# Evaluation Of Decision Trees In Operations Management Accounting Essay

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The main aim of this study is to identify the most influential variables of decision trees. First, we are going to explain a few things about what decision trees are, where they came from, where they are used and what types of decision trees exist. Advantages and disadvantages is also an essential part of this study. Then we are going to present some examples from the business world.

## INTRODUCTION

Decision trees come from the Decision theoryÂ . Decision theory is a theory about decisions. The subject is not a very unified one. On the contrary, there are many different ways to theorize about decisions, and therefore also many different research traditions. Decision theory provides the necessary knowledge with related analytical techniques in order to help aÂ decision makerÂ to choose among a set of alternativesÂ and their possibleÂ consequences. The probability to occur each possible consequence is known. Therefore, each alternative is connected with a probability distribution, and a choice among probability distributions. When the probability distributions are unknown, one speaks about and can choose the best alternative. Decision theory recognizes that the range produced by using aÂ certain criterion has to be sequent with the decision maker's objectives. Decision theory can be used to conditions of certainty,Â risk,Â orÂ uncertainty. This theory is used in economics, psychology, philosophy, mathematics and statistics. It Â is concerned with identifying theÂ values, uncertainties and other issues relevant in a givenÂ decision. The results are considered to beÂ rational and optimal. Decision theory is related to the Â game theory. There are certain stages in decision theory:

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Identification of the problem

Obtaining necessary information

Production of possible solutions

Evaluation of such solutions

Selection of a strategy for performance

(http://pespmc1.vub.ac.be/ASC/DECISI_THEOR.html)

## COMPARISON OF DECISION THEORY

Decision Theory consists of three subcategories, decision criteria, decision trees and game theory. Decision criteria represent a distribution of results

according to the various states of nature.Â The probabilities are considered

known or can be calculated. Decision trees are used in more complex situations, we are going to analyze decision trees further. Game theory aims to analyze and evaluate various "strengths decisions" under competitive conditions. The main feature of the game theory over the other

decision problems is that the body of the decision ("Player" of the problem) maximizes a function of payment that depends on the decisions of the other

competitors (players).Â So the benefit of a player may be

opposite with the benefit of another player.Â As a result, a decision that seems reasonable, can lead to disaster.

(http://bs.teikoz.gr/dinopoulou/teaching/OpRe/OperRes_print08-09B.pdf)

## DEFINITION OF DECISION TREES

Decision Trees are useful tools that help people choose between several actions. They provide a highly effective structure where someone can explore the options that he has and can investigate the possible outcomes of choosing those alternatives. They also help you to balance the risks and rewards associated with each possible action. Those characteristics make them particularly useful for choosing between different strategies, projects or investment opportunities, particularly when the resources are limited. A decision tree classifies the data items with a series of questions about the features associated with the items. Each question consists a node, and every internal node points to all possible answers. The questions are formed hierarchy and are encoded as a tree. In many problems decision trees play an important role.

## Algorithm

the algorithm used to calculate and maximize the gain in decision trees is :

The algorithm is based onÂ Occam's razor and is consideredÂ heuristic. Occam's razor is formalized using the concept ofÂ information entropy:

WhereÂ :

E(S)Â is theÂ information entropy of the subsetÂ SÂ ;

nÂ is the number of possible values of the attribute inÂ SÂ (entropy is referred to one only chosen attribute)

fS(j)Â is the frequency (proportion) of the valueÂ jÂ in the subsetÂ S

log2Â is theÂ binary logarithm

Entropy is used in order to decide which node will be split next by the algorithm. So, the higher the entropy, the higher the possibility to improve the classification.

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(http://en.wikipedia.org/wiki/ID3_algorithm)

## Classification Tree

In cases, where there are different pieces of information, we can use a classification tree. We can measure and determine the most predictable outcome. Solving a classification decision tree we use a binary method of categories and subcategories to define the different variables of an alternative result. This kind of tree can be used in probability and statistics.

## Regression Tree

This type of decision tree is used when you are using different information to define only one single preset outcome. During the process of constructing this tree the different pieces of data are divided into sections and then into sub groups. This kind of tree is used mainly in real estate calculations.

## Tree Boost

When we want to improve the accuracy of the decision making process we are using tree boost. We can choose only one variable and then calculate and minimize all the possible mistakes. This minimization can provide us with more specific information. This kind of tree is used mainly in accounting and mathematics.

## Decision Tree Forests

Decision tree forests consist of several different decision trees that were grouped in order to calculate a more certain outcome. Sometimes, the decision tree forests are used to estimate the general outcome of a particular event based on what all the different decision trees subsequent.

## Classification and Regression Tree

This type of decision tree is used to predict the result of an event with the assistant of dependent factors to make the most logical conclusion. To do this we can use both interim indicators (what has happened) and real time indicators (what happens now) or even specific cut categories to examine the expected result. This is used mainly in science.

## K Means Clustering

K Mean consists the least accurate method of decision trees. Using this process combines all the different factors that you have identify previously where you conclude that all of the clusters are the same. This hypothesis can cause some of the predicated conclusions to be hugely different. This tree is used mainly in surveys and studies on the field of genetics.

## How to use decision trees

Decision Tree starts with a decision that you need to make. You can start drawing a small square to represent the decision on the left hand side of a piece of paper. From this box you draw out lines towards the right for each possible solution, and in order not to get confused you can write a short description of the solution along the line. At the end of each line, you put each result. If the result of taking that decision is uncertain, you should draw a small circle. If the result is another decision that you need to make, you draw another square. Squares represent decisions, and circles represent uncertain alternatives. Write the decision above the square or circle. Starting from the new decision squares on your diagram, draw out lines representing the alternatives that you could select. From the circles draw lines representing possible results. Again make a brief note on the line saying what it means. Continue doing this until you have drawn out as many of the possible conclusions and decisions as you can see from the original decisions.

(http://www.mindtools.com/dectree.html)

## Designing a decision tree

The symbols in a decision tree are geometric shapes used to define the different actions that can arise during a process. Although flowcharts can include also text descriptive the symbols on the chart have a different shape in order to give visual cues to the reader and understand the chart. Usually, without even reading the text, a user can quickly reach the general process based mainly on the order of the symbols..The decision nodes are commonly represented by squares. The chance nodes are represented by circles and the end nodes are represented by triangles.

## EXAMPLE 1:

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An industry is going to expand its facilities in order to achieve a bigger altitude of productivity and a smaller cost.As they noticed the growing demand of their products, they are expecting to keep it for the next years.According to the predictions of the marketing department even if the production department empoyees disagree with this estimation, they beleive that the firm have to study the scenario of low demand.

## SOLUTION:

The values are calculated as follows:

## A. Building of big unit and growing demand for the 7-year period.

Profits:500.000*7years=(3.500.000)

Minus unit cost 2m =1,5 m

## B. Building of big unit and reduced demand for the 7-year period.

Profits:100.000*7 years =(700.000)

minus unit cost 2m = (loss)

## C. Building of small unit, growing demand the first 2 years, decision to expand and continuously growing demand for the next 5 years.

Profits: 300.000 * 2years = 600.000

*5 years=(3,6m)

Minus Unit cost 1m

Minus expand cost 1,5m=1,1m

## D. Building of small unit, growing demand the first 2 years, decision to expand and continuously reduced demand for the next 5 years.

Profits:300.000 *2 years= 600.000

100.000 *5years=(1,1m)

Minus Small unit cost 1m

Expand cost

## E. Building of small unit, growing demand the first 2 years, decision to not expand and continuously growing demand for the next 5 years.

Profits: 300.000*2years=

300.000*5years=(2,1m)

Minus Small unit cost 1m

## F. Building of small unit, growing demand the first 2 years, decision to not expand and reduced demand for the next 5 years.

Profits:300.000*2years=

150.000*5years=(1,35m)

Minus Small unit cost 1m

## G. Building of small unit, low demand the first 2 years, decision to not expand and continuously low demand for the next 5 years.

Profits:150.000*7 years=(1,05m)

Minus Small unit cost 1m

## =50.000

(Pandelis Ipsilandis, 2006)

## EXAMPLE 2:

The owner of a computer store is wondering what he should do with his business over the next 5 years. The owner sees three options. The first is to enlarge his current store, the second is to locate at a new site and the third is wait and do nothing. The expand or move does not take a lot of time so the store does not lose revenue. In case that nothing is done and strong growth occure at the first year, then expansion will consider again. Waiting more than a year will allow competition to move and expansion will no longer be an option.

Strong growth because of increased population has a 55 percent probability.

Strong growth because of increased population gives annual return of \$195,000 per year. Weak growth mean annual return of \$115,000.

In case of expansion, strong growth gives annual return of \$190,000 and weak growth gives \$100,000.

In case of no changes, there will be \$170,000 returns per year in strong growth and \$105,000 if there is weak growth.

Expansion costs \$87,000.

New site costs \$210,000.

If there is strong growth on existing site and there is an expansion at the second year, the cost will be \$87,000.

Operational costs are equal.

## SOLUTION:

The values are calculated as follows:

\$195,000*

5yrs

\$210,000

\$765,000

\$115,000*

5yrs

\$210,000

\$365,000

\$190,000*

5yrs

\$87,000

\$863,000

\$100,000*

5yrs

\$87,000

\$413,000

\$170,000*1yr+

\$190,000*

4yrs

\$87,000

\$843,000

\$170,000*

5yrs

\$0

\$850,000

## DO NOTHING NOW,WEAK GROWTH

\$105,000*

5yrs

\$0

\$525,000

(Jay Heizer & Barry Render,2011)

Decision Trees are pretty easy to understandÂ almost for everyone. That is very important because they can be used in many different types of problems. Decision Trees are mapped nicely to a set of business rulesÂ . As we said and before because of their easiness in understanding they can be applied to real problemsÂ too . In decision trees we can't make any prior assumptions about the data, while we are able to process both numerical and categorical data. They are useful tools for operational decision making. Using decision trees enables effective use of backdata, while probability allows flexibility. Last but not least, decision trees encourage clear thinking and planning.

(decision_tree_primer_v5)