laid by Forrester (1961) in his
Industrial Dynamics. The basis for many of the models in literature is the classical stock
management structure (Sterman 2000), used to understand the inventory dynamics of
supply chains, as well as determine the best ordering policy in the face of stationary
demand patterns. Other aspects of production systems include capacity utilisation and
expansions, workforce inventory interaction, forecasting, management of backlogs, etc
(Sterman 2000).
This paper presents the preliminary system dynamics (SD) model developed to
understand and analyze the project implementation dynamics of the Million SoUL
project. The SD model brings together elements of new product diffusion dynamics,
production-inventory dynamics, workforce interactions, and project dynamics. The next
section describes the project under study and its performance. The key reference modes
are identified and the possible events in the project that might explain the dynamics are
explored. A high-level causal loop model is then described, identifying three key causal
loops that explain the observed dynamics. The detailed stock-flow based SD model is
then presented. Simulation results show that the SD model captures the actual project
dynamics accurately. Observations are drawn from the simulation results and the
changing loop dominances. The paper concludes with a discussion and the way forward.
THE MILLION SoUL PROJECT AND ITS PERFORMANCE
The project discussed in this paper is the Million Solar Urja! Lamp (SoUL) project,
planned and implemented by Indian Institute of Technology Bombay, India during
2014-2015 (Sawal et al. 2015). The goal of the project was to provide high quality, clean
energy access in the form of a solar study lamp to one million school students in rural
India in a rapid and cost-effective manner. The crux of the project involves localization,
where in local Assembly-Distribution (A-D) centers were set up in the blocks selected
for intervention’. The A-D centers catered to the demands in their block and 1-2
adjoining blocks, as the case may be. Further, local people were recruited from across
the blocks, trained and employed at the A-D centers to assembly and distribute the
lamps. The SoUL lamps were sold at Rs. 120 to school going children in their respective
schools. The purchase of the lamps was optional. The distribution of lamps was carried
out in multiple blocks simultaneously until the overall target of reaching one million
students was completed. Care was taken to ensure that a significant percentage of the
intervention blocks’ student population was covered. Once the distribution was
completed in a block, the A-D center was closed. Multiple local repairs centers, operated
by trained locals, were established to ensure that after-sales services were provided to
the student beneficiaries. The project was implemented in two phases. In Phase 1
(January 2014 to April 2015), about 735,000 lamps were distributed, and in Phase 2
(November 2015 to April 2016), 265,000 lamps were distributed. Over the course of the
project, about 54 A-D centers and 350 repair and maintenance centers were in
operation, providing solar study lamps across 97 blocks in the states of Odisha, Madhya
Pradesh, Maharashtra and Rajasthan in India. In this paper, the distribution dynamics
pertaining to Phase 1 of the project is discussed.
The week-wise distribution and the cumulative distribution of the overall project
performance aggregated across all A-D centers and blocks are shown in Figure 1. The
progress of the project is plotted from week 0 (when project started) until week 76
when the Phase 1 distribution was completed. At the outset the adoptions of the solar
lamps by the students seems to mimic the classical S-Shaped growth (e.g. Bass model) of
innovation diffusion. However, upon careful inspection of the cumulative distribution
dynamics, the following points emerge:
e Itis observed that from week 0 until week 8, there is no sale of lamps; and from
week 8 to about week 25 the sales shows a limited linear growth.
e It is observed that from week 25 to about week 44 there seems to be an
exponential growth in sales, followed by an increase in sales at an even higher
rate of growth (surprisingly) from week 45-55. This is contrary to what one may
expect under classical S-Shaped growth where the point of inflection occurs at
halfway mark, after which the growth in sales happens at a decreasing rate.
e Next, it is seen that after week 56, the sales increases at a decreasing rate,
exhibiting a classical goal-seeking behavior, finally saturating at 740112 lamps
(includes the sample lamps used in marketing) at week 76.
e Also, a clear breaks in distribution are observed in week 45 and in weeks 55-56.
1 Urja means Energy in Hindi/ Sanskrit
? Blocks are sub-districts, also known as talukas or tehsils. The rural intervention blocks were chosen
based on percentage of households that depend on kerosene as their primary source of lighting and the
backward nature of the blocks.
60000 800000
lB Distribution |=©—— Cumulative Distribution
45000 600000
3 £
= 3
& 30000 400000 §
@ &
g 2
§ &
7 §
15000 200000
8 © 0 6 PB Hw PH HD Hw P HS P HS W
Week
Figure 1. The actual aggregated weekly and cumulative distribution of lamps (reference modes)
These observations necessitate a closer look at the other events of project that might
have influenced the dynamics.
As mentioned earlier, the project involves the local assembly of solar lamps by locally
trained people. Thus, the supply of kits and the availability of manpower can be
expected to influence the distribution dynamics. As seen from Figure 2, the first supply
of components started in week 8, steadily increasing over the weeks with significant
deliveries happening after week 36. The last shipment of components was on week 56.
The first employee training happened in week 0 (the week of first training is taken as
week 0 for modeling purposes), creating a workforce between weeks 18 to 35. What is
not apparent from these figures is that the total supply was 747950 component kits, but
the total distribution was only 740112 lamps. The difference, due to a loss of lamps as
scrap, can be attributed to the quality of the assembly and distribution process. It was
discovered that the initial trainings were only on the technical aspects of the lamp
assembly. After observing the performance, additional quality improvement programs
were carried out as part of the project to reduce the defectives, beginning in week 20.
Since distribution of the lamps was primarily via schools, the school-working calendar?
also affected the distribution pace.
Further, the original project deadline was to complete the distribution in 6 months (24
weeks). However, due to supply delays and delays in setting up new A-D centers, the
project deadline was continually shifted with an eventual deadline of 64 weeks. Figure 1
demonstrates that this deadline was also not met, perhaps due to a lack of motivation to
complete the project, trained local people moving on to other opportunities, or a slower
pace of work etc. This is perhaps akin to the popular “90% syndrome” in project
management dynamics literature (Ford and Sterman 1999).
3 In India, the school-working calendar varies across states, but typically, the academic session starts by
July; with short break (a week or less) in mid-October, end of December, and summer breaks in the
months of April-June.
100 60000
I Employees Hired and Trained. +=—— Supply Quantity
75 45000
50 30000
Employees
Quantity (lamps)
25 15000
0 ull 0
Gh GS DG P Bm WB W H O09 A Bw DP HS GD Hm BW 10
Week
Figure 2. Aggregated employees hiring and supply of components, over weeks
MODEL DEVELOPMENT
In this paper, a system dynamics model is developed to help explain the distribution
dynamics (see Figure 1) as observed in the project. In this model, the supply of
components to A-D centers and the hiring and training of local employees are
considered as exogenous variables. This is to help uncover the other project dynamics
that influences the distribution. The causal loop diagram with the key variables along
with the essential stocks and flows are shown in Figure 3. An important distinction is
made between the student beneficiaries (adopters of the lamp) and the lamp itself. The
student beneficiaries are captured as stocks of Potential Adopters and Adopters. The
Adoption Rate is governed by dynamics similar to the Bass Diffusion model but
constrained by the school working calendar as will be discussed further. The Supplying
of lamps components increases the stock of Lamp Kits at A-D centers. Assuming
sufficient demand and capacity, these lamp kits are distributed, increasing the Lamps
Distributed. As the lamps are distributed, the actual project progress is compared with
the planned project progress. As the gap in progress increases, project managers
perceive pressure to complete the project. The model captures that they respond with
efforts to increase demand by increasing advertising efforts. As more Adopters adopt the
technology it increases demand, which when satisfied, increases the Lamps Distributed,
improving the project progress and reducing the shortfall. However, in the long run,
working under the pressure of deadlines increases fatigue among the employees that
decreases their productivity and the available capacity, leading to lesser lamps begin
distributed, and thus a smaller increase in Lamps Distributed. This eventually reduces
the pressure to complete the project, reducing fatigue.
The desired assembly distribution rate is constrained by the demand or the lamp kits in
A-D centers, with the eventual assembly and distributions constrained additionally by
the available capacity. Also, similar to any production process operating at given
Process Quality, Scraps are also generated at the A-D centers that decrease the perceived
quality levels. As the perceived levels fall below the desired quality level, Quality
Improvement Programs are initiated which increases the Process Quality, resulting in
reduced defects and scrap.
Perceived
Quality level
Desired Quality
~ Desired to + Level
Improve Quality
ios ) Quality improvement
Soran programs
= Process Quality
Defects
Lamps Kits in Lamps ‘Actual project
su A-D centers Distributed % re
Supplying Distributing eas Pens
+
Progress
Desired Assembly Distribution Rate . Pressure to
Distirbution et + complete project
+ +
Available capacity
Fatigue
Demand .
School Working + s
Calendar + Employee
productivity Efforts to Increase
Adopters
Potential [S24
Adopters
Advertising
Efforts
Figure 3. Basic causal loop diagram
THE STOCK-FLOW SD SIMULATION MODEL
A complete Stock-Flow based system dynamics simulation model, of the above CLD is
developed (see Figure 4). It is described in this section. The underlying equations are
presented in the Appendix.
An additional loop for the identification, dispatch and replacement of defective
components by the suppliers is added (see top left of Figure 4). The defective
components, identified by inspection and testing at the A-D centers are moved into a
stock of defectives at A-D centers. These defectives are then dispatched to the suppliers
who replace them with good components after some delay.
The adopters or beneficiaries are divided into two stocks of Adopters and Active
Adopters (see bottom left of Figure 4). The Adopters are those who have adopted the
technology and are ready to buy the lamp, while Active Adopters are those who have
actually purchased the solar lamp. The Adoptions due to Advertising and the Adoptions
due to Word of Mouth that drives Adoption Rate is similar to the classical Bass Diffusion
model. However, in this model, the Adoption Rate is also influenced by the School
Working Calendar, as follows:
Adoption Rate =
(Adoptions due to Advertising + Adoptions due to Word of Mouth)* School
Working Calendar
In the weeks the schools are in full session, School Working Calendar takes value 1 to
indicate a regular adoption rate. In the week with breaks, inations, and
other holidays, the School Working Calendar takes a value < 1 (0.2 in our case) to
indicate lower rates of adoption.
The human resource (employees) is split across three stocks, Idle New Hires, Trainees,
and Experienced Employees, each with their own productivity levels (see bottom right of
Figure 4). The Idle New Hires refers to those employees who are hired but are idle due
to unavailability of lamp components at the A&D centers to work on.
There are four table functions in this model: Utilisation, Quality Improvement Efforts,
Advertising Efforts and Motivation, as shown in Figures 5(a) - 5(d). The Utilisation
appears in the capacity management loop that determines the weekly assembly
distribution rate, as follows:
Assembly Distribution Rate = Available Capacity*Utilisation
Utilisation=f (Schedule Pressure) =f (Desired AssemblyDistributionRate/
Available Capacity)
The Utilisation table function is shown in Figure 5(a). The normal utilisation is taken as
1.0. When the Schedule Pressure is less than 1.0, the assembly distribution rate equals the
desired rate. As the Schedule Pressure increases beyond 1, the Utilisation also increases
and saturates at 1.25. This indicates the possible speeding up of activities and overtime
the employees may work to meet increased demand.
Next, the Quality Improvement Effort, shown in Figure 5(b), appears in the quality
improvement loop, and helps determine the overall rate at which the Process Quality
level changes, as follows:
Process Quality = INTEG(Change in Process Quality)
Change in Process Quality =(Desired Quality Level - Process Quality) *
Quality Improvement Effort
Quality Improvement Effort=£ (Perceived Quality Ratio)
Perceived Quality Ratio = SMOOTH(Actual Quality Level/Desired Quality Level,
Smoothing Delay)
Actual Quality Level = Cumulative Distribution/ (Cumulative Distribution +
Cumulative Scraps)
As seen from Figure 5(b), when the Actual Quality is equal to or more than the Desired
Quality, then no further quality improvement efforts (=0.0) are needed. When the
Perceived Quality Ratio is close to 1, the required quality improvements efforts are low
(<=0.4) . And when the Perceived Quality Ratio is close to 0, then maximum efforts to
improve quality is needed (indicated by 1.0).
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Next, the Advertising Efforts, shown in Figure 5(c), appears in the demand stimulation
loop, and helps determine the overall Adoptions due to Advertising, as follows:
Adoptions due to Advertising = Potential Adopters * Advertising Coefficient
Advertising Coefficient= Normal advertising coefficient*Advertising Efforts
Advertising Efforts = f(Project Pressure)
Project Pressure = (Fraction of Work Remaining-Planned Fraction of Work
Remaining) /Planned Fraction of Work Remaining
As seen from Figure 5(c), when the project pressure is less than 0.5, the advertising
efforts remain at the normal rate of 1. However, as the pressure increases to one, the
advertising efforts increases, reaching a maximum value of 4.0, resulting in a four-fold
increase in advertising coefficient and the Adoptions due to Advertising. It is noted that
the Planned Fraction of Work Remaining is an indicative of the planned project progress,
and is computed using a classical Bass Diffusion model (see top right of Figure 4).
Finally, the motivation appears in the fatigue and capacity loop, as follows:
Capacity of Experienced employees = Motivation*Standard capacity of
Experienced Employee*Experienced Employees
Motivation = £ (Fatigue)
The Fatigue is modeled as a stock, which builds-up slowly over time depending on the
project pressure. As seen from Figure 5(d), when fatigue crosses 1, the motivation
rapidly decreases and saturates at 10%.
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Figure 5. Table functions used in the model
SIMULATION RESULTS AND ANALYSIS
Model verification
The above simulation model was implemented using Vensim® PLE. Before calibrating
of the specific scenario on hand, the model was verified. First, the dimensional
consistency was verified and the model was tested for robustness at extreme conditions
(Barlas, 1996). When any one of the three, Supply Rate or the Hiring or Adopters are 0,
then the Distribution rate is 0, irrespective of the values of the other two variables.
Other combined parameter settings were also verified to ensure the model behavior is
as expected. For instance, suppose that the initial quality level is 0, but the supply rate
has a pulse input of 1000 as time 40, then the quality improvement efforts does not begin
until the distribution takes place, and the system performance (cumulative scraps and
cumulative distribution) are observed.
Model Calibration
The school working calendar is a proportionality constant with value 1 on school
working weeks, and value 0.2 on school non-working weeks. The parameter values
were set based on the actual project performance data (both quantitative and
qualitative), is shown in Table 1. Further, the Supply Rate and Hiring are exactly as in
Figure 2, captured using PULSE function in Vensim. The project was rolled out such that
the total target, beginning at 1 million was revised downwards (a decision based on
fund availability). This is captured in the Target Distribution parameter (as 1000000-
STEP(100000,15)-STEP(100000,35)-STEP(55000,40)). It is noted that in week 15 the target
distribution was reduced to 900000, and the next revision was only in week 35.
However, by 35 weeks almost all the required manpower was already hired (see Figure
2) and the required number of A-D centers established. Hence the initial value of
Potential Adopters was set at 900000.
Table 1: Parameter Settings
Parameter Value
Error Rate 0.025/week
Average Dispatch Delay 1 week
Average Replacement Delay 3 week
Fraction continuing 0.8/week
Work Experience Delay 2 week
Demand per Beneficiary
1 Lamp/ Beneficiary
Standard Capacity of New Employees
10 Lamps/ Week/ Employee
Standard Capacity of Experienced Employees
60 Lamps/ Week/ Employee
Target Delivery Delay 1 Week
Smoothing Delay 4 Week
The diffusion parameters of WoM Coefficient and Normal Advertising Coefficient were
determined empirically by calibrating the model against the actual project performance
(Figure 1). The WoM Coefficient at 0.12 and the Normal Advertising Coefficient at 0.005
was found to give the closest fit to the actual data.
10
Simulation Results
The model is simulated with a time step of 0.125 weeks. Figures 6 show the plots of
Distribution Rate and the Cumulative Distribution, comparing the simulation results and
the actual data. As seen from the figure, the model is able to quite accurately replicate
the project dynamics.
The dynamic behavior of the other variables was explored to help understand the shifts
in loop dominance. Towards that, three plots are presented in Figure 7. The top-most
plot in Figure 7 presents the quality improvement effects. It clearly shows that the
scraps were generated at an increasing rate from week 8. In week 20, the project
initiated quality improvement programs, which, after some delay increased the process
quality to the desired levels by week 30. This significantly reduced the rate of growth of
scraps from week 22 onwards.
Next, the middle plot in Figure 7 shows the Assembly Distribution Rate, the Distribution
Possible and the Demand of Lamps. Only at the initial weeks (week 8 to 15) and the
closing weeks (week 65 onwards), the Distribution Rate is constrained by the material
available (captured by Distribution Possible). During weeks 15 to 55 the distribution
rate is determined only by the demand of lamps from the field. However, in weeks 46 to
49, the Assembly Distribution Rate was lower than the demand. This was due to the
available capacity utilisation where in the employees were unable to keep pace with the
demand. Also, from week 55-65, the Assembly Distribution Rate is again determined by
the available capacity of the employees. To further understand the sudden increase in
Demand rate (weeks 45 to 55) and the sudden decrease in assembly distribution rate
are shown in the bottom-most plot in Figure 7. It depicts the effect of project pressure
on the project dynamics. Until week 23 the project pressure was low, considering the
school working calendar and the fact that the manpower (employees) were still being
recruited and trained. From weeks 24-35 the project pressure grows indicating the
increasing shortfall between the planned project progress and the actual project
progress. After week 35, when project pressure cross 0.5, the Advertising coefficient also
increases, peaking at 0.2 in week 46. This increase in Advertising coefficient causes an
increase in demand of lamps, during the weeks 45-55. Once the project pressure crosses
the threshold pressure of 1, it starts to add to the fatigue. As fatigue grows beyond 1 in
week 54, the capacity of experience employees begins to fall, reaching a new low after
week 58. This reduction in the capacity of experience employees causes the reduction in
the assembly distribution rate after week 55.
11
Lamps/Week
Lamps
Distribution Rate
50,000
37,500
25,000
12,500
8 16 24 32 40 48 56 64 7T2 80
Time (Week)
Distribution Rate : Simulated
Distribution Rate : Actuals
Cumulative Distribution
800,000
600,000
400,000
200,000
8 16 24 32 40 48 56 64 72 80
Time (Week)
Cumulative Distribution : Simulated
Cumulative Distribution : Actuals
Figure 6. Simulated results vs. Actual data for the reference modes
12
Quality Improvement
Assembly Distribution Rates and its caus
200,000
150,000
100,000
50,000
Assembly Simulated
Distribution s
Demand of Lamps : Simulated
Project Pressure Effects,
2 Dmal
02 Week
40,000 Lamps’ Week
1S) Dmal
1S Week
30,000 Lamps/Week
S Dmal
© Dmal
0 Week
0 Lamps W
4 8 i216 20 2428 DGS
Time (Week)
Project Pressure: Simulated Dial
Fatigue: Simulate Dmnl
Advertsing Coefficient: Simulated Wee
Capacity of | Simulated Lamps/Week
Figure 7. The dynamic behavior of key model variables
DISCUSSION
This paper presents a preliminary model towards understanding the dynamics of the
Million Solar Urja Lamp project. A brief background of the project is given and the actual
project performance discussed. The key reference modes are identified and the possible
events in the project that might explain the dynamics are explored. A high-level causal
loop diagram was developed to identify three key causal loops that explain the observed
dynamics: the quality improvement loop, demand stimulation loop and the work
fatigue loop. A detailed stock-flow based system dynamics model was then developed,
tested, calibrated and simulated. Simulations show that the model explains the actual
project dynamics. The dynamic behaviors of the other variables are also explored to
help understand the shifts in loop dominance within the model.
The model provides a variety of insights from a project management perspective. The
school-working calendar plays a critical role in project timing that needs to be
accounted for in project planning. This speaks to a larger need to consider constraints
on adoption for project management. In this case, because implementation took place in
a school setting, adoption was limited to when children were in school despite
advertising efforts. There may be similar place-based limitations in other technology
interventions that should be considered in project management. The model also
highlights the importance of continuous quality control, which is particularly critical
when assembly is established locally. Understanding the flow of scraps and its impact
on perceived quality allows project managers to trigger quality control, in this case
through providing quality control programs to reduce the number of defective lamps.
Disaggregating beneficiaries from the technology intervention allowed us to unpack
their dynamics and explore how they interacted with employee capacity. The model
makes it explicit that adopters drive demand for the technology that affects the desired
assembly distribution rate creating schedule pressure. However, even if there is
sufficient employee capacity to assemble and distribute technology they are constrained
by the availability of supplies, potentially slowing cumulative distribution (project
progress). We demonstrated how this has interesting implications for employee fatigue,
where project pressure created by a low level of cumulative distribution builds project
pressure leading to fatigue. Employee fatigue can lower motivation, limiting the
capacity of employees. The takeaway is that project managers should consider and
manage employee fatigue, especially in light of distribution slowdowns or supply
shortages. We found that project managers also reacted to pressure to complete the
project by increasing advertising to spur demand for the technology. The model
demonstrates that this will only be effective if there is sufficient employee capacity and
supply to meet increased demand. These factors may play a role in other efforts to
provide technology interventions with a locally sourced workforce, assembly and
distribution.
The model was presented and discussed with Million SoUL project managers. The
managers felt that the model helped make it quite clear to them that school working
calendar plays a critical role in the project roll-out and needs to be factored in their
project planning. The managers also mentioned that the slow build of fatigue due to
protracted project activities and its influence on the dynamics during the last few weeks
was a new insight. Also, since a large part of the project management team efforts was
actually focused on ensuring the supply of components to the A-D centers, the
14
replacement of defectives, and the assembly of lamps, the view presented in that model
that demand for lamps as the driving force, was a new learning to them. The managers
also pointed out that the Supply Rate and Hiring were key project management
decisions, with Supply Rate constrained by the suppliers’ capacities and Hiring reflecting
the decision to expand to new blocks. The model could be used as a tool to aid in these
decisions in the future A few what-if scenarios are being designed to help deepen the
understanding of the project dynamics and inform future implementation. Further, it
was suggested to include the cost or expenditure dynamics as part of the model. Work is
ongoing to include these dynamics as part of future system dynamics project models.
The contributions of the paper can be viewed from two aspects, over and above the
learning of modelers and the project management team. One, we have shared an
interesting case study, walking though the background, reference models, model
elicitation, casual loop modeling, detailed SD modeling and analysis, which one may find
useful to replicate in other settings or provide insights for future project
implementation. Two, in the model the technology intervention (solar lamp) is
considered distinct from the beneficiaries of the solar lamp although they are inter-
connected; the project progress is explicitly captured along with its influence on both
the demand (Adopters) as well as supply (assembly and distribution). This construct
may be useful in modeling other large-scale technology interventions.
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15
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16
APPENDIX
The complete model documentation, as obtained from Vensim is presented here.
(01)
(02)
(03)
(04)
(05)
(06)
Active Adopters= INTEG (
Active Adoption Rate,
0)
Units: Beneficiary
Active Adoption Rate=
Distribution Rate/Demand per Beneficiary
Units: Beneficiary/Week
Actual Quality Level=
IF THEN ELSE(Cumulative Distribution+Cumulative Scraps=0,1,Cumulative Distribution
/(Cumulative Distribution+Cumulative Scraps))
Units: Dmnl
Adjustment Time=
Al
Units: Week
Adopters= INTEG (
Adoption Rate-Active Adoption Rate,
0)
Units: Beneficiary
Adoption Rate=
(Adoptions due to Advertisting + Adoptions due to Word of Mouth)*School Working
Calendar
(07)
(08)
(09)
(10)
ay
(12)
Units: Beneficiary/Week
Adoptions due to Advertisting=
Potential Adopters*Advertising Coefficient
Units: Beneficiary/Week
Adoptions due to Word of Mouth=
WoM Coefficieint*(Adopters+Active Adopters)*Potential Adopters/(Adopters+
Active Adopters+Potential Adopters)
Units: Beneficiary/Week
Advertising Coefficient=
Normal advertising coefficient*Advertising Efforts
Units: 1/Week
Advertising Efforts = WITH LOOKUP (
Project Pressure,
({(-1,0)-(1.5,4)],(-1,1),(0,1),(0.25,1),(0.5,1),(0.6,1.2),(0.7,1.5),(0.8
,1.8),(0.9,2.2), (4,3), (1.1,3.5), (1.25,4),(1.5,4) ))
Units: Dmnl
Assembly Distribution Rate=
Available Capacity*Utilisation
Units: Lamps/Week
attrition=
Idle new hires*(1-Fraction Continuing)
Units: Employee/Week
17
(13) Available Capacity=
Capacity of Experienced employees+Capacity of new employees
Units: Lamps/Week
(14) Average Dispatch Delay=
Units: —
(15) Avg Replacement delay=
Units: week
(16) Capacity of Experienced employees=
Motivation*Standard capacity of Experienced Employee*Experienced Employees
Units: Lamps/Week
(17) Capacity of new employees=
(Trainees+Idle new hires)*Standard Capacity of a new employee
Units: Lamps/Week
(18) Change in fatigue=
Realised Pressure/Adjustment Time
Units: 1/Week
(19) Change in Process Quality=
Indicator for start of Quality improvement programs*(Desired Quality Level
-Process Quality)*Quality Improvement Effort
Units: 1/Week
(20) Cumulative Distribution= INTEG (
Distribution Rate,
Units: Lamps
(21) Cumulative Scraps= INTEG (
Scrap Rate,
0)
Units: Lamps
(22) Defective replacement rate=
DELAY N{( Defectives Dispatch Rate , Avg Replacement delay , 0 ,3 )
Units: Lamps/Week
(23) "Defectives at A-D centers"= INTEG (
Defectives Generation Rate-Defectives Dispatch Rate,
Units: Lamps
(24) Defectives awaiting replacement at Suppliers= INTEG (
Defectives Dispatch Rate-Defective replacement rate,
0)
Units: Lamps
(25) Defectives Dispatch Rate=
Indicator for start of dispatches*"Defectives at A-D centers" /Average Dispatch Delay
Units: Lamps/Week
(26) Defectives Generation Rate=
(27)
(28)
(29)
(30)
BY
(32)
(33)
(34)
Error Rate*"Lamps kits in A-D centers”
Units: Lamps/Week
Demand of Lamps=
Adopters*Demand per Beneficiary*School Working Calendar
Units: Lamps
Demand per Beneficiary=
Al;
Units: Lamps/ Beneficiary
Desired Assembly Distribution Rate=
MIN(Distribution Possible,Demand of Lamps)/Target Delivery Delay
Units: Lamps/Week
Desired Quality Level=
0.995
Units: Dmnl
Distribution Possible=
"Lamps kits in A-D centers"
Units: Lamps
Distribution Rate=
Assembly Distribution Rate*Process Quality
Units: Lamps/Week
Error Rate=
0.025
Units: 1/Week
"Exp. Adoption Rate"=
("Exp. advt. coefficient"*Planned Potential Adopters + ("Exp. WoM coefficient"
*(Planned Adopters)*Planned Potential Adopters/(Planned Adopters+Planned
Adopters
(35)
(36)
(37)
(38)
9)
)))*Expected School Calendar
Units: Beneficiary/Week
"Exp. advt. coefficient"=
Units: 1/Week
"Exp. WoM coefficient"=
0.12
Units: 1/Week
Expected School Calendar=
0.3*PULSE( 0, 10 ) + 0.3*PULSE( 10, 4) +0.3*PULSE( 14 ,9 ) + 1*PULSE(
23, 20)+ 1*PULSE( 43, 2 )+ 1*PULSE( 45, 9 )+ 1*PULSE( 54, 2)
+ 1*PULSE( 56 , 13 ) +0.25*PULSE( 69, 12 )+1*PULSE(81,32)
Units: Dmnl
Experience Rate=
DELAY N( Starting Rate , Work Experience Delay ,0,3)
Units: Employee/Week
Experienced Employees= INTEG (
Experience Rate,
0)
Potential
19
(40)
(41)
(42)
(43)
(44)
(45)
(46)
(47)
(48)
(49)
(50)
GY)
Units: Employee
Fatigue= INTEG (
Change in fatigue,
0
Units: Dmnl
FINAL TIME = 80
Units: Week
The final time for the simulation.
Fraction Continuing=
0.8
Units: 1/Week
Fraction of Work Remaining=
(Target Distribution-Cumulative Distribution) /Target Distribution
Units: Dmnl
Hiring=
14*PULSE(0,1)+41*PULSE(1,1)+15*PULSE(12,1)+8*PULSE(13,1)+19*PULSE(15,1)+38
*PULSE(18,1)+45*PULSE(19,1)+37*PULSE(20,1)+34
*PULSE(22,1)+81*PULSE(23,1)+88*PULSE(24,1)+29*PULSE(26,1)+36*PULSE(28,1)+
66*PULSE(29,1)+44*PULSE(31,1)+8*PULSE(32,1)+52
*
PULSE(33,1)+25*PULSE(34,1)+81*PULSE(35,1)+19*PULSE(44,1)
Units: Employee/Week
50*PULSE(1,1)+80*PULSE(10,1)+100*PULSE(20,1)
Idle new hires= INTEG (
Hiring-attrition-Starting Rate,
1)
Units: Employee
Indicator for start of dispatches=
STEP(1,16)
Units: Dmnl
Indicator for start of Quality improvement programs=
STEP(1, 21)
Units: 1/Week
Initial Quality Level=
0.825
Units: Dmnl [0.5,1,0.025]
INITIAL TIME =0
Units: Week
The initial time for the simulation.
"Lamps kits in A-D centers"= INTEG (
Defective replacement rate+Supply Rate-Distribution Rate-Defectives Generation Rate
-Scrap Rate,
0)
Units: Lamps
Motivation = WITH LOOKUP (
Fatigue,
([(0,0)-(1.8,1)],(0,1), (0.25, 1),(0.5,1),(0.75,1),(0.9,0.98),(1,0.9),(1.1
20
(52)
(53)
(64)
(55)
(56)
(57)
(58)
(59)
,0.6),(1.25,0.2), (1.5,0.1),(1.75,0.1) ))
Units: Dmnl
Normal advertising coefficient=
Units: 1/Week
Perceived Quality Ratio=
SMOOTH (Actual Quality Level/Desired Quality Level,Smoothing Delay)
Units: Dmnl
Planned Adopters= INTEG (
“Exp. Adoption Rate",
0)
Units: Beneficiary
Planned Fraction of Work Remaining=
Planned Potential Adopters/(Planned Adopters+Planned Potential Adopters)
Units: Dmnl
Planned Potential Adopters= INTEG (
-"Exp. Adoption Rate",
900000)
Units: Beneficiary
Potential Adopters= INTEG (
-Adoption Rate,
900000)
Units: Beneficiary
Process Quality= INTEG (
Change in Process Quality,
Initial Quality Level)
Units: Dmn]
Project Pressure=
MAX(Fraction of Work Remaining-Planned Fraction of Work Remaining,0)/Planned
Fraction of Work Remaining
(60)
(61)
(62)
(63)
Units: Dmnl
Quality Improvement Effort = WITH LOOKUP (
Perceived Quality Ratio,
({(0,0)-(1.1,1.1)],(0,1),(0.1,1), (0.2,0.98),(0.299389,0.957346),(0.401222
0.943128), (0.49287 2,0.92891),(0.613035,0.881517),(0.706721,0.819905),(0.798371
0.706161), (0.87169,0.559242),(0.92057,0.383886),(0.955193,0.246445),(1,0)
(11,0) ))
Units: Dmnl
Realised Pressure=
SMOOTH(MAX(Project Pressure-Threshold Work Pressure,0),Smoothing Delay)
Units: Dmnl
SAVEPER =
TIME STEP
Units: Week [0,?]
The frequency with which output is stored.
Schedule Pressure=
(Desired Assembly Distribution Rate/MAX(1,Available Capacity))
21
(64)
(65)
(66)
(67)
(68)
(69)
(70)
ce)
(72)
(73)
(74)
Units: Dmnl
School Working Calendar=
0.2*PULSE( 0, 10 ) + 0.2*PULSE( 10, 4) +0.2*PULSE( 14,11) + 1*PULSE
(25, 18 )+ 0.2*PULSE( 43 , 2 )+ 1*PULSE( 45 ,9 )+ 0.2*PULSE(54, 2)
+ 1*PULSE( 56 ,13 ) +0.2*PULSE( 69 , 12 )+1*PULSE(81,32)
Units: Dmnl
Scrap Rate=
(1-Process Quality)*Assembly Distribution Rate
Units: Lamps/Week
Smoothing Delay=
4
Units: Week
Standard Capacity of a new employee=
10
Units: Lamps/Week/Employee
Standard capacity of Experienced Employee=
60
Units: Lamps/(Week*Employee)
Start Delay=
au
Units: Week
Starting Rate=
Idle new hires*Utilisation/Start Delay
Units: Employee /Week
Supply Rate=
1010*PULSE(7,1)+1010*PULSE(8,1)+4545*PULSE(11,1)+4040*PULSE(12,1)+2800*PULSE
(13,1)+3900*PULSE(14,1)+2800*PULSE(15,1)+4040*PULSE(16,1)+1010*PULSE(17,1)
+1010*PULSE(18,1)+6600*PULSE(19,1)+12221*PULSE(20,1)+2020*PULSE(21,1)+4500
*PULSE(22,1)+6262*PULSE(23,1)+34946*PULSE(24,1)+34542*PULSE(25,1)+11211*PULSE
(26,1)+3535*PULSE(27,1)+20200*PULSE(28,1)+12120*PULSE(29,1)+6969*PULSE(30,
1)+10100*PULSE(31,1)+21210*PULSE(32,1)+17170*PULSE(33,1)+19190*PULSE(34,1)
+9090*PULSE(35,1)+39289*PULSE(36,1)+31100*PULSE(37,1)+41915*PULSE(38,1)+16160
*PULSE(39,1)+10100*PULSE(40,1)+11110*PULSE(41,1)+24650*PULSE(42,1)+8383*PULSE
(43,1)+31815*PULSE(44,1)+31310*PULSE(45,1)+15150*PULSE(46,1)+38770*PULSE(47
,1)+11615*PULSE(48,1)+29290*PULSE(49,1)+57241*PULSE(50,1)+15150*PULSE(51,1
)+48278*PULSE(52,1)+27068*PULSE(53,1)+505*PULSE(54,1)
Units: Lamps/Week
Target Delivery Delay=
at
Units: Week
Target Distribution=
1e+06-STEP(100000,15)-STEP(100000,35)-STEP(55000,40)
Units: Lamps
Threshold Work Pressure=
1
Units: Dmnl
22
(75)
(76)
(77)
(78)
(79)
TIME STEP = 0.125
Units: Week [0,?]
The time step for the simulation.
Trainees= INTEG (
Starting Rate-Experience Rate,
Units: Employee
Utilisation = WITH LOOKUP (
Schedule Pressure,
([(0,0)-(2.5,1.25)],(0,0),(0.25,0.25),(0.5,0.5),(0.75,0.75),(1,1),(1.25,
1.1), (1.5,1.17),(1.75,1.21), (2,1.25),(2.25,1.25),(2.5,1.25) ))
Units: Dmnl
({(0,0)-(2.5,2)],(0,0),(0.249491,0.32),(0.5,0.64),(0.75,0.86),(1,
1),(1.25,1.1),(1.5,1.17),(1.75,1.21),(2,1.25),(2.25,1.25),(2.5,1.
25))
WoM Coefficieint=
Units: 1/Week
Work Experience Delay=
2
Units: Week
23
