Control Theory Case Study

Control Theory Case Study

Control
theory originated with the goal of managing small, mechanical operations (such
as the thermostat example in your lecture) but it has since been applied in
broader contexts. For this assignment, select a service operation (a bank,
hospital, auditing company, financial consulting, etc.) and apply control
theory to a particular process within the business. Explain how the concepts
found in control theory can be used to ensure the smooth operation of the
process. In a bank, a process to which we could apply control theory could be
managing the length of the lines. In financial consulting, control theory could
be applied to maintaining the balance between risk and return.

For this assignment, begin by choosing
and describing a specific process within a service operation. Describe what the
goals would be (maintain risk levels, manage queue lengths, maintain medicine
inventory, etc.) and then explain, using relevant vocabulary, how control
theory can be used to keep the goals on target. Use research to both find
details about your selected type of business and also to learn more about
control theory concepts. Be specific in your description and give concrete
examples of what must be done. To support your arguments, create two graphs:
the first should depict the feedback loop in the operation and the second
should show the stability of the operation (how the value of the objective will
behave over time). The online lecture has examples for both of these graphs.

Control Theory
Lecture

The
control theory explains how to control a parameter. For example, you can
control the temperature inside your home by using a thermostat. This device
either activates the furnace to heat the house or the air conditioner to cool the
house. Managerial control processes in business work similarly.

The Control Loop

The
figure below shows a control loop. On the left is the thermostat setting. In
winter if you were to set the thermostat at 70º Fahrenheit (F), the living room
slowly cools down below 70º F because it loses heat. A sensor continually
measures the living room temperature and compares it with the target
temperature of 70º F. If the temperature falls below 70º F the thermostat turns
the furnace on. When the temperature rises above 70º F the thermostat turns the
furnace off.

Thermostat Control

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In
the control loop or feedback loop the sensor measures the temperature and
communicates this to the comparator in the thermostat. Imagine a situation
where you need to use a fireplace to heat your home, manually control the
opening and closing of vents, and add firewood based on your perception of the
ambient temperature. Manual control is more difficult and inaccurate.

In
an automated heating system the thermostat uses the power of the furnace. So in
any control system the controller component needs power. Similarly a manager
needs to possess powers to manage the business such as the authority to spend
money within the specified budget. A manager also requires to posses the
authority to reward and impose deterrents to monitor employee behavior.

Another
thing to note about the control process is stability. The following
figure displays a temperature and time graph for thermostatic control of
temperature in the house.

Room Temperature Over time

As
you can observe the furnace is switched on when the temperature reaches 70º F,
and switched off when the temperature reaches (70 + x)º F, where x refers to a
value specified to ensure stable operation and avoid overheating. If the value
of x is too large, the average temperature will be more than 70º F. If the
value of x is too small or if the heating and cooling of the room happens too
fast, it will result in instability and temperature fluctuations.

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In
the figure below the thermostat switches the furnace on and off haphazardly,
which results in the wear and tear of the control mechanism.

Let’s
discuss an example to illustrate instability in the business environment. The
customers in a restaurant complain that the coffee is not hot enough. If the
cook turns up the temperature setting too much, the coffee becomes too hot and
the customers complain. If the cook sets the temperature setting too low the
customers complain that the coffee is cold. When you design a business control
system you need to ensure that control processes are stable.

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Entropy

In
a business environment, you often need to control various complex variables.
For example, you are the manager of the manufacturing department in a company,
and you are asked to increase the productivity of employees in the department.
To do this you may need to ensure high employee morale, the timely delivery and
quality of the raw materials, the smooth operation of machinery, and conducive
working conditions. Any of these variables can go awry. For example, working
conditions may be bad because of poor air conditioning, dirt, or harmful fumes.
The manager needs to ensure that remedial actions are taken immediately. To
handle such contingencies and measure the degree of disorder, the concept of
entropy is applied. The term originates from the word
“thermodynamics.”

Observe
the figure below. You have to communicate this figure to a friend over the
phone by describing it in your own words as best as you can. At the other end
your friend is listening to you, with a paper and a pencil. She has to
reproduce the figure as closely as possible.

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You
may ask your friend, “Draw a circle with a diameter of 3 inches. Draw a
square at the center of the circle with side dimensions of 1 inch. Draw nine circles,
each 1/10 inch in diameter, and darken the circles. These circles should be
drawn in a 3×3 lattice where each circle is at a distance of 1/4 inch from its
neighbor.” Given these instructions your friend may be able to produce a
replica of the figure. The amount of instructions you give over the phone is
the amount of disorder or entropy in the figure.

Observe
the figure below. It is similar to the previous figure except that the nine
points are strewn inside the circle. To describe this figure to your friend
over the phone, you need to provide more details. You’ll need to describe the
position of each circle in a coordinate system, such as a graph paper. In this
figure the content, amount of disorder, or entropy is greater than in the
earlier figure.

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Now
imagine that the nine circles in the figure below are nine sheep grazing in a
circular field, and that the square in the middle is a fenced area. Assume that
a shepherd rounds up the flock at the end of the day into nine stalls in the
shelter, as in the figure from the previous page.

The
controlling action of the shepherd reduces the entropy of the system.

Control
thus reduces the entropy or disorder in a system.

The
ideal situation is one where you are able to measure the entropy in a business
before and after a manager performs controlling actions, so that you can assess
the work of the manager. But it is not possible to measure entropy.

For
example, it is very difficult to measure the entropy of something as simple as
a scribble. Observe the figure below. According to some mathematical theories
the entropy of a scribbled figure is infinite.

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Thus
only subjective measures of entropy are available to assess managerial actions.

If
you were told that a football team scored 20 points when coach A trained the
team, and the team scored 30 points when coach B trained the team, can you
conclude that coach B is better than coach A? No. You need to consider other
factors such as the opposing teams, how well they played, who coached them, and
so on.

Similarly
you cannot conclude that manager A produced a profit of $1 million and manager
B produced a profit of $2 million without considering the economic conditions,
competition, and political climate of the business.