Overview of Decision Trees and Multi-Stage Decision Problems - Essay Example

Performance Management Table of Contents Overview of Decision Trees and Multi-Stage Decision Problems 3 Decision Trees 3 Multi-Stage Decision Problem4 Constructing the Tree 4 Evaluating the Decision 9 Imperfect Information 10 10 Example 10 Perfect Information 11 The Value of Perfect and Imperfect Information 12 Value of Imperfect Information 12 Value of Perfect Information 13 References 16 Overview of Decision Trees and Multi-Stage Decision Problems Decision Trees The concept of decision tree can be described as a diagrammatic representation which is generally created with the intent of making decisions by taking into consideration all the possible probabilities of the activities and their outcomes. It takes the shape of a ‘schematic tree shaped’ figure that projects all the courses of actions. Each of these actions is represented in the branches of the tree. One such structure has been provided below for lucid comprehension purpose (Quinlan, 1986). Figure 1: Source: (Quinlan, 1986). The above provided graphical tree structure projects a brief understanding regarding the functionality of the decision tree. The concept of decision tree has gained significant amount of importance in the present day business scenario. This concept can be explained with the help of an example. For instance, within a business organisation, often it happens that the managers and the leaders find it seemingly difficult in order to make proper decisions. This is due to the fact that in almost every situation, the outcomes of certain decision steps are unpredictable. In such cases, the decision tree provides a clear picture regarding the type of outcomes or consequences that might be attained through implication of a specific decision step (Sobolev Institute of Mathematics, 2009). Multi-Stage Decision Problem The concept of multi-stage decision problem can also be described with the example of decision tree structure. It can be comprehended that the decision tree is an interlinked representation of all the possible decisive steps that can be taken for achieving something. Thus, a wrong decisive step in the preliminary stage of the tree structure might create issues for the later stages. This concept is known as the multistage decision problem (Hoyland & Wallace, 2001). Constructing the Tree As already stated above, the decision tree can be constructed in a similar context to that of a tree structure. This tree structure generally starts from the left end of the sheet and moves along to the right end. In this regard, all the nodes within the decision tree describe the possible courses of action that can considered in the decision making process. The choices of the decision completely depend on the managers based on the consequences which they are capable of undertaking (University of Regina, 2013). Taking an instance of marketing practice in this context a proper comprehension can be gained. For instance, a company wants to launch a new product within the market however the current state of the market projects low subsidization support from the government and high inflation rate. Now, the company needs to decide on multiple factors such as whether to price the product as (high or low) or whether to launch the product when the economy and the inflation rate stabilize. All these factors will be present in the box nodes of the decision tree and the estimated consequences that might arise due to taking of these decisions will be mentioned in the circle nodes of the decision tree (University of Regina, 2013). Figure: 2 The above provided diagram of the decision tree describes the concept of certainty and uncertainty in a detailed manner. The first box to the left end of the paper describes the decision that needs to be taken. The two branches that come out of this decision box describe the possible outcomes as a result of choosing this decision. As can be witnessed that the top branch that comes out of the decision box has no nodes attached to it and thus it can be considered as outcome with certainty. However, by taking into consideration the second branch that comes out of the decision box, it can be termed as outcomes with uncertainty as it has got two more branches coming out of it (University of Regina, 2013). Example Description of the Business Expansion Process with the Help of Decision Tree Figure: 3 The above provided diagram provides a specific understanding of the business expansion process using the decision tree structure. The primary decision has been represented by (0). This decision is regarding the expansion of a business process through bringing about development. The decision process also requires the investment of £10 million. From the (0) decision node, there emerges two branches which describe whether the decision regarding the business expansion will continue or not. Here (1) node describes the decision getting successfully accepted whereas the (13) node describes the failure of the decision. After the decision has been taken, the next step is regarding taking another decision that might be in the context of expanding the manufacturing plant or not. This decision can be understood by observing the node (3). Now, from this node, three possibilities are ought to emerge as can be understood from the provided diagram. These three possibilities include whether to drop the decision of the manufacturing plant expansion or whether to expand it in a small scale or in a large scale. These three decisions can be understood by observing the nodes (2), (4) and (12). Based on the selection of one of these three nodes, the related decision is needed to be made regarding the time period for the expansion process for the node (2) and node (4) i.e. either two years, three years and five years. All these explanation processes generally help in describing the way in which the concept of decision tree provides assistance in terms of making effective decisions within business processes. This is due to the fact that this concept provides the decision maker with the leverage of taking into consideration all the possibilities and their related outcomes before the individual comes up with an effective decision. Evaluating the Decision The evaluation process of a decision tree can generally be explained in the context of analysing every single decision node present within the tree structure in order to ensure that an effective decision along with its related consequences or outcomes gets undertaken. The evaluation pattern of the decision tree generally begins from the right hand side and forwards towards the left hand side which is completely opposite to the direction in which the decision tree gets constructed. Adding to that, in the evaluation process, all the decisions and their relative outcomes (squares and the circles) get labelled with numeric values. The numbering gradually starts from the right hand side bottom node of the tree and goes up eventually as shown in the above provided diagram (Osei-Bryson, 2004). Apart from just the labelling, each and every outcome from the decision making process is provided with a probabilistic value. These values are also known as the expected probabilistic values. Based on the level of the expected value, the management within an organisation decides the decision process to be selected. Despite its multiple aspects, this process of decision making is not considered accurate due to a few factors that have been discussed below: (Osei-Bryson, 2004). The first downfall in the context of using the expected value for the decision making process is that these expected values provides long average outcomes that only proves its validity in case the decisions undergo multiple repetitions. Thus, the chances of attaining similarity between the real outcome and the expected value gradually decreases The second downfall being that the process of attaining exactness in the estimated probabilistic values is highly complex. This is due to the fact that the presumed situation and the real life scenario do not match every time The third downfall being that the concept of expected value in the decision making process only works when the chances of the investors falling into the risk factor are quite low. This is mainly due to the reason that during such instances none of the risk handlers remain available On the contrary to the positive facts, all these above mentioned points describe the negative consequences of using the decision tree concept within the process of organisational decision making (Osei-Bryson, 2004). Imperfect Information Imperfect information can be described as a scenario where the level of information existing in between two parties involved in a transaction process is variable. This gradually results in poor decision making due to the fact that none of the two involved parties possess full information regarding the product or service being exchanged. Multiple instances exist in this context. A few of these instances have been mentioned in the example section (Marshall University, n.d.). Example In this regard, an example of car selling process is considered. In this process, it is necessary that both the seller and buyer of the vehicle should have equal and complete knowledge about the car being purchased. However, the real scenario often appears to be quite different than what is being expected. Very often, it happens that the seller of the car possesses much more information in comparison with the buyer. This is due to that fact that the seller remains confined to the car for a higher duration as compared to the buyer. As a matter of fact, the seller will have higher knowledge of the car’s features such as its quality, design and performance among others (Aliev, 2013). Apart from the above described example, imperfect information also results in market failures. Often the buyers are considered to have a good understanding of the values they are purchasing in the form of products and services. However, depending on the current level of competitiveness and the availability of the substitutes, customers often tend towards buying low priced goods and thus it creates subsidy regarding the quality and the reliability factor. Perfect Information Perfect information from a decision making perspective can be described as the scenario in which each of the involved parties possess equal and complete information about the products and the services being exchanged. This forms a vital factor in the context of achieving effective marketing decisions. Multiple instances can be explained in this regard. A few of such instances have been provided as follows. One such instance can be found in the area of stock market (Ammons, 2008). When it comes to buying and selling of shares, both the parties involved in the exchange process possess complete information about the shares, the expected rises and falls along with various other information regarding the company to which the stocks belong. As a result of the attained information by the buying party, appropriate decision can be taken regarding which share to purchase in due time (Distance Learning Module for Management Science, n.d.). Another such instance in this context is the game of chess in which both the players possess sound information about the game. In such a game, the higher is the knowhow of the game possessed by the players, the more will be their chances of winning it. The Value of Perfect and Imperfect Information The value of the perfect and the imperfect information can be illustrated by the elaboration of the provided problem. Value of Imperfect Information (Problem 1). An assumption has been made that a person needs to accomplish a particular task. However, the chance that the work to be accomplished will be a success is only 20% and the chance of failure is 80%. Besides, the estimated profit that can be attained is about $320,000. Only two options exist. The first option being that the task can be commenced for attaining accomplishment and the other option being that the task cannot be commenced. Moreover, the cost of conducting this task will cost about $15,000. Therefore, a question arises that will it be profitable to conduct the task? This can be explained using the concept of decision tree. Figure: 4 Source: (Kaplan Financial Limited, 2012) Expected Value (EV) (Task Commencement) = (£305, 000 × 0.2) + (-£15,000 × 0.8) = £49, 000. Now, since the resultant expected value is positive for this problem, so it will be profitable to commence this task. Value of Perfect Information (Problem 2). A person owns a food outlet and provides mid-day meals to multiple neighbouring business organisations. As far as the price factor is concerned, every meal pack costs the person an amount of $8 for preparing. As a result, the individual charges the organisation an amount of $10 for every meal he provides to them. Thus, the profit rate attained by the man per meal is $2. Now, the problem arises regarding how many meal packs should be prepared by this man every day for meeting the requirements. Assuming the case where the demand count for the meals is equal to supply. The demand expectations for every day may be (40, 50, 60, or 70). Explanation Assuming the payoff table in this context be the following: Table: 1 The expected value for each of the choice that can be made is as follows In case of 40 meals, the expected value (EV) = (1*80) = 80 In case of 50 meals, the expected value (EV) = (0.10*0 + 0.90*100) = 90 In case of 60 meals, the expected value (EV) = (0.10*(-80) + 0.20*20 + 0.70*120) = 80 In case of 70 meals, the expected value (EV) = (0.10*(-160) + 0.20*(-60) + 0.40*40 + 0.30*140) = 30 Thus, taking into consideration the expected value outcomes, it can be stated that the person should prepare a total of 50 meals every day, wherein the EV is 90. References Ammons, D. N., 2008. Tools for Decision Making: A Practical Guide for Local Government. SAGE. Aliev, R. A., 2013. Uncertain Preferences and Imperfect Information in Decision Making. Home. [Online] Available at: http://link.springer.com/chapter/10.1007%2F978-3-642-34895-2_3 [Accessed June 19, 2014]. Distance Learning Module for Management Science, No Date. Decision Theory- Decision Tables and Decision Trees, Game Theory. Introduction and Basic Terms. [Online] Available at: http://orms.pef.czu.cz/text/game-theory/DecisionTheory.html [Accessed June 19, 2014]. Hoyland, K. & Wallace, S. W., 2001. Generating Scenario Trees for Multistage Decision Problem. Department of Industrial Economics and Technology Management, pp. 295-307 Kaplan Financial Limited, 2012. The Value of Imperfect Information. Decision Trees. [Online] Available at: http://kfknowledgebank.kaplan.co.uk/KFKB/Wiki%20Pages/The%20Value%20of%20Imperfect%20Information.aspx [Accessed June 19, 2014]. Marshall University, No Date. Decision Making Models. Dallas Brozik, pp. 1-3. Osei-Bryson, K. M., 2004. Evaluation of Decision Trees: A Multi-Criteria Approach. Department of Information Systems and the Information Systems Research Institute, pp. 1933 – 1945. Quinlan, J. R., 1986. Induction of Decision Trees. Kluwer Academic Publishers, pp. 81-106. Sobolev Institute of Mathematics, 2009. What is a Decision Tree? Siberian Branch of the Russian Academy of Sciences, pp. 1-4. University of Regina, 2013. Decision Tree Construction. From Data to Trees: Quinlans ID3 Algorithm for Constructing a Decision Tree. [Online] Available at: http://www2.cs.uregina.ca/~dbd/cs831/notes/ml/dtrees/4_dtrees2.html [Accessed June 19, 2014]. Read More