CU-BBA-SEM-V-Operation Research-Second Draft

PERT is an acronym for Program (Project) Evaluation and Review Technique, in which planning, scheduling, organizing, coordinating and controlling uncertain activities take place. The technique studies and represents the tasks undertaken to complete a project, to identify the least time for completing a task and the minimum time required to complete the whole project. It was developed in the late 1950s. It is aimed to reduce the time and cost of the project. PERT uses time as a variable which represents the planned resource application along with performance specification. In this technique, first of all, the project is divided into activities and events. After that proper sequence is ascertained, and a network is constructed. After that time needed in each activity is calculated and the critical path (longest path connecting all the events) is determined. Definition of CPM Developed in the late 1950s, Critical Path Method or CPM is an algorithm used for planning, scheduling, coordination and control of activities in a project. Here, it is assumed that the activity duration is fixed and certain. CPM is used to compute the earliest and latest possible start time for each activity. The process differentiates the critical and non-critical activities to reduce the time and avoid the queue generation in the process. The reason for the identification of critical activities is that, if any activity is delayed, it will cause the whole process to suffer. That is why it is named as Critical Path Method. In this method, first of all, a list is prepared consisting of all the activities needed to complete a project, followed by the computation of time required to complete each activity. After that, the dependency between the activities is determined. Here, ‘path’ is defined as a sequence of activities in a network. The critical path is the path with the highest length. History of PERT In 1958, the U.S. Navy introduced network scheduling techniques by developing PERT as a management control system for the development of the Polaris missile program. PERT’s focus was to give managers the means to plan and control processes and activities so the project could be completed within the specified time period. The Polaris program involved 250 prime contractors, more than 9,000 subcontractors, and hundreds of thousands of tasks. PERT was introduced as an event-oriented, probabilistic technique to increase the Program Manager’s control in projects where time was the critical factor and time estimates were difficult to make with confidence. The events used in this technique represent the start and finish of the activities. PERT uses three-time estimates for each activity: optimistic, pessimistic, and most likely. An expected time is calculated based on a beta probability distribution for each activity from these estimates. 201 CU IDOL SELF LEARNING MATERIAL (SLM)

10.2 PROCESS PERT charts depict events, activities, duration and dependency information to complete a project. Each chart starts from an initiation node (which is also called an event) and from which the first activity, or activities, originates. If multiple activities begin at the same time, they all start from the same node or branch, or fork out from the starting point. Each activity is represented by a line which states its name or other identifier, its duration, the number of people assigned to it, and in some cases the initials of the personnel assigned. The other end of the activity line is terminated by another node also called event which identifies the start of subsequent activity. While events consume no time, and use no resources, an activity is the actual performance of a task and hence it consumes time, requires resources (such as labour, materials, space, machinery), and represents the time, effort and resources required to move from one event to another. For example ‘fit sample making’ is an activity that ends with an event ‘fit sample sent for approval’. The estimated time (TE) taken to move from one event to another is calculated as the weighted average of optimistic time (O) or minimum possible time required to accomplish an activity, pessimistic time (P) or maximum possible time required to accomplish the same activity and the most likely time (M) time required to accomplish the activity (TE = (O + 4M + P) ÷ 6). As against this the Lead time is the time by which a predecessor event must be completed in order to allow sufficient time for the activities that must elapse before a specific PERT event is completed. Each activity is connected to its successor activities forming a network of nodes and connecting lines. The chart is complete when all final activities come together at the completion node. When slack time (excess time and resources available in achieving this event) exists between the end of one activity and the start of another, the usual method is to draw a broken or dotted line between the end of the first activity and the start of the next dependent activity. In the PERT chart, the Critical Path is the longest possible continuous pathway taken from the initial event to the terminal event. It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount. Applications of CPM / PERT These methods have been applied to a wide variety of problems in industries and have found acceptance even in government organizations. These include:  Construction of a dam or a canal system in a region  Construction of a building or highway 202 CU IDOL SELF LEARNING MATERIAL (SLM)

 Maintenance or overhaul of airplanes or oil refinery  Space flight  Cost control of a project using PERT / COST  Designing a prototype of a machine  Development of supersonic planes 10.3 METHODS TO CALCULATE NETWORK To conduct PERT Analysis, three-time estimates are obtained (optimistic, pessimistic, and most likely) for every activity along the Critical Path. Then use those estimates in the formula below to calculate how much time for each project stage:  Optimistic Time (O): the minimum possible time required to accomplish a task, assuming everything proceeds better than is normally expected.  Pessimistic Time (P): the maximum possible time required to accomplish a task, assuming everything goes wrong (excluding major catastrophes).  Most likely Time (M): the best estimate of the time required to accomplish a task, assuming everything proceeds as normal. Table 10.1 Optimistic/most likely/pessimistic time Example of the three-time estimates 203 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 10.1: Critical Path Example of a Critical Path Nodal Diagram Definition Critical Path: The longest path of scheduled activities that must be met to execute a project. How to Use the PERT Chart Formula Using the optimistic, most likely, and pessimistic time estimates, you can use the PERT formula to calculate the expected duration of a task: (O + (4*M) + P) / 6 The result is a weighted average, which is an average from multiplying each element by a factor that reflects its importance. You can think of this as the expected time, though often the calculation will bend towards the pessimistic. The result of this formula will be the value that you’ll assign to the arrows in our PERT chart example. What is the PERT Chart Standard Deviation? To determine the standard deviation of the estimated duration of an activity, subtract the pessimistic number from the optimistic one and divide the results by six. The larger your results, the less confidence you have in your estimate, and vice versa. (P-O) / 6 PERT Charts in Project Management A PERT chart network diagram includes numbered nodes, directional arrows and divergent arrows that illustrate the minimum time and duration of activities. Directional arrows represent the activities, while nodes are milestones. Our PERT chart example will allow you to see these elements. 204 CU IDOL SELF LEARNING MATERIAL (SLM)

As stated, the use of the PERT chart gives project managers a tool to estimate the time and resources needed to complete their project tasks, which is crucial during the initiation and planning phases. When it comes to starting a project, the early steps involve taking all those tasks you collected that lead to your final deliverable and organizing them in a schedule. Knowing the amount of time it’ll take to complete each task, especially the riskier ones, is fundamental for project managers. How to Make a PERT Chart? Use a PERT chart in the planning phase of your project. Here are the steps in broad strokes before we get to our PERT chart example:  Begin by identifying the project milestones and then break those down into individual tasks.  Figure out the sequence of the tasks and their dependencies.  Make the PERT diagram — we’ll show you a PERT chart example in the section below!  Do an estimate for each task and the time it will take to complete it.  Calculate the critical path and identify any possible slack.  You have your PERT chart! Remember, the PERT chart is a living document that must be returned to and revised as needed as the project progresses. PERT Chart Example Let’s move these concepts from abstraction to reality. To better understand the power of a PERT chart in project management, let’s make one together. For our PERT chart example, we’ll create a project around building a website. The PERT chart will allow us to visualize our project’s activities and milestones to quickly uncover the critical path. Observe the PERT Chart example below, and we’ll walk through how we created it. 205 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 10.2: PERT chart Advantages and Disadvantages of PERT Analysis Understanding the advantages and disadvantages of utilizing PERT analysis will give program managers and project personnel a better understanding of the realities of their schedules. It takes an experienced program manager to truly utilize the benefits a PERT analysis can provide a project team.  Advantages: Provides Program Managers information to evaluate time and resources on a project. It helps give them the necessary information to make informed decisions and set a realistic schedule.  Disadvantages: The analysis can be highly subjective and be influenced by a few outspoken team members. It also required a lot of time to continually update the analysis as a program progresses. Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) Although Critical Path Method (CPM) and PERT are conceptually similar, some significant differences exist mostly due to the type of projects best suited for each technique. PERT is better to use when there is much uncertainty and when control over time outweighs control over costs. PERT handles uncertainty of the time required to complete an activity by developing three estimates and then computing an expected time using the beta distribution. CPM is better suited for well-defined projects and activities with little uncertainty, where 206 CU IDOL SELF LEARNING MATERIAL (SLM)

accurate time and resource estimates can be made. The percentage of completion of the activity can be determined. 10.4 PROJECT CRASHING No matter how much time and attention is paid to plan a project, obstacles can still arise and delay completion. That’s where project crashing comes in. Project crashing in project management is a method used to speed up a project’s timeline by adding additional resources without changing the scope of the project. Crashing activities in project management could include adding extra personnel to a task to finish it more quickly, or it could involve paying a premium for a faster result. Example- Let’s considers this simple project crashing example. A team is tasked with launching a magazine to celebrate your company’s 50th anniversary, but delays in approving the lead feature have caused the project to fall behind. In order to ensure the magazine is in hand by the anniversary party, an element of the project’s scope that can’t be changed, it is decided to pay a rush fee for the printer. This project crashing step helped in meeting the immovable deadline, but it also increased the project budget. Different Interpretations of Project Crashing Project crashing as a term is not etched in stone, and can mean a few different things. It could refer to spending more money to get things done faster. It can also refer to pinpointing the critical path, providing greater resources there, without necessarily thinking about being efficient. Or, one can review the critical path and see if there are any activities that can be shortened by an influx of resources. A related method for truncating a schedule is called fast tracking. This is when tasks are overlapped that were originally scheduled to run separately. But, this course of action should not be taken without first analysing its feasibility and risk. Whichever route is initiated, it’s always wise to give it thought and analysis. What Prompts Crashing in Project Management? When would a project manager want to increase investment to complete the project earlier? After all, a lot of time and effort went into the project planning and schedule. Obviously, since project crashing requires higher costs, it wouldn’t be used unless there’s an emergency. One reason for using project crashing would be if the project was scheduled unrealistically, and this wasn’t clear until the project has already been executed. This can even happen at the planning stage if the sponsor, customer or stakeholder insists on a due date that isn’t feasible. Another reason is that, during the process of a change control analysis (which shows impact on the time, cost, scope or other project factors), an issue comes up that must be addressed immediately. As issues arise in the course of managing a project that take it off track, the project manager must figure out a way to lock back to the schedule baseline. 207 CU IDOL SELF LEARNING MATERIAL (SLM)

As noted above, other than project crashing, there is the fast tracking method. Though we’re discussing project crashing, it’s important to touch on when fast tracking is preferable. Sometimes you can use either, but if the project is already over-budget and you don’t have funds, then fast tracking is the likely option. Best Practices When Crashing a Project Project crashing is usually a last resort, and it’s not without substantial risks. There are some things you need to consider before taking your project down this road. For one, are the tasks you’re looking to crash in the critical path? These tasks are going to impact the delivery of your project. If the tasks aren’t in the critical path, you can probably ignore them. Another thing to consider is the length of the tasks. A short task will be hard to speed up, especially if it doesn’t repeat throughout the project. Long tasks are going to usually have some fat to trim. But regardless of the task, the need is to have resources available. If there is no access to the right resources, then it makes no sense for the project crashing. Having to get new materials or team members is likely going to be too costly to be effective. Another consideration is if it would take too long to ramp up the project crashing; for instance, if the project involves very specific skills and onboarding new team members would be costly and time consuming. While it might seem logical to crash at the end of the project when it is becoming clear you’re not going to hit your target, most experts suggest avoiding that scenario. Project crashing is most effective earlier in the timeline, usually when a project is less than halfway done. Project Crashing Management Stages Once the decision is made to use project crashing, there are some steps to get the desired results. 1. Critical Path The first thing to do is analyse the critical path of a project. This will help in determining which tasks can be shortened to bring the project to a close sooner. Therefore, if it is not done already, calculate the critical path, see which tasks are essential and which are secondary to the project’s success. 2. Identify Tasks Get a list of all the tasks at hand, then meet with those who have been assigned to complete them. Ask if they believe any of the tasks they’re responsible for are in the critical path and can be cut down. Then, start looking for ways to tighten up those tasks. 3. What’s the Trade Off? Once it is narrowed down to the tasks in the critical path that is believed to be shortened, start calculating how much adding more resources will cost. Find the tasks that can be 208 CU IDOL SELF LEARNING MATERIAL (SLM)

allocated additional resources, and come in sooner with the least amount of strain on budget. 4. Make Choice When it is known about what to spend for each of the tasks in the critical path, then make a decision and choose the least expensive way forward. Project crashing is not just adding resources to get done faster, but it’s getting the most in return for that extra expense. 5. Create a Budget Like any project, once it is decided on a plan, ensure to pay for it. Making a project crashing budget is the next step in executing the project crashing plan. Then update the baseline, schedule and resource plan to align with the new initiative. 10.5 SUMMARY  Some projects can be defined as a collection of interrelated activities which must be completed in a specified time according to a specified sequence and require resources, such as personnel, money, materials, facilities and so on.  For instance, like the projects of construction of a bridge, a highway, a power plant, repair and maintenance of an oil refinery and so on.  The growing complexities of today’s projects had demanded more systematic and more effective planning techniques with the Objectives of optimising the efficiency of executing the project.  Efficiency here refers to effecting the utmost reduction in the time required to complete a project while ensuring optimum utilisation of the available resources. Project management has evolved as a new field with the development of two analytic techniques for planning, scheduling and controlling projects. These are the Critical Path Method (CPM) and the Project Evaluation and Review Technique (PERT).  PERT and CPM are basically time-oriented methods in the sense that they both lead to the determination of a time schedule.  A PERT chart is a project management tool used to schedule, organise, and coordinate tasks within a project. PERT stands for (Program Evaluation Review Technique), a methodology developed by the U.S. Navy in the 1950s to manage the Polaris submarine missile program.  The Critical Path Method (CPM) is one of several related techniques for doing project planning. CPM is for projects that are made up of a number of individual “activities.” If some of the activities require other activities to finish before they can start, then the project becomes a complex web of activities. 209 CU IDOL SELF LEARNING MATERIAL (SLM)

 Project scheduling through PERT/CPM takes place through three phrases such as planning, scheduling and controlling. However a project can be crashed.  The aim of crashing is to achieve the maximum decrease in schedule for minimum additional cost. This can be done by addressing productivity issues being experienced by the current resources and trying to find ways of increasing their efficiency. Moreover, it is done by increasing the assignment of resources on critical path activities. 10.6 KEYWORDS  PERT-Program Evaluation and Review Technique (PERT) is a method used to examine the tasks in a schedule and determine a Critical Path Method variation (CPM).  CPM- The critical path method (CPM) is a step-by-step project management technique for process planning that defines critical and non-critical tasks with the goal of preventing time-frame problems and process bottlenecks.  Project Crashing- Project crashing is when you shorten the duration of a project by reducing the time of one or more tasks. Of course, this also adds to the cost of the overall project. Therefore, the primary objective of project crashing is to shorten the project while also keeping costs at a minimum.  Standard Deviation- In Statistics and Probability Theory, Standard Deviation (SD) measures the amount of Variation from Average or Mean. In the current context Average or Mean is represented by Weighted Average calculated using PERT formula. A low value of SD indicates that data points are very close to the Mean.  PERT Chart- A PERT chart is a project management tool that provides a graphical representation of a project's timeline. The Program Evaluation Review Technique (PERT) breaks down the individual tasks of a project for analysis. 10.7 LEARNING ACTIVITY 1. For the project 210 CU IDOL SELF LEARNING MATERIAL (SLM)

Find the earliest and latest expected time to each event and also critical path in the network. ___________________________________________________________________________ ___________________________________________________________________________ 2. A project has the following times schedule Construct the network and compute 211 1. TE and TL for each event 2. Float for each activity CU IDOL SELF LEARNING MATERIAL (SLM)

3. Critical path and its duration ___________________________________________________________________________ ___________________________________________________________________________ 10.8 UNIT END QUESTIONS A. Descriptive Questions Short Questions: 1. What kind of benefits accrue through PERT? 2. What are the uses of CPM? 3. What is the critical path? 4. What are the disadvantages of PERT analysis? 5. How would you determine the standard deviation of the estimated duration of an activity? Long Questions 1. Explain PERT through network analysis. 2. What does it lead to crashing in project management? 3. What are the methods used to calculate networks? 4. Write the best practices for crashing the management. 5. What are the ways to develop a PERT chart? B Multiple Choice Questions 1. Which are stages of project crash management? a. Critical path b. Identify tasks c. Trade offs d. All of these 2. Which technique is suitable to use when there is much uncertainty and when control over time outweighs control over costs? a. PERT b. CPM c. Project Crashing d. None of these 212 CU IDOL SELF LEARNING MATERIAL (SLM)

3. Which is not a step involving PERT chart? a. Begin by identifying the project milestones b. Figure out a single task and its dependency c. Make the PERT diagram d. Calculate the critical path 4. Which is the correct PERT formula? a. (O + (5*M) + P) / 6 b. (O + (4*M) + P) / 7 c. (O + (4*M) + P) / 6 d. (O + (4*N) + P) / 6 5. Which year witnessed the introduction of network scheduling techniques by developing PERT as a management control system? a. 1958 b. 1968 c. 1948 d. 1957 Answers 1-d 2-a 3-b 4-c 5-a 10.9 REFERENCES References  PERT/CPM Operation Research Application in Apparel Industry - Apparel Resources India  The Application of Network Techniques (PERT/CPM) to the Planning and Control of an Audit on JSTOR  N. Bauer, \"Rising from the Ashes,\" PM Network 18, no. 5 (May 2004): 2432. Textbooks  Operation research: PERT, CPM and cost analysis, by KantiSwarup, Publisher New Delhi: Discovery Pub. House, 2006  Moder, J. J., Phillips, C. R., &Davis, E. W. (1983). Project Management with CPM,  PERT and Precedence Diagramming. New York. http://doi.org/10.1016/0016- 213 CU IDOL SELF LEARNING MATERIAL (SLM)

 0032(65)90247-4  Operation Research: Pert, CPM& Cost Analysis: PERT, CPMand Cost Analysis (DPH Mathematics Series) Hardcover – 1 January 1993 by S. C. Sharma (Author) Websites  PERT Analysis - AcqNotes  PERT Chart: The Ultimate Guide (with Examples) - ProjectManager.com  What is Project Crashing in Project Management? | Wrike  Operations Research: Lesson 21. PROJECT EVALUATION AND REVIEW TECHNIQUE (PERT) (iasri.res.in) 214 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT 11 – DECISION THEORY AND DECISION TREES STRUCTURE 11.0 Learning Objectives 11.1 Introduction 11.2 Risk & Uncertainty 11.3 Payoff Table 11.4 Regret Table 11.5 Decision Making Under Uncertainty 11.6 Summary 11.7 Keywords 11.8 Learning Activity 11.9 Unit End Questions 11.10 References 11.0 LEARNING OBJECTIVES After studying this unit, you will be able to: ● Identifyfirst-hand information on various theories of decision ● Obtain the objective of decision tree for an organisation ● Comprehend the purpose of payoff and regret table 11.1 INTRODUCTION Decision theory deals with methods for determining the optimal course of action when a number of alternatives are available and their consequences cannot be forecast with certainty. It is difficult to imagine a situation which does not involve such decision problems, but we shall restrict ourselves primarily to problems occurring in business, with consequences that can be described in dollars of profit or revenue, cost or loss. For these problems, it may be reasonable to consider as the best alternative that results in the highest profit or revenue, or lowest cost or loss, on the average, in the long run. This criterion of optimality is not without shortcomings, but it should serve as a useful guide to action in repetitive situations where the consequences are not critical. (Another criterion of optimality, the maximization of expected 215 CU IDOL SELF LEARNING MATERIAL (SLM)

utility, provides a more personal and subjective guide to action for a consistent decision- maker.) The simplest decision problems can be resolved by listing the possible monetary consequences and the associated probabilities for each alternative, calculating the expected monetary values of all alternatives, and selecting the alternative with the highest expected monetary value. The determination of the optimal alternative becomes a little more complicated when the alternatives involve sequences of decisions. In another class of problems, it is possible to acquire often at a certain cost additional information about an uncertain variable. This additional information is rarely entirely accurate. Its value hence, also the maximum amount one would be willing to pay to acquire it should depend on the difference between the best one expects to do with the help of this information and the best one expects to do without it. What is a Decision Tree? A decision tree is a support tool with a tree-like structure that models probable outcomes, cost of resources, utilities, and possible consequences. Decision trees provide a way to present algorithms with conditional control statements. They include branches that represent decision-making steps that can lead to a favourable result. Figure 11.1: Decision tree analysis The flowchart structure includes internal nodes that represent tests or attributes at each stage. Every branch stands for an outcome for the attributes, while the path from the leaf to the root represents rules for classification. Decision trees are one of the best forms of learning algorithms based on various learning methods. They boost predictive models with accuracy, ease in interpretation, and stability. The tools are also effective in fitting non-linear relationships since they can solve data-fitting challenges, such as regression and classifications. 216 CU IDOL SELF LEARNING MATERIAL (SLM)

 Decision trees are used for handling non-linear data sets effectively.  The decision tree tool is used in real life in many areas, such as engineering, civil planning, law, and business.  Decision trees can be divided into two types; categorical variable and continuous variable decision trees. 11.2 RISK & UNCERTAINTY Decision making is certainly the most important task of a manager and it is often a very difficult one. The domain of decision analysis models falls between two extreme cases. This depends upon the degree of knowledge we have about the outcome of our actions. One “pole” on this scale is deterministic. The opposite “pole” is pure uncertainty. Between these two extremes are problems under risk. The main idea here is that for any given problem, the degree of certainty varies among managers depending upon how much knowledge each one has about the same problem. This reflects the recommendation of a different solution by each person. Probability is an instrument used to measure the likelihood of occurrence for an event. When probability is used to express uncertainty, the deterministic side has a probability of one (or zero), while the other end has a flat (all equally probable) probability. This paper offers a decision making procedure for solving complex problems step by step. It presents the decision analysis process for both public and private decision making, using different decision criteria, different types of information and information of varying quality. It describes the elements in the analysis of decision alternatives and choices, as well as the goals and objectives that guide decision making. 11.3 PAYOFF TABLE Business decisions are, by nature, often tough calls to make. They can involve decisions about someone's employment, the organization's financial future, or its strategic direction. The good news, however, is that these important decisions don't have to be guesses or full of conjecture. Instead, business statistics and other forms of analysis can provide decision-makers with valuable tools to guide them to the right course of action. Two of these important tools are the payoff table and the decision tree. In fact, an accurate decision tree or payoff table is often the difference between simply hoping an alternative will work and knowing that it'll work. Payoff Tables and Decision Trees While both tools provide some of the same information, they have a few notable differences. A payoff table is a tool that provides information about the probability of various outcomes-- usually related to potential profit or loss. A decision tree also provides some of the same type 217 CU IDOL SELF LEARNING MATERIAL (SLM)

of information, but it's more informative in terms of the consequences of actions or decisions. Let's illustrate each of these with an example. Applying a Payoff Table and Decision Tree Let's imagine that you're the CFO of a medical group that employs several different types of specialty physicians. Coincidental events beyond your control have resulted in the nearly simultaneous departure of all but one of the eight orthopaedic surgeons. The CEO has asked you to research and recommend a course of action moving forward. You'll be considering several options including:  Replacing all departing surgeons with full-time employees (the status quo or default action)  Using contracted, temporary physicians (known as locums)  Discontinuing the service line altogether Obviously, each of these options is a legitimate possibility, but are they equally as impactful? Let's use a payoff table to find out. As we build our table, it's important to remember that we're accounting for all outcomes or influences--including those outside your span of control. In this scenario, you'll use the reference data provided below, but you'll want to keep in mind that the projections made by a payoff table or decision tree are only as the data upon which they are based. In our payoff table, the term alternative is used to describe one of the possible courses of action. As we analyse, it's important to remember that you're not making a decision in isolation. Since the situation will influence how patients or customers behave, we'll not be looking only at the three alternatives, but also at the impact if we lose, gain, or retain our customers during the process. Table 11.1: Example Payoff Table 11.4 REGRET TABLE Payoff table show the payoff (profit or loss) for the range of possible outcomes based on two factors: 1. Different decision choices 218 CU IDOL SELF LEARNING MATERIAL (SLM)

2. Different possible real world scenarios For example, suppose Geoffrey Ramsbottom is faced with the following pay-off table. He has to choose how many salads to make in advance each day before he knows the actual demand.  His choice is between 40, 50, 60 and 70 salads.  The actual demand can also vary between 40, 50, 60 and 70 with the probabilities as shown in the table - e.g.,P (demand = 40) is 0.1.  The table then shows the profit or loss - for example, if he chooses to make 70 but demand is only 50, then he will make a loss of $60. Table 11.2: Daily supply and demand The question is then which output level to choose. Maximax- The Maximax rule involves selecting the alternative that maximises the maximum payoff available. This approach would be suitable for an optimist, or 'risk-seeking' investor, who seeks to achieve the best results if the best happens. The manager who employs the Maximax criterion is assuming that whatever action is taken, the best will happen; he/she is a risk-taker. So, how many salads will Geoffrey decide to supply? Looking at the payoff table, the highest maximum possible pay-off is $140. This happens if we make 70 salads and demand is also 70. Geoffrey should therefore decide to supply 70 salads every day. Maximin-The maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. The investor would look at the worst possible outcome at each supply level, then select the highest one of these. The decision maker therefore chooses the outcome which is guaranteed to minimise his losses. In the process, he loses out on the opportunity of making big profits. This approach would be appropriate for a pessimist who seeks to achieve the best results if the worst happens. So, how many salads will Geoffrey decide to supply? Looking at the payoff table,  If we decide to supply 40 salads, the minimum pay-off is $80. 219 CU IDOL SELF LEARNING MATERIAL (SLM)

 If we decide to supply 50 salads, the minimum pay-off is $0.  If we decide to supply 60 salads, the minimum pay-off is ($80).  If we decide to supply 70 salads, the minimum pay-off is ($160). The highest minimum payoff arises from supplying 40 salads. This ensures that the worst possible scenario still results in a gain of at least $80. Minimax Regret- The minimax regret strategy is the one that minimises the maximum regret. It is useful for a risk-neutral decision maker. Essentially, this is the technique for a 'sore loser' who does not wish to make the wrong decision. 'Regret' in this context is defined as the opportunity loss through having made the wrong decision. To solve this a table showing the size of the regret needs to be constructed. This means we need to find the biggest pay-off for each demand row, then subtract all other numbers in this row from the largest number. For example, if the demand is 40 salads, we will make a maximum profit of $80 if they all sell. If we had decided to supply 50 salads, we would achieve a nil profit. The difference or 'regret' between that nil profit and the maximum of $80 achievable for that row is $80. Regrets can be tabulated as follows: Table 11.3: Regrets The maximum regrets for each choice are thus as follows (reading down the columns):  If we decide to supply 40 salads, the maximum regret is $60.  If we decide to supply 50 salads, the maximum regret is $80.  If we decide to supply 60 salads, the maximum regret is $160.  If we decide to supply 70 salads, the maximum regret is $240. A manager employing the minimax regret criterion would want to minimise that maximum regret, and therefore supply 40 salads only. 220 CU IDOL SELF LEARNING MATERIAL (SLM)

Note that the above techniques can be used even if we do not have probabilities. To calculate expected values, for example, we will need probabilities. 11.5 DECISION MAKING UNDER UNCERTAINTY An interesting example:  • “Deal or no deal?”  • TV game shows  • Losses vs Gains  • Risk-averse vs risk-seeking  • A natural decision-making experiment Future probabilities estimated or known:  • Expected Value (EV)  • Expected Opportunity Loss (EOL) Decision making with probabilities  If probabilistic information regarding the states of nature is available, one may use the expected value (EV) approach  Here the expected return for each decision is calculated by summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring  The decision yielding the best expected return is chosen  The expected value of a decision alternative is the sum of weighted payoffs for the decision alternative  The expected value (EV) of decision alternative di is defined as: where: N = the number of states of nature, P (sj) = the probability of state of nature sj, Vij = the payoff corresponding to decision alternative di and state of nature sj Expected Monetary Value (EMV) EMV for the specified course of action is the weighted average payoff, i.e., the sum of the product of the payoff for the several combinations of courses of action and states of nature multiplied by the probability of occurrence of each outcome 221 CU IDOL SELF LEARNING MATERIAL (SLM)

Expected Profit with Perfect Information (EPPI)  EPPI is the maximum attainable expected monetary value (EMV) based on perfect information about the state of nature that will occur  EPPI may be defined as the sum of the product of best state of nature corresponding to each optimal course of action and its probability Expected Value of Perfect Information (EVPI)  EVPI is defined as the maximum amount one would pay to obtain perfect information about the state of nature that would occur  EMV* represents the maximum attainable expected monetary value given only the prior outcome probabilities, with no information as to which state of nature will actually occur Expected Opportunity Loss (EOL)  Another useful way of maximizing monetary value is to maximize the EOL or expected value of regret  The conditional opportunity loss (COL) for a particular course of action is determined by taking the difference between the payoff value of the most favourable course of action and some other course of action  Thus, opportunity loss can be obtained separately for each course of action by first obtaining the best state of nature for the prescribed course of action and then taking the difference between that best outcome and each outcome for those courses of action Sources of probabilities:  Sample Information - a study or research analysis of the environment is used to assess the probability or occurrence of the event  Historical Records - available from files  Subjective Probabilistic - probability may be subjectively assessed based on judgment, sample information and historical records 11.6 SUMMARY 222 CU IDOL SELF LEARNING MATERIAL (SLM)

 Decision theory is theory about decisions. Almost everything that a human being does involves decisions. Therefore, to theorize about decisions is almost the same as to theorize about human activities. However, decision theory is not quite as all- embracing as that. It focuses on only some aspects of human activity.  In particular, it focuses on how we use our freedom. In the situations treated by decision theorists, there are options to choose between, and we choose in a non- random way. Our choices, in these situations, are goal-directed activities. Hence, decision theory is concerned with goal-directed behaviour in the presence of options.  Decision theory is the principle associated with decisions. Decision theory provides a formal structure to make rational choices in the situation of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice.  In many instances, the choice of the best act is not made in one stage, and the decision problem involves a sequence of acts, events, acts, events.  There may be a number of basic alternatives, each leading to one of a number of situations depending on the outcome of a certain random process. At each such situation, a number of other alternatives may be available which also lead to a new set of situations depending on another set of events and so on, with acts followed by events, followed by acts, events.  In this regard, there is a need to make an analysis on Decision Trees. Once the tree is drawn, it is scrutinized from right to left. The aim of analysis is to determine the best strategy of the decision maker that means an optimal sequence of the decisions. To analyse a decision tree, managers must know a decision criterion, probabilities that are assigned to each event, and revenues and costs for the decision alternatives and the chance events that occur.  It could be briefly mentioned that decision theory is a structure of logical and mathematical concepts which is intended to assist managers to formulate rules that may lead to a most beneficial course of action under the given circumstances.  Decision theory divides decisions into three categories that include decisions under certainty; where a manager has far too much information to choose the best alternative, decisions under conflict; where a manager has to anticipate moves and countermoves of one or more competitors and lastly, decisions under uncertainty; where a manager has to dig-up a lot of data to make sense of what is going on and what it is leading to. It is established that decision theory can be applied to conditions of certainty, risk, or uncertainty.  Decision theory identifies that the ranking produced by using a criterion has to be consistent with the decision maker's objectives and preferences. 223 CU IDOL SELF LEARNING MATERIAL (SLM)

11.7 KEYWORDS  Decision Tree- A decision tree is a support tool with a tree-like structure that models probable outcomes, cost of resources, utilities, and possible consequences. Decision trees provide a way to present algorithms. They automate trading to generate profits at a frequency impossible to a human trader.  Payoff Table- A profit table (payoff table) can be a useful way to represent and analyse a scenario where there is a range of possible outcomes and a variety of possible responses. A payoff table simply illustrates all possible profits/losses and as such is often used in decision making under uncertainty.  Regret Table- 'Regret' in this context is defined as the opportunity loss through having made the wrong decision. To solve this a table showing the size of the regret needs to be constructed. This means we need to find the biggest pay-off for each demand row, then subtract all other numbers in this row from the largest number.  Expected Monetary Value- Expected monetary value (EMV) is a risk management technique to help quantify and compare risks in many aspects of the project. EMV is a quantitative risk analysis technique since it relies on specific numbers and quantities to perform the calculations, rather than high-level approximations like high, medium and low.  Expected Value of Perfect Information- The expected value of perfect information is the price that a healthcare decision maker would be willing to pay to have perfect information regarding all factors that influence which treatment choice is preferred as the result of a cost-effectiveness analysis. 11.8 LEARNING ACTIVITY 1. A grocery receives its weekly supply of eggs every Thursday morning. This shipment must last until the following Thursday when a new shipment is received. Any eggs left unsold by Thursday are destroyed. Eggs sell for $10 per hundred and cost $8 per hundred. The weekly demand for eggs at this grocery varies from week to week. From past experience, the following probability distribution is assigned to weekly demand: Demand (hundreds of eggs): 10 11 12 13 14 Probability: 0.1 0.2 0.4 0.2 0.1 This pattern of demand remains stable throughout the year the demand for eggs is not seasonal, and the trend is flat. The problem is: How many eggs should be ordered for delivery every Thursday? 224 CU IDOL SELF LEARNING MATERIAL (SLM)

___________________________________________________________________________ ___________________________________________________________________________ 2. You are considering buying a ticket for a certain lottery. The ticket costs $100 and the lottery will be conducted only once. This is a rather crude lottery: a coin will be tossed; if it turns up heads, you will receive $250; if it turns up tails, you will get nothing. Should you buy this ticket or not? ___________________________________________________________________________ ___________________________________________________________________________ 11.9 UNIT END QUESTIONS A. Descriptive Questions Short Questions 1. What is the need of decision theory? 2. When is the decision tree used? 3. When is a payoff table applied? 4. What is the objective of the regret table? 5. What is expected opportunity loss? Long Questions 1. How would you make a decision in the uncertainty case being a manager? 2. When is the regret strategy applied? Explain with an example. 3. How would you make a decision when all the probabilities are at your disposal? 4. How far a decision tree ensures to make the right decision? 5. Give an overall brief on theory of decision. B Multiple Choice Questions 1. Which are sources of probabilities? 225 CU IDOL SELF LEARNING MATERIAL (SLM)

a. Sample information b. Historical records c. Subjective probabilistic d. All of these 2. Which could be defined as the maximum amount one would pay to obtain perfect information about the state of nature that would occur? a. Expected value of perfect information b. Expected opportunity loss c. Expected monetary value d. Expected probabilistic result 3. Which is a tool that provides information about the probability of various outcomes usually related to potential profit or loss? a. Decision tree b. Payoff table c. Regret table d. None of these 4. Which statement is not truly related to the decision tree? a. Decision trees are used for handling non-linear data sets effectively b. The decision tree tool is used in real life in many areas, such as engineering, civil planning, law, and business c. Decision trees can be divided into three types; categorical variable, continuous variable and decision trees d. Decision trees are one of the best forms of learning algorithms 5. Which could be an example of decision making under uncertainty? e. Invest or not to invest f. Buying a car in boom period g. Visiting a doctor in pink of health h. Apply a strategy without considering pros and cons in real life Answers 1-d 2-a 3-b 4-c 5-a 226 CU IDOL SELF LEARNING MATERIAL (SLM)

11.10 REFERENCES References  What is Decision Tree Analysis? Definition, Steps, Example, Advantages, Disadvantages - The Investors Book  Decision Trees for Decision Making (hbr.org)  International Journal of Operational Research (IJOR) Inderscience Publishers - linking academia, business and industry through research  Decision Theory, Decision Theory Lecture Notes, Decision Theory Definition (civilserviceindia.com) Textbooks  Gilboa, I., 2011. Making Better Decisions: Decision Theory in Practice, Wiley- Blackwell, Chichester, West Sussex and Malden, MA. [658.403 G46]  Peterson, M., 2009. An Introduction to Decision Theory, Cambridge University Press, New York. [519.542 P485 i61]  Ben-Haim, Y. 2001. Information-gap Decision Theory: Decisions under Severe Uncertainty. San Diego: Academic Press.  ch3000.pdf (yorku.ca) Websites  Microsoft PowerPoint - MECH3010_1314_03_decision_theory [Compatibility Mode] (ibse.hk)  DECISION-MAKING UNDER RISK in Quantitative Techniques for management Tutorial 03 September 2021 - Learn DECISION-MAKING UNDER RISK in Quantitative Techniques for management Tutorial (10069) | Wisdom Jobs India  Decision Making under Uncertain and Risky Situations (soa.org)  https://corporatefinanceinstitute.com/resources/knowledge/other/decision-tree/  Predicting Business Outcomes Using Payoff Tables & Decision Trees | Study.com  Home (kaplan.co.uk) 227 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT 12 – DECISION MAKING STRUCTURE 12.0 Learning Objectives 12.1 Introduction 12.2 Expected value 12.3 EVPI 12.4 Decision tree analysis 12.5 Summary 12.6 Keywords 12.7 Learning Activity 12.8 Unit End Questions 12.9 References 12.0 LEARNING OBJECTIVES After studying this unit, you will be able to:  Identify the expected value.  Describe EVPI.  Describe the decision tree analysis. 12.1 INTRODUCTION Decisions have to be taken in this complex world. Making a decision solely on a single criterion appears insufficient in which the decision makes process deals with complex organizational environment. It is impossible to squeeze the complexity of opinions, motivations and the goals found in organizations into a single objective. Therefore, decisions may involve several objectives that are conflicting in nature. Decision maker may be an individual or a group of individuals. The presence of several criteria which are wholly or partially contradictory in nature leads to the development of multi-criteria decision-making problems or multi-criteria optimization problems. Therefore, decision making is a multi criteria optimization. Some timedecisions are analytical and it requires the data. Operational research is only the means of taking the decision and provides the data to manager to take the appropriate and valid decision. The managers use this quantitative data for taking the decisions and find out the better decision. Hence, it is used to solve complex problems. In 228 CU IDOL SELF LEARNING MATERIAL (SLM)

operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis. The expected value (EV) is an anticipated value for an investment at some point in the future. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values. By calculating expected values, investors can choose the scenario most likely to give the desired outcome. Scenario analysis is one technique for calculating the expected value (EV) of an investment opportunity. It uses estimated probabilities with multivariate models to examine possible outcomes for a proposed investment. Scenario analysis also helps investors determine whether they are taking on an appropriate level of risk given the likely outcome of the investment. The EV of a random variable gives a measure of the center of the distribution of the variable. Essentially, the EV is the long-term average value of the variable. Because of the law of large numbers, the average value of the variable converges to the EV as the number of repetitions approaches infinity. The EV is also known as expectation, the mean or the first moment. EV can be calculated for single discrete variables, single continuous variables, multiple discrete variables, and multiple continuous variables. For continuous variable situations, integrals must be used. EVPI helps to determine the worth of an insider who possesses perfect information. The expected value with perfect information is the amount of profit foregone due to uncertain conditions affecting the selection of a course of action. Given the perfect information, a decision-maker is supposed to know which particular state of nature will be in effect. Thus, the procedure for the selection of an optimal course of action, for the decision problem It is the price that would be paid to get access to the perfect information. This concept is mainly used in health economics. It is one of the important tools in decision theory. When a decision is taken for new treatment or method, there will be always some uncertainty about the decision as there are chances for the decision to turn out to be wrong. The expected value of perfect information (EVPI) is used to measure the cost of uncertainty as the perfect information can remove the possibility of a wrong decision.The formula for EVPI is defined as follows:It is the difference between predicted payoff under certainty and predicted monetary value. EVPI = EPC - EMV Decision tree analysis is the process of drawing a decision tree, which is a graphic representation of various alternative solutions that are available to solve a given problem, in order to determine the most effective courses of action. Decision trees are comprised of nodes 229 CU IDOL SELF LEARNING MATERIAL (SLM)

and branches - nodes represent a test on an attribute and branches represent potential alternative outcomes. A decision tree is a tree-like model that acts as a decision support tool, visually displaying decisions and their potential outcomes, consequences, and costs. From there, the “branches” can easily be evaluated and compared in order to select the best courses of action. Decision tree analysis is helpful for solving problems, revealing potential opportunities, and making complex decisions regarding cost management, operations management, organization strategies, project selection, and production methods. 12.2 EXPECTED VALUE The expected value (EV) is an anticipated value for an investment at some point in the future. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values. By calculating expected values, investors can choose the scenario most likely to give the desired outcome. EV=∑P(Xi)×Xi Where: EV – the expected value P(Xi) – the probability of the event Xi – the event Scenario analysis is one technique for calculating the expected value (EV) of an investment opportunity. It uses estimated probabilities with multivariate models to examine possible outcomes for a proposed investment. Scenario analysis also helps investors determine whether they are taking on an appropriate level of risk given the likely outcome of the investment. The EV of a random variable gives a measure of the center of the distribution of the variable. Essentially, the EV is the long-term average value of the variable. Because of the law of large numbers, the average value of the variable converges to the EV as the number of repetitions approaches infinity. The EV is also known as expectation, the mean or the first moment. EV can be calculated for single discrete variables, single continuous variables, multiple discrete variables, and multiple continuous variables. For continuous variable situations, integrals must be used. Expected value is a commonly used financial concept. In finance, it indicates the anticipated value of an investment in the future. By determining the probabilities of possible scenarios, one can determine the EV of the scenarios. The concept is frequently used with multivariate models and scenario analysis. It is directly related to the concept of expected return. 230 CU IDOL SELF LEARNING MATERIAL (SLM)

Example of Expected Value (Multiple Events) You are a financial analyst in a development company. Your manager just asked you to assess the viability of future development projects and select the most promising one. According to estimates, Project A, upon completion, shows a probability of 0.4 to achieve a value of $2 million and a probability of 0.6 to achieve a value of $500,000. Project B shows a probability of 0.3 to be valued at $3 million and a probability of 0.7 to be valued at $200,000 upon completion. In order to select the right project, you need to calculate the expected value of each project and compare the values with each other. The EV can be calculated in the following way: EV (Project A) = [0.4 × $2,000,000] + [0.6 × $500,000] = $1,100,000 EV (Project B) = [0.3 × $3,000,000] + [0.7 × $200,000] = $1,040,000 The EV of Project A is greater than the EV of Project B. Therefore, your company should select Project A. Note that the example above is an oversimplified one. A real-life example will likely assess the Net Present Value (NPV) of the projects instead of their EV. However, NPV calculations also consider the EV of different projects. 12.3 EVPI The expected value of perfect information is the price that a healthcare decision maker would be willing to pay to have perfect information regarding all factors that influence which treatment choice is preferred as the result of a cost-effectiveness analysis. This is the value (in money terms) of removing all uncertainty from such an analysis. EVPI is calculated as the difference in the monetary value of health gain associated with a decision between therapy alternatives between when the choice is made on the basis of with currently available information (i.e., uncertainty in the factors of interest) and when the choice is made based on perfect information (no uncertainty in all factors). The Expected Value of Perfect Information It is the price that would be paid to get access to the perfect information. This concept is mainly used in health economics. It is one of the important tools in decision theory. When a decision is taken for new treatment or method, there will be always some uncertainty about the decision as there are chances for the decision to turn out to be wrong. The expected 231 CU IDOL SELF LEARNING MATERIAL (SLM)

value of perfect information (EVPI) is used to measure the cost of uncertainty as the perfect information can remove the possibility of a wrong decision. The formula for EVPI is defined as follows: It is the difference between predicted payoff under certainty and predicted monetary value. EVPI = EPC – EMV The EVPI is also equal to expected opportunity loss. It provides a criterion to examine ordinarily forecasters that are imperfectly informed. It can be used to reject proposals that are costly. It is helpful when a decision is taken regarding a forecasting offer. It can be determined simultaneously with the elimination of uncertainty of all parameters that were involved in model-based decision-making. It determines how best a decision-maker could do if the decision-maker is certain about the state of nature that will occur. The researcher keeps gathering information until the certainty is reached.The major advantage of EVPI is that it is very easy and simple to compute. There must be equality between the probability of happening of an uncertain event and the probability related to the perfect test result. Hence EVPI is easy to calculate and can be determined directly. EVPI helps to determine the worth of an insider who possesses perfect information. The expected value with perfect information is the amount of profit foregone due to uncertain conditions affecting the selection of a course of action. Given the perfect information, a decision-maker is supposed to know which particular state of nature will be in effect. For example, if the decision-maker is certain that the state of nature S1 will be in effect, he would select the course of action A3, having maximum payoff equal to Rs 200. Similarly, if the decision-maker is certain that the state of nature S2 will be in effect, his course of action would be A1 and if he is certain that the state of nature S3 will be in effect, his course of action would be A2. The maximum payoffs associated with the actions are Rs 200 and Rs 600 respectively. The weighted average of these payoffs with weights equal to the probabilities of respective states of nature is termed as Expected Payoff under Certainty (EPC).Thus, EPC = 200 * 0.3 + 200 * 0.4 + 600 *0.3 = 320 The difference between EPC and EMV of optimal action is the amount of profit foregone due to uncertainty and is equal to EVPI. Thus, EVPI = EPC - EMV of optimal action = 320 - 194 = 126 It is interesting to note that EVPI is also equal to EOL of the optimal action. Cost of Uncertainty 232 CU IDOL SELF LEARNING MATERIAL (SLM)

This concept is similar to the concept of EVPI. Cost of uncertainty is the difference between the EOL of optimal action and the EOL under perfect information. Given the perfect information, the decision-maker would select an action with minimum opportunity loss under each state of nature. Since minimum opportunity loss under each state of nature is zero, therefore, EOL under certainty = 0 *0.3 + 0 *0.4 + 0 * 0.3 = 0 Thus, the cost of uncertainty = EOL of optimal action = EVPI The process of calculating the EVPI, the dis-benefit of making a decision based on less than perfect information, is complex and applicable only in a few situations. The principle is relatively straightforward, the difficulty arises in estimating first the degree of uncertainty attached to different alternatives, and secondly the degree to which those uncertainties are independent of each other. 12.4 DECISION TREE ANALYSIS Decision tree analysis is the process of drawing a decision tree, which is a graphic representation of various alternative solutions that are available to solve a given problem, in order to determine the most effective courses of action. Decision trees are comprised of nodes and branches - nodes represent a test on an attribute and branches represent potential alternative outcomes. Decision tree analysis is a powerful decision-making tool which initiates a structured nonparametric approach for problem-solving. It facilitates the evaluation and comparison of the various options and their results, as shown in a decision tree. It helps to choose the most competitive alternative. It is a widely used technique for taking crucial decisions like project selection, cost management, operations management, production method, and to deal with various other strategic issues in an organization. A decision tree is a tree-like model that acts as a decision support tool, visually displaying decisions and their potential outcomes, consequences, and costs. From there, the “branches” can easily be evaluated and compared in order to select the best courses of action. Decision tree analysis is helpful for solving problems, revealing potential opportunities, and making complex decisions regarding cost management, operations management, organization strategies, project selection, and production methods. Drawing a decision tree diagram starts from left to right and consists of “burst” nodes that split into different paths. Nodes are categorized as Root nodes, which compile the whole sample and is then split into multiple sets; Decision nodes, typically represented by squares, are sub-nodes that diverge into further possibilities; and the Terminal node, typically 233 CU IDOL SELF LEARNING MATERIAL (SLM)

represented by triangles, is the final node that shows the final outcome that cannot be further categorized. Branches, or lines, represent the various available alternatives, and sub-nodes can be eliminated via Pruning. Decision trees can be hand-drawn or created with the use of decision tree software. Analysis can be performed manually, via decision tree analysis in R, or via automated software. The steps in decision tree analysis consist of: 1. Define the problem area for which decision making is necessary. 2. Draw a decision tree with all possible solutions and their consequences. 3. Input relevant variables with their respective probability values. 4. Determine and allocate payoffs for each possible outcome. 5. Calculate the Expected Monetary Value for every chance node in order to determine which solution is expected to provide the most value. Circles represent chance nodes in a tree diagram. Popular applications include: decision tree analysis in risk management, decision tree analysis in healthcare, decision tree analysis in capital budgeting, decision tree business analysis, and decision tree analysis in finance. A decision tree is the graphical depiction of all the possibilities or outcomes to solve a specific issue or avail a potential opportunity. It is a useful financial tool which visually facilitates the classification of all the probable results in a given situation. Steps in Decision Tree Analysis Now, you must be wondering, how to initiate the decision tree analysis for solving a particular issue? Following steps simplify the interpretation process of a decision tree: 234 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 12.1: The steps in decision tree analysis 1. The first step is understanding and specifying the problem area for which decision making is required. 2. The second step is interpreting and chalking out all possible solutions to the particular issue as well as their consequences. 3. The third step is presenting the variables on a decision tree along with its respective probability values. 4. The fourth step is finding out the outcomes of all the variables and specifying it in the decision tree. 5. The last step is highly crucial and backs the overall analysis of this process. It involves calculating the EMV values for all the chance nodes or options, to figure out the solution which provides the highest expected value. Decision Tree Analysis Example To enlighten upon the decision tree analysis, let us illustrate a business situation. ABC Ltd. is a company manufacturing skincare products. It was found that the business is at the maturity stage, demanding some change. After rigorous research, management came up with the following decision tree: 235 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 12.2: The decision tree analysis example In the above decision tree, we can easily make out that the company can expand its existing unit or innovate a new product, i.e., shower gel or make no changes. Given below is the evaluation of each of these alternatives: Expansion of Business Unit: If the company invests in the development of its business unit, there can be two possibilities, i.e.: 40% possibility that the market share will hike, increasing the overall profitability of the company by ₹2500000; 60% possibility that the competitors would take over the market share and the company may incur a loss of ₹800000. To find out the viability of this option, let us compute its EMV (Expected Monetary Value): New Product Line of Shower Gel If the organization goes for new product development, there can be following two possibilities:  50% chances are that the project would be successful and yield ₹1800000 as profit; 236 CU IDOL SELF LEARNING MATERIAL (SLM)

 50% possibility of failure persists, leading to a loss of ₹800000. To determine the profitability of this idea, let us evaluate its EMV Do Nothing If the company does not take any step, still there can be two outcomes, discussed below:  40% chances are there that yet, the organization can attract new customers, generating a profit of ₹1000000;  60% chances of failure are there due to the new competitors, incurring a loss of ₹400000. Given below is the EMV in such circumstances: Interpretation Business organizations need to consider various parameters during decision making. A decision tree analysis is one of the prominent ways of finding out the right solution to any problem. Advantages of Decision Tree Analysis 237 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 12.3: Advantages of decision tree analysis  Depicts Most Suitable Project/Solution: It is an effective means of picking out the most appropriate project or solution after examining all the possibilities.  Easy Data Interpretation and Classification: Not being rocket science, decision tree eases out the process of segregation of the acquired data into different classes.  Assist Multiple Decision-Making Tools: It also benefits the decision-maker by providing input for other analytical methods like nature’s tree.  Considers Both, Categorical and Numerical Data: This technique takes into consideration the quantitative as well as the qualitative variables for better results.  Initiates Variable Analysis: Its structured phenomena also facilitate the investigation and filtration of the relevant data. Disadvantages of Decision Tree Analysis Decision tree analysis has multidimensional applicability. However, its usage becomes limited due to its following shortcomings: 238 CU IDOL SELF LEARNING MATERIAL (SLM)

Figure 12.4: Disadvantages of decision tree analysis  Inappropriate for Excessive Data: Since it is a non-parametric technique, it is not suitable for the situations where the data for classification is vast.  Difficult to Handle Numerous Outcomes: If there are multiple possible results of every decision, it becomes tedious to compile all these on a decision tree.  Chances of Classification Errors: A less experienced decision tree maker usually makes a mistake while putting the variables into different classes.  Impact of Variance: Making even a slightest of change becomes problematic since it results in a completely different decision tree.  Unsuitable for Continuous Variables: Incorporating many open-ended numerical variables increases the possibility of errors.  Sensitive towards Biasness: A decision tree maker may lay more emphasis on preferable variables which may divert the direction of analysis.  Expensive Process: Collection of sufficient data, its classification and analysis demand high expense, being a resource-intensive process. 12.5 SUMMARY 239 CU IDOL SELF LEARNING MATERIAL (SLM)

 In operations research, decision tree analysis holds an equal significance as that of PERT analysis or CPM. It presents a complex decision problem, along with its multiple consequences on paper.  This enables the decision-maker to figure out all the possible options available with him/her and thus, simplifies the task.  Scenario analysis is one technique for calculating the expected value (EV) of an investment opportunity. It uses estimated probabilities with multivariate models to examine possible outcomes for a proposed investment. Scenario analysis also helps investors determine whether they are taking on an appropriate level of risk given the likely outcome of the investment.  The EV of a random variable gives a measure of the center of the distribution of the variable. Essentially, the EV is the long-term average value of the variable. Because of the law of large numbers, the average value of the variable converges to the EV as the number of repetitions approaches infinity. The EV is also known as expectation, the mean or the first moment. EV can be calculated for single discrete variables, single continuous variables, multiple discrete variables, and multiple continuous variables. For continuous variable situations, integrals must be used.  Expected value is a commonly used financial concept. In finance, it indicates the anticipated value of an investment in the future. By determining the probabilities of possible scenarios, one can determine the EV of the scenarios. The concept is frequently used with multivariate models and scenario analysis. It is directly related to the concept of expected return.  The expected value of perfect information is the price that a healthcare decision maker would be willing to pay to have perfect information regarding all factors that influence which treatment choice is preferred as the result of a cost-effectiveness analysis. This is the value (in money terms) of removing all uncertainty from such an analysis. EVPI is calculated as the difference in the monetary value of health gain associated with a decision between therapy alternatives between when the choice is made on the basis of with currently available information (i.e., uncertainty in the factors of interest) and when the choice is made based on perfect information (no uncertainty in all factors).  The EVPI can then be used as a necessary requirement for determining the potential efficiency of further primary research. Applying this decision rule, additional research should be considered only if the EVPI exceeds the expected cost of the research. EVPI can also be estimated for individual parameters (or groups of parameters) contained in the model, termed partial EVPI or expected value of partial perfect information (EVPPI). EVPPI considers particular elements of the decision problem in 240 CU IDOL SELF LEARNING MATERIAL (SLM)

order to direct and focus research towards the specific areas where the elimination of uncertainty has the most value. This can be particularly relevant to the design of any future research. On the basis of EVPI and EVPPI calculations, the potential value of a future trial, or other research designs, can be evaluated.  A decision tree is a decision-support model that encapsulates the questions and the possible answers and guides the analyst toward the appropriate result, and can be used for prediction models coupled with classification. Decision tree analysis looks at a collection of data instances and given outcomes, evaluates the frequency and distribution of values across the set of variables, and constructs a decision model in the form of a tree.  Have you ever made a decision knowing your choice would have major consequences? If you have, you know that it’s especially difficult to determine the best course of action when you aren’t sure what the outcomes will be.  Decision tree analysis can help you visualize the impact your decisions will have so you can find the best course of action. In this article, we’ll show you how to create a decision tree so you can use it throughout the project management process 12.6 KEYWORDS  Probability:The quality or state of being probable; the extent to which something is likely to happen or be the case.  Decision Tree:decision tree is the graphical depiction of all the possibilities or outcomes to solve a specific issue or avail a potential opportunity.  Pruning:It is just the reverse of splitting, where the decision tree maker can eliminate one or more sub-nodes from a particular decision node.  Nodes:a point in a network or diagram at which lines or pathways intersect or branch.  Branch: A branch denotes the various alternatives available with the decision tree maker. 12.7 LEARNING ACTIVITY 1. Analyze the decision tree for manufacturing company with their skin care products. ___________________________________________________________________________ ___________________________________________________________________________ 2. How to calculate EVPI for a company? 241 CU IDOL SELF LEARNING MATERIAL (SLM)

___________________________________________________________________________ ___________________________________________________________________________ 12.8 UNIT END QUESTIONS A. Descriptive Questions Short Questions 1. What is the expected value of the best decision? 2. Why is expected value useful? 3. What is EVPI? 4. What is the purpose of EVPI? 5. What is a decision tree? Long Questions 1. Why is it important to know EVPI? 2. What are the advantages and disadvantages of decision tree analysis? 3. Explain the steps in decision tree analysis. 4. Explain Expected value. 5. Explain how to calculate EVPI. B Multiple Choice Questions 1. Which is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility? a. Decision tree b. Graphs c. Trees d. Neural Networks 2. Which representDecision nodes? a. Disks b. Squares c. Circles d. Triangles 3. What is a Decision Tree? 242 CU IDOL SELF LEARNING MATERIAL (SLM)

a. Flow-Chart. b. Structure in which internal node represents test on an attribute, each branch represents outcome of test and each leaf node represents class label. c. Flow-Chart & Structure in which internal node represents test on an attribute, each branch represents outcome of test and each leaf node represents class label. d. None of these 4. What do you need to determine before you can calculate expected value? a. Number of people playing b. Probability of winning c. Name of game d. Names of people playing 5. Which is subtracted to get the expected value of perfect information is calculated? a. The minimum expected opportunity loss from the expected opportunity loss with perfect information. b. The maximum EMV from the minimum expected opportunity loss. c. The maximum EMV from the expected return with perfect information. d. EVSI from the expected return with perfect information. Answers 1-a 2-b 3-b 4-b 5-a 12.9 REFERENCES References  Song, Y. and Lu, Y., (2015). Decision tree methods: applications for classification and prediction. Shanghai Archives of Psychiatry, 27(2), pp.130-135.  Mittal, K., Khandunja, D. and Chandra, P., (2017). An Insight into “Decision Tree Analysis”. World Wide Journal of Multi disciplinary Research and Development, 3(12), pp.111-115.  Rokach, L. and Maimon, O., (2005). Decision Trees. Data Mining and Knowledge Discovery Handbook, pp.165-192. Textbooks  Rossi, F. and Tsoukias, A., (2009). Algorithmic decision theory. Berlin: Springer. 243 CU IDOL SELF LEARNING MATERIAL (SLM)

 Winston, W. L. (1997), Operations Research: Applications and Algorithms, Duxbury, Belmont, CA.  Hillier, F. S. and G. J. Lieberman (1995), Introduction to Operations Research, McGraw-Hill, Columbus, OH. Websites  https://corporatefinanceinstitute.com/resources/knowledge/other/expected-value/  https://theinvestorsbook.com/decision-tree-analysis.html  https://www.chegg.com/homework-help/definitions/expected-value-of-perfect- information-31 244 CU IDOL SELF LEARNING MATERIAL (SLM)