(upbeat music)
Hello.
I'm Professor Rick Jerz and I welcome
you back to another session of Business Analytics.
One overriding theme of this topic is that business
decisions have financial consequences.
In this session, we are going to explore how businesses make decisions
under uncertainty and how a modeling technique called
"decision trees" can help companies select the best alternative
by calculating expected payoffs of alternatives.
We are going to see that some decisions involve risk and that it would be helpful
if we have some way of analyzing the risk of decisions.
Risk involves uncertainty or probabilities.
So in this session, we are also going to be introduced to some basic probability
concepts in the context of this decision making environment.
Let's get started.
The goals of this session are as follows:
To understand how businesses make decisions.
To model business decisions using decision trees.
To understand sensitivity analysis.
And learn to use Excel for decision analysis using decision trees.
Business decisions drive businesses.
Being able to make sound business decisions can improve
the operations of a business, and improve profitability.
Some people think that business decisions are made through gut feel, or intuition.
And perhaps, gut feel and intuition are always present in all business decisions.
But I believe that if you have better-educated workers
and managers who understand some decision-making tools and techniques,
knowing how to apply these tools and techniques can lead to better decisions.
Decisions fall into two major categories: those under certainty
and those under uncertainty.
Sometimes these are referred to as "deterministic" and "probabilistic."
Certainty means that the relevant parameters, such
as cost, capacity, and demand, are all known values.
When we know for certain which of the possible future conditions will happen,
the decision is usually relatively straightforward:
simply choose the alternative that has the best payoff.
This might sound relatively simple, but we still need to know how
to calculate payoff.
Payoff is typically profits minus costs, or something similar.
Uncertainty means that it is impossible to assess
the likelihood of various possible future events.
When we are uncertain about these future events,
we might still make statements like, "This probably will happen,"
and the word “probably” gets us to think about the mathematical term,
"probability." So decisions under uncertainty
somehow have to deal with probabilities and expectations.
Also, an uncertain event implies that there are at least two
or more outcomes, each with a probabilty and an economic consequence.
Well, as some of you might already know, dealing
with probabilities, mathematically, can become a bit challenging.
In this course, we will learn about calculating uncertainty.
In most businesses, uncertainty is much more common than certainty.
For example, uncertainty can include product and service
configuration, product pricing, staffing, location planning,
facility sizing, customer support levels, and investment decisions.
Some causes of this uncertainty are people's behaviors,
equipment failures, the weather, and even politics.
What are the characteristics of most decisions?
We have a set of possible future conditions that will have
a bearing on the decision results.
We have a list of alternatives from which to choose.
We have a known payoff for each alternative under each possible
future condition.
Given these characteristics, our solution is to choose
the alternative with the highest expected value.
Sometimes authors refer to this as the "expected value," or EV,
and some refer to this as the "expected monetary value," or EMV.
This solution seems so easy to say, "choose
the alternative with the highest expected value,"
but how do we really calculate the highest expected value?
One technique that many businesses use to make good decisions
is to "model" the scenario before making your decision.
And many models are built around quantitative approaches.
Modeling allows us to analyze the trade-offs
of various alternatives, and establish priorities.
A model, however, is an abstraction of reality.
One might build a "physical" model to help analyze a scenario.
For example, what a building
might look like, or a new bridge spanning the Mississippi River.
A smaller physical model can be helpful.
Models can also take the form of a schematic.
This word, "schematic," is a fancy word to describe a picture, or a figure.
And models can be mathematical, as in a set of equations.
The kind of model that one might choose to build for a particular business
scenario does depend upon a couple factors.
Cost can vary between the building of these different kinds of models.
The kind of information that we get out of a model might also vary.
How well a model helps us understand the real business situation can vary.
And models vary in their flexibility.
Namely, how many factors can we adjust, and ask
different kinds of what-if questions.
In this session,
we will learn about a very interesting model called a "decision tree."
Decision trees are a structured tool to help make sequential decisions
in the face of uncertainty.
Decision trees provide both a visual advantage and a calculated results advantage.
Here are some of the key characteristics of decision trees.
Decision trees are composed of nodes.
There are two kinds of nodes, a decision node, represented by a square,
and an event node, represented by a circle.
A decision tree also has branches, as in physical tree branches.
Branches leaving square nodes represent alternatives.
Branches leaving the circular nodes represent chance outcomes.
For chance outcomes, the probabilities for all branches must add up to one.
We refer to this as being "collectively exhaustive."
Also, the branches must be "mutually exclusive."
This means that each of these branches must represent one kind of outcome.
Each final branch of a decision tree must have a numeric value,
either cost, revenue, or something like this.
Time gets represented from left to right.
However, we actually analyze a decision tree from right to left.
When we are done with this analysis, we choose
the highest expected value alternative.
In some situations, we might try to minimize the cost of a decision.
In these cases, we choose the lowest expected cost.
Here is an example of a business decision to make.
Below the business scenario, I represent this problem with a decision tree.
You should be able to note the various decision nodes and event nodes.
Notice that every final branch ends with a value.
Also, take note of the visual appearance of this decision tree.
We still have to analyze this model to help us make the decision.
Should we build a small or a large video arcade?
Here are the steps of constructing a decision tree.
Start by defining the problem.
This step seems relatively simple,
but it is essential in the overall decision-making process.
Based upon logical or sequential
order of events, do the following: add decision nodes,
start with one.
Add branches for alternative decisions
and/or event nodes.
Add event nodes.
Add chance outcomes to these event nodes,
repeat these steps one through four for all of the alternatives.
At terminating branches, show ending values.
Add probabilities to branches emanating from event nodes.
Here is how we solve a decision tree.
Start with the final branches, and evaluate each event node
and each decision node.
For an event node, compute the expected value as the weighted average.
This weighted average involves multiplying the value times
the probability for each branch, and adding them together.
Write this expected value above the event node.
For a decision node, pick the branch with the highest expected value.
Write this number above the decision node.
Cross out, or prune, the branches not selected.
The decision tree is solved when you have evaluated all nodes.
The expected value of the optimal decision
is the expected value of the starting node of the tree.
Let's try to construct and solve a decision tree for the example
in the reading for Bill Sampras' summer job decision.
I like this problem
because it contains both deterministic and probabilistic events.
We must first define the problem.
This problem that Bill faces is, should he take an immediate offer
from John, wait for another offer from Vanessa,
or wait until the summer and go through the regular campus
recruiting process, and hopefully get a job that way?
If we think about the timing of these events, Bill can decide
whether or not to take John's offer right now.
This is a certain event.
If Bill doesn’t take John’s offer,
well, this gets more interesting because of uncertain events.
This is the first decision Bill must make, and since it's under his control,
we represent this as a square decision node.
In Step 2, we add branches for alternative decisions.
In this case, there are two alternative decisions:
to accept John's offer and to reject John's offer.
Yes, we realize that this particular decision is relatively simple.
It is always best to learn a complex method with a simple example.
In some scenarios, we might have more than two alternatives
emanating from a decision node.
In Step 3, we add event nodes.
The next event that Bill faces is to wait for an offer from Vanessa.
We represent the event using a circle node because it is outside Bill's control.
In Step 4, we add chance outcomes.
In this case, this particular node has only two outcomes.
Either Vanessa does or does not make Bill an offer.
We must repeat these four steps for every branch
until every branch has no other decision or event associated with it.
For example, the "offer from Vanessa" branch contains a decision node.
If Vanessa make Bill an offer, he must decide to accept or reject it.
This is a decision node because it's under Bill's control.
The offer from Vanessa has one deterministic result, a job offer value.
In Step 6, we show ending values at all terminating branches.
One interesting aspect of this particular problem is that if Bill waits
to go through the recruiting process, he isn't sure that he will get an offer,
and if he does, what the job salary might be.
Bill does some research, using historical records, and attempts
to define the various probabilities associated with different yearly salaries.
The last branch illustrates that 5% of candidates
do not get an offer, represented by a zero salary.
This event is also avaiable to Bill even if he does not get an offer from Vanessa.
In step 7, we must produce probabilities
for each outcome emanating from an event node.
In step 6, Bill did this by researching historical data.
In this course, we will spend a lot of time talking about event probabilities.
Sometimes we will have historical or sample data, and sometimes we will not.
For example, how do we know the likelihood that Vanessa will make an offer?
If we don't have data, we should use our best estimate.
In this problem, we are told that Bill estimates a 60% chance
of getting an offer and a 40% chance of not getting an offer from Vanessa.
Notice that these outcomes are collectively exhaustive
and mutually exclusive.
We have identified all possible outcomes,
and their probabilities sum to exactly one.
To solve this decision tree, we start with the final branches
and evaluate each event node and each decision node.
The final event nodes in this decision tree is to "wait
for the recruiting process." We calculate this node's expected value
as a weighted average calculation, meaning we multiple the salary
by the probability for each branch, then add these values together.
We calculate $11,580.
In my next session,
I will show you how to use Excel to calculate this weighted average.
When we work up to an event node, such as accept or reject Vanessa's
offer, we evaluate which branch provides the greatest expected value.
We write this value ahead of the decision node and can cross out,
or prune, those branches with a lower expected value.
For example, if we estimate that Vannessa might make an offer of $14,000,
this is greater than $11,580,
so we cross out "Reject Vannessa's Offer."
We continue working our way up this decision tree to the first node,
again, always picking the alternative with the greatest expected value.
The final decision tree provides the logic for Bill's decision.
Bill should reject John's offer, hoping to get an offer from Vanessa.
If Vanessa makes Bill an offer, this is the one he accepts.
If he doesn't get an offer from Vanessa, he should go through the
recruiting process, focusing on having a good interview to get his best offer.
Bill's expected income is $13,032.
Of course, if Vanessa makes a $14,000 offer and Bill
accepts this, he does better than his expected salary.
It now seems like we are finally done analyzing this decision, but not quite so.
Remember that some of the values we used in this decision tree were certain.
The $12,000 offer from John, for example, was certain.
Others values were uncertain.
Wherever we have an uncertain value, we might want to explore a little further
by asking, "How would my decision change if some of these unknown values
were to change?" This questioning process
sometimes is referred to as "what-if analysis."
The more technical term for this is "sensitivity analysis."
When we do sensitivity analysis, we determine the range of values
for which an alternative has the best expected payoff.
Sensitivity analysis is not easy, and it does take time.
The author says, "it's as much an art
as it is a science." Okay, we have learned this decision
tree modeling technique that helps us make decisions.
One problem that you probably notice about this
technique is that it can involve a lot of calculations,
especially for larger models and sensitivity analysis.
Some of my colleagues say that they don't see
this decision tree technique being used much in companies.
Yes, I understand what they are saying.
The modeling and calculations can take too much time.
However, in our next session, we will learn how to create decision trees
with Excel to make modeling, calculation,
and sensitivity analysis more effortless.
Remember, however, that this is just a model trying
to represent the real world, and models are abstractions of the real world.
Models have limitations.
Quantitative information may be over-emphasized over qualitative
information.
Throughout this analysis of Bill Sampras' problem,
we assumed that he would be happy with any of the alternative job offers.
But in reality, different jobs may appeal to people differently.
Jobs are not necessarily all equal.
Models may be incorrectly applied, and results misinterpreted.
This is why we are learning about this decision modeling technique, so that
you will apply this technique properly, and not misinterpret the results.
Other people who have not been exposed to decision tree
models might not understand your results.
Another limitation is that non-qualified
users may not comprehend the model's rules.
You have learned this technique as you use it to help make at work,
don't be surprised if when you show it to your manager,
or your coworkers, that they look at you and say, "Huh?" Lastly,
the use of models does not guarantee good decisions.
If Bill does receive an offer from Vanessa and accepts it,
it is no guarantee that Bill has made the best decision.
Perhaps if Bill had accepted John's offer, that a year from now, Bill would've
been promoted to being the, oh, let's say, vice president of John's company.
Maybe accepting John's offer would have led to higher future salaries.
When building business models, you must decide when to call it quits.
For example, in Bill's scenario, maybe there is a way to model
next year's potential income and the following years.
Maybe lifelong earnings potential.
We could do this,
but it will take more time, and time means more money in business.
We have to decide when to call it quits.
In my next session, I will show you various ways
to use Microsoft Excel to solve these decision tree problems.
(upbeat music)
Thanks for taking time to spend some moments with me.
I hope that you have enjoyed what I have shared with you.
If you ever have any questions or need my help, please let me know.