1.

Go to “Help” in Stella and analyze the implications of using the “SMTHN” (or “smooth”)
function. Discuss why it makes sense to use the smooth function in the model.

Using the "SMTHN" or "smooth" function in Stella can result in more accurate simulations, making it
helpful for analysing complicated systems. Additionally, the "SMTHN" function can help stabilize the
model, resulting in more consistent and reliable simulations. Furthermore, using the "SMTHN" function
provides better and more interpretable representations of the model results. For further explanation,
the SMTHN function is a tool that performs an nth-order exponential smooth of input using an
exponential averaging time, an order number of n, and an optional initial value. It smooths out changes
and highlights trends by setting up a cascade of n first-order exponential smooths, each with an
averaging time of averaging time/n. The function maintains continuity by using the first value of input
data as the initial value. The value of n should be specified as an integer between 1 and 255 (and will
be truncated silently if it's outside this range). If you enter a number outside this range, SMTHN will just
use the closest number within the range without notifying you. To put it another way, SMTHN analysis
your data, smooths it out using a number of processes, and then returns the final smoothed output. A
person who uses this function can control how much smoothing happens and how quickly it reacts to
changes.
 2. Explain the equation for Ordering. What is the effect of Time to adjust capacity and why is the
term Capacity/Lifetime included? Using the option Uniflow ensures that Ordering cannot go
negative. Why is this reasonable assumption?

The equation of ordering is;

Ordering = (Desired_capacity-Capacity)/Time_to_adjust_capacity+Capacity/Lifetime
The "Time to adjust capacity" in the ordering equation refers to how long it takes for a system to change
its capacity or capability to produce something. This has the impact of being cost-effective and having
the capacity to quickly meet customer demands. It is crucial to take this into account when calculating
ordering since it affects how quickly a system or organization responds to changes and other complex
situations in the real world. In contrast, the ordering equation's "Capacity/Lifetime" term denotes the
relationship between the system's lifetime (or how long it lasts or is operational) and capacity (or how
much it can handle). This ratio shows the system's effectiveness and efficiency over time. A system
that has a larger capacity in relation to its lifespan is more effective and able to manage demand for an
extended length of time, ensuring the system's long-term sustainability and performance. In Stella
software, the Uniflow option have the flow to move in only one direction and the flow volume only takes
on non-negative values. Uniflow ensures that the variable "Ordering" cannot go negative. This is a
reasonable assumption because in real-world scenarios because Ordering negative quantities of
something doesn't make practical sense. A person will not surely buy the good if it is negative. It should
be involving a positive quantity of items/orders. Negative orders can lead to unexpected behaviors or
errors in calculations, and can affect in simulating the result. And so, a person will ensure that ordering
cannot go negative to achieved beautiful outcomes.
 3. The model is initialized in equilibrium with both Capacity and Consumption equal to 100 units
per year. Test your answer by simulating over a 40-year period. Price elasticity equals zero such
that the loop through Consumption is deactivated. Explain the purpose of initializing the model
in equilibrium.

The purpose of initializing the model in equilibrium is to set the model's initial conditions to a state where
all variables and relationships inside the model are balanced and stable. Moreover, ensuring the model
is in equilibrium is important in analyzing the system for effective accuracy of the model.

Show in Graph 1: Ordering, Delivering, and Scrapping. Show in Graph 2: Capacity, Consumption, and
Under construction
 4. Go to “Help” in Stella and analyze the implications of using the “step” function. There is no need
to discuss why this function is included. Introduce a step addition to Consumption of 10 units/year
after 2 years. Use the default values of all other parameters. Explain behaviour of both graphs
and then simulate the model to test your explanation. The new equation for Consumption should
now be like this: 100*Perceived_price^Price_elasticity+step(10,2)

The STEP built-in creates a one-time step change of a specified height at a specified time. The height
and time values can be variables or constants. This means that the "step" function allows modelers to
simulate the effects of sudden interventions or changes in the system. As shown in the graph in number
3, the Consumption follows the original equation. Now, when added by a step function of Consumption
of 10 units/year after 2 years, there is a sudden increase in Consumption as shown now in the Graph.
The Consumption graph shows a steady increase, but after 2 years, it shifts by 10 units/year,
maintaining this level for the rest of the simulation.
 5. Insert a “Knob” in the Interface tab. Select “N” with min and max values of 0 and 8, respectively.
The knob can be turned around to adjust the value, or exact value can be keyed in directly into
the field. N 6 4 0 8 Simulate the model with N=6 rather than N=1. Show the simulation results
and explain behavior of both graphs.

The use of a knob is to adjust the input values in your model by dragging it up or down.
You can control size, color, and the range over which a knob operates. Knobs can be used with any
model variable, but will require activation via the override button ( ) for variables that aren't constants.
For stocks, a knob controls the initial value.

If N represent the number of units/cycles produced in the process, setting it to 6 instead to 1 would
likely to result in higher production process and led to increase of outputs. As shown in the graph, where
N is an external input to ordering, there is an increase and then sudden decrease. These changes may
vary depending on the customer demands. If there is an increase of demands, it would likely to result
of higher production outputs. If there will be less demands, then the result is less outputs. In graph 1,
the ordering, delivering and scrapping lines shows they are almost the same as it changes over time.
Graph 2 is likely similar to graph 1 but the Consumption remains the same. We can observe in both
graphs how sensitive the model is when changing the equation.

6. Insert a “Slider” in the Interface tab. Select “Time to adjust capacity” with min and max values of
0 and 3, respectively. The slider can be adjusted, or exact value can be keyed in directly into the
field. Now that N = 6, set Time to adjust capacity = 0.5 rather than 2.0. Explain and test by
simulating the model and showing both graphs.
The time to adjust capacity using slider allows to control the system when its adjusted-on time as it
meets fluctuation on demands and respond quickly in customer/consumer behavior ensuring the
system remains effective. In this part, the time to adjust capacity is change into 0.5 instead of 0.2.
Adjustments in the time to adjust capacity affects the ordering, delivering, and scrapping in graph 1 as
it shows a faster adjustment in the capacity of a system. In graph 2, we see that the capacity and under
construction levels are more closely aligning with the consumption levels as the demand changes over
time.
7. Reset Time to adjust capacity to 2 years, leaving N = 6 as is. Insert a slider for Construction time
with min and max values of 2 and 6, respectively. Set to 0.5 year. Explain and simulate to test
the model and show both graphs.
The construction time slider allows us to control the time it takes to finish what the production is
creating/building. Setting it to 0.5 and setting the time to adjust capacity back to 2 years means the new
construction projects are completed/finish quickly allowing to respond quickly to the changes of
demands. In graph 1, we can see the levels of delivering adjusts faster as it closely like the levels in
ordering to meet customer demands while the scrapping had higher level over the system. In graph 2,
the capacity and under construction shows a maintaining a similar level flow as it responds to changes
in demand while the consumption maintains a steady level all through the system.

8. Reset Construction time to 4 years. Now set the Price elasticity to -0.2 using a knob with min
and max values under your discretion. Keep the default value of Time to change PP (perceived
price) equal to 1 year. Discuss how quick and strong this feedback loop is relative to the loop
through Ordering and Capacity. Explain behavior and simulate to test the model and show both
graphs.
Price elasticity of demand is a measure of the change in demand for a certain product to a change in
its price. The price elasticity is set to -0.2 with a min and max of -1.2 and 0.8. The feedback loop through
price elasticity with -0.2 is slow as changes in price have impact in consumption and also the effect od
construction time of 4 years. The feedback loop through the capacity and ordering involves changes in
demand affecting ordering and capacity adjustments. In graph 1, the ordering, delivering, and scrapping
shows similar levels in flow as it adopts to the changes in demands. In graph 2, the capacity and under
construction also has similar levels in flow while there is a sudden steady of decrease in consumption
over time.