Module 5.pdf

Decision Support Systems College of Computing and Informatics 1 Module 5 Chapter 8- Prescriptive Analytics: Optimization and Simulation Analytics, Data Science, & Artificial Intelligence Systems For Decision Support This Presentation is mainly dependent on this textbook 2 Contents o 8.2 – Model-Based Decision Making o 8.3 – Structure of Mathematical Models for Decision Support o 8.4 – Certainty, Uncertainty, and Risk o 8.6 – Mathematical Programming Optimization o 8.7 – Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking o 8.8 – Decision Analysis with Decision Tables and Decision Trees o 8.9 – Introduction to Simulation o 8.10 – Visual Interactive Simulation 3 Weekly Learning Outcomes 1. Understand the applications of prescriptive analytics techniques in combination with reporting and predictive analytics 2. Understand the basic concepts of analytical decision modelling 3. Understand the concepts of analytical models for selected decision problems, including linear programming and simulation models for decision support 4. Explain the basic concepts of optimization and when to use them 5. Describe how to structure a linear programming 6. Explain what is meant by sensitivity analysis, what-if analysis, and goal seeking 7. Understand the concepts and applications of different types of simulation 8. Understand potential applications of discrete event simulation 4 Required Reading  Chapter 8 (sections 8.2 to 8.4 and 8.6 – 8.10): “Prescriptive Analytics: Optimization and Simulation” from “Analytics, Data Science, & Artificial Intelligence: Systems for Decision Support”. Recommended Reading  Artificial Intelligence: Systems for Decision Support”: Monte Carlo Simulation https://www.palisade.com/risk/monte_carlo_simulation.asp  It’s Only Logical: Decision Tables and Decision Trees https://medium.com/analysts-corner/its-only-logical-decision-tables-and-decision-trees-12a8b52243ea Recommended Video  Decision Trees & Decision Tables https://www.youtube.com/watch?v=A5-w3mof-3I 5 8.2 Model-Based Decision Making Prescriptive Analytics Model Examples Identification of the Problem and Environmental Analysis Model Categories Current Trends in Modeling 6 Prescriptive Analytics Model Examples Modeling is a key element for prescriptive analytics. Depending on the problem we are addressing, there are many classes of models, and there are often many specialized techniques for solving each one. Prescriptive analytics involves the application of mathematical models, sometimes the term data science is more commonly associated with the application of such mathematical models. 7 Identification of the Problem and Environmental Analysis It is important to analyze the scope of the domain and the forces and dynamics of the environment when making a decision. A decision maker needs to identify the organizational culture and the corporate decision-making processes. 1. Environmental scanning and analysis is the monitoring, scanning, and interpretation of collected information. 2. Variable Identification is critical, as are the relationships among the variables. 1. Influence diagrams can facilitate the identification process. 2. A cognitive map, can help a decision maker develop a better understanding of a problem, and variable interactions. 8 Identification of the Problem and Environmental Analysis 3. Predictive analytics (forecasting) is essential for constructing and manipulating models because the results of an implemented decision occur in the future. There is no point in running a what-if (sensitivity) analysis on the past because decisions made then have no impact on the future. Online commerce and communication has created an immense need for forecasting and an abundance of available information for performing it. These activities occur quickly, yet information about such purchases is gathered and should be analyzed to produce forecasts. Forecasting models use product life-cycle needs and information about the marketplace to analyze the situation. 9 Model Categories The following table classifies decision models into seven groups and lists several representative techniques for each category. Each technique can be applied to a static or a dynamic model, which can be constructed under assumed environments of certainty, uncertainty, or risk. 10 Model Categories (cont.) To expedite model construction, we can use special decision analysis systems that have modeling languages and capabilities embedded in them. These include spreadsheets, data mining systems, online analytic processing (OLAP) systems, and modeling languages. Model Management: Models must be managed to maintain integrity, and applicability. This is done with the aid of model-based management systems, which are analogous to database management systems (DBMS). Knowledge-based Modeling DSS: use quantitative models, whereas expert systems use qualitative, knowledge-based models in their applications. 11 Current Trends in Modeling One trend in modeling involves the development of model libraries and solution technique libraries. There is a clear trend toward developing and using cloud-based tools and software to run software to perform modeling, optimization, simulation, etc. With management models, the amount of data and model sizes is large, necessitating data warehouses and parallel computing for solutions. There is a trend toward making analytics models transparent to decision makers, and using influence diagrams (a model of a model to help in analysis). Many decision makers accustomed to slicing and dicing data cubes are now using OLAP systems that access data warehouses. 12 8.3 Structure of Mathematical Models for Decision Support Components of Decision Support Mathematical Models Examples of Components of Models The Structure of Mathematical Models 13 Components of Decision Support Mathematical Models Quantitative models are made up of four basic components: result variables, decision variables, uncontrollable variables, and intermediate result variables. Mathematical relationships link these components together. In non-quantitative models, the relationships are symbolic or qualitative. The results of decisions are determined based on decisions made, uncontrollable variable, and relationships among variables. The modeling process involves identifying the variables and relationships. Solving a model determines the values of these and the result variable(s). 14 Components of Decision Support Mathematical Models Result/Outcome/Output Variables: reflect level of effectiveness of a system. Decision Variables: Decision variables describe alternative courses of action. The decision maker controls the decision variables. Uncontrollable Variables/Parameters: fixed/varying factors that affect the result variables but are not under the decision maker control. Intermediate Result Variables: reflect intermediate outcomes in models. 15 Components of Decision Support Mathematical Models Examples 16 The Structure of Mathematical Models 17 8.4 Certainty, Uncertainty, and Risk Decision Making under Certainty Decision Making under Uncertainty Decision Making under Risk (Risk Analysis) 18 Decision Making under Certainty In decision making under certainty, complete knowledge is available so decision maker know the outcome of each course of action. This is done with structured problems and short time horizons (up to 1 year). Outcomes are not 100% known, but this assumption simplifies the model. The decision maker is viewed as a perfect predictor of the future because it is assumed that there is only one outcome for each alternative. Certainty models are easy to develop and solve, and yield optimal solutions. Financial models are constructed under assumed certainty. 19 Decision Making under Uncertainty Decision maker considers situation where several outcomes are possible for each course of action. In contrast to the risk situation, the decision maker does not know, or cannot estimate, the probability of occurrence of the possible outcomes. Modeling such situations involves assessment of the decision maker’s attitude toward risk. Instead of dealing with uncertainty, manager’s sometimes attempt to obtain more information so that the problem can be treated under certainty. If more information is not available, the problem must be treated under a condition of uncertainty, which is less definitive than the other categories. 20 Decision Making under Risk (Risk Analysis) Risk analysis is a decision-making method that analyzes risk associated with alternatives, each with a given probability of occurrence. The probabilities that the given outcomes will occur are assumed to be known or can be estimated. Under these assumptions, the decision maker can assess the degree of risk associated with each alternative (calculated risk). Risk analysis can be performed by calculating the expected value of each alternative and selecting the one with the best expected value. 21 8.6 Mathematical Programming Optimization Overview Linear Programming Model Implementation Modeling in LP: An Example 22 Overview Mathematical programming are tools that helps decision makers allocate scarce resources among competing activities to optimize a measurable goal. Linear programming (LP) is the best-known technique in a family of optimization tools called mathematical programming. In LP, all variable relationships are linear. Applications include supply chain management, product decisions, etc. LP allocation problems usually display the following characteristics: o Limited quantity of resources, most are used in product/service production. o Two or more ways resources can be used. Each is called a solution/program. o Each activity where resources are used, yields a return in terms of stated goal. 23 Linear Programming Model The LP allocation model is based on the following economic assumptions: o Returns from allocations are independent and measured by a common unit o The total return is the sum of the returns yielded by the different activities. o All data are known with certainty, and resources are used economically Allocation problems have a large number of possible solutions. Depending on the assumptions, the number of solutions can be either infinite or finite. Different solutions yield different rewards. The solution with highest degree of goal attainment is called optimal solution, and found by a special algorithm 24 Linear Programming Model (cont.) Every LP model is composed of: o Decision variables: Unknown values that are being searched for o Objective Function: A linear mathematical function that relates the decision variables to the goal, measures goal attainment, and is to be optimized o Coefficients: indicate contribution to objective of one unit of a decision variable o Constraint: Linear (in)equalities that limit resources o Capacities: Describe upper and lower limits on the constraints and variables o Input/output & Coefficients: Indicate resource utilization for a decision variable 25 Implementation Implement the model in “standard form”, where constraints are written with decision variables on the left and a number on the right. Alternatively, use spreadsheet to calculate the model in a less rigid manner. LP models can be specified directly in a number of user-friendly modeling systems. Models are specified in the same way they are defined algebraically. Optimization models can be solved by mathematical programming methods: o Assignment & Network models for planning and scheduling o Dynamic, Goal, Linear, Nonlinear and Integer programming o Investment & Replacement o Simple inventory models & Transportation 26 Modeling in LP: An Example MBI Corporation, which manufactures special-purpose computers, needs to make a decision: How many computers should it produce next month at the Boston plant? MBI is considering two types of computers: o CC-7, which requires 300 days of labor and $10,000 in materials, & o CC-8, which requires 500 days of labor and $15,000 in materials. The profit contribution of each CC-7 is $8,000, and of each CC-8 is $12,000. The plant has a capacity of 200,000 working days per month, and the material budget is $8 million per month. Marketing requires that at least 100 units of the CC-7 and at least 200 units of the CC-8 be produced each month. Problem: Maximize the company’s profits by determining how many units of the CC-7 27 and how many units of the CC-8 should be produced each month. Modeling in LP: An Example (cont.) The problem is to find the values of the decision variables X1, X2, such that the value of the result variable Z is maximized, subject to a set of linear constraints that express the technology, market conditions, and other uncontrollable variables. The mathematical relationships are all linear equations and inequalities. 28 Modeling in LP: An Example (cont.) Theoretically, any allocation problem of this type has an infinite number of possible solutions. Using special mathematical procedures, the LP approach applies a unique computerized search procedure that finds the best (optimal) solution/s (ex. maximizes total profit) in a matter of seconds. Excel ‘add-in Solver’ is used to obtain an optimal (best) solution to this problem. Open spreadsheet DS498_week7-Ch8d.xlsx 1. Activate ‘Solver’ Under the Data tab and on the Analysis ribbon. If it is not there, you should be able to enable it by going to File -> Excel’s Options Menu and selecting Add-ins. 29 Modeling in LP: An Example (cont.) 2. Enter these data directly into an Excel spreadsheet. 3. Identify the goal (by setting Target Cell equal to Max). 4. Identify decision variables (by setting By Changing Cells). 5. Identify constraints on labor capacity, budget, and the desired minimum production of the two products X1 and X2. 6. Clicking on the Solver Add-in opens a dialog box, o Specify the cells or ranges that define the objective function cell, decision/changing variables (cells), and the constraints. o Select the solution method (usually Simplex LP) o solve the problem. 7. Next, we select all three reports—Answer, Sensitivity, and Limits (optimal solution of X1 30 = 333.33, X2 = 200, Profit = $5,066,667) 8.7 Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking Multiple Goals Sensitivity Analysis Types of Sensitivity Analysis What-If Analysis What-If Analysis Example Goal Seeking Goal Seeking Example 31 Multiple Goals Today’s management systems are complex, and managers want to attain simultaneous goals, some of which may conflict. Transform a multiple-goal problem into a single-measure-of effectiveness problem before comparing the effects of the solutions. Certain difficulties may arise when analyzing multiple goals: o It is difficult to obtain the organization’s goals explicitly o Goals are viewed differently at various levels of the organization o Goals and their importance change in response to the organization o Complex problems are solved by decision makers with different agendas 32 Sensitivity Analysis Sensitivity analysis assesses impact of input data changes on proposed solution. Sensitivity analysis allows for: o Adaptation to conditions of different decision-making situations o Provides a better understanding of the model o Permits the input of data to increase model confidence. 33 Sensitivity Analysis (cont.) Sensitivity analysis tests relationships such as the following: Impact of parameter change, and decision variables on outcome variable(s) The effect of uncertainty in estimating external variables The effect of different dependent interactions among variables The robustness of decisions under changing conditions Sensitivity analyses are used for: Revising models to eliminate too-large sensitivities Detailing variables and obtaining estimates of sensitive external variables Altering a real-world system to reduce actual sensitivities 34 Types of Sensitivity Analysis The two types of sensitivity analyses are automatic and trial and error. Automatic Sensitivity Analysis: This is performed in standard quantitative model implementations such as LP. It is usually limited to one change at a time, and only for certain variables. It is powerful because of its ability to establish ranges and limits very fast Trial-and-error Sensitivity Analysis: Impact of changes in variable(s) is determined by trial-and-error approach When changes are repeated, better and better solutions may be discovered. Such experimentation has two approaches: what-if analysis and goal seeking. 35 What-If Analysis What-if analysis is structured as: What will happen to the solution if an input variable, assumption, or parameter value is changed? o Total inventory cost if the carrying inventories cost increases by 10%? o Market share if the advertising budget increases by 5%? With the appropriate user interface, managers can ask a computer model these types of questions and get immediate answers. Performs multiple cases and change the percentage, or other data as needed. What-if analysis is common in many decision systems. Users are given the opportunity to change their answers to the system’s questions, and a revised recommendation is found. 36 What-If Analysis Example A what-if query for a cash flow problem: the user changes the cells containing the initial sales (from 100 to 120) and the sales growth rate (from 3% to 4% per quarter), the program immediately re-computes the value of the annual net profit cell (from $127 to $182). 37 Goal Seeking Goal seeking calculates the values of the inputs necessary to achieve a desired level of an output (goal). The following are some examples: o Annual R&D budget is needed for an annual growth rate of 15% by 2018? o How many nurses needed to reduce the average waiting time of a patient in the emergency room to less than 10 minutes? Computing A Break-even Point By Using Goal Seeking: o Determining the value of the decision variables that generate zero profit. o Some modeling software packages can directly compute break-even points, which is an important application of goal seeking. o Sensitivity analysis as the prewritten routines present a limited opportunity for asking what-if questions. 38 Goal Seeking In a financial planning model, the internal rate of return (IRR) is the interest rate that produces a net present value (NPV) of zero. Given a stream of annual returns in Column E, we can compute the NPV of planned investment through goal-seeking. An NPV equal to zero determines the IRR of this cash flow, including the investment. We set the NPV cell to 0 by changing the interest rate cell. The answer is 38.77059%. 39 8.8 Decision Analysis with Decision Tables & Decision Trees Decision Tables Decision Tables Example Decision Trees 40 Decision Tables Decision tables organize information in systematic, tabular form for analysis. Treating Uncertainty: Several methods are available for handling uncertainty. o Optimistic approach: assumes and selects best outcomes for alternatives o Pessimistic approach: assumes worst outcome for alternatives; selects the best o Another approach simply assumes that all states of nature are equally possible. When possible, analysts should attempt to gather information to treat the problem under assumed certainty. Treating Risk: The most common method for solving this risk analysis problem is to select the alternative with the greatest expected value. 41 Decision Tables Example An investor estimates: solid growth (50%), stagnation (30%), and inflation (20%) Expected value is computed by multiplying result probabilities and adding them Bond investment yields an expected return of 12(0.5) + 6(0.3) + 3(0.2) = 8.4% This approach can sometimes be a dangerous strategy such as a financial advisor presents a $1,000 investment with 0.9999 chance to double your money, and 0.0001 chance you’ll lose $500,000. The expected value of this investment is $949.80 The potential loss could be catastrophic for any investor 42 Decision Trees Decision trees are alternative representations of a decision table; it shows a problem’s relationship graphically and handles complex situations compactly. TreeAge Pro & PrecisionTree are systems that show decision trees in practice. You can apply mathematical programming to decision-making situations under risk. These include simulation, certainty factors, and fuzzy logic. A simplified investment case of multiple goals is shown in the table. The three goals are yield, safety, and liquidity. This situation is under assumed certainty. 43 8.9 Introduction to Simulation Major Characteristics of Simulation Advantages of Simulation Disadvantages of Simulation The Methodology of Simulation Simulation Types Monte Carlo Simulation Discrete Event Simulation 44 Major Characteristics of Simulation Simulation involves building a model of reality to the extent practical. Simulation models may suffer from fewer assumptions about the decision situation as compared to other prescriptive analytic models. Simulation is a technique for conducting experiments. Therefore, it involves testing specific values of the decision or uncontrollable variables in the model and observing the impact on the output variables. Simulation is used only when a problem is too complex to be treated using numerical optimization techniques. Complexity in this situation means either that the problem cannot be formulated for optimization, that the formulation is too large, that there are too many interactions among the variables. 45 Advantages of Simulation Simulation is used in decision support modeling for the following reasons: The theory is straightforward, and model is built from manager’s perspective. Time compression is attained quickly to give idea of policies’ long-term effects. Descriptive rather than normative, allowing managers to ask what-if questions, and use a trial-and-error approach with less expense and risk. Requires intimate knowledge; model builder constantly interact with manager. Can handle a variety of problem types and higher-level managerial functions. Produces performance measures, and includes real complexities of problems. Can readily handle relatively unstructured problems. 46 Disadvantages of Simulation An optimal solution cannot be guaranteed, but relatively good ones are generally found. Simulation model construction can be a slow and costly process, although newer modeling systems are easier to use than ever. Solutions and inferences from a simulation study are usually not transferable to other problems because the model incorporates unique problem factors. Simulation is sometimes so easy to explain to managers that analytic methods are often overlooked. Simulation software sometimes requires special skills because of the complexity of the formal solution method. 47 The Methodology of Simulation Simulation involves setting up a model of a real system through the steps: Define the problem: Examine problem, and specify need for simulation Construct model: Determine variables, relationships, and gather data. Test and validate model: Ensure model properly represents studied system. Design experiment: There are two conflicting objectives: accuracy and cost. Conduct experiment: can involve issues like number generation. Evaluate results: Statistical tools/sensitivity analyses used to interpret results. Implement results: Managerial involvement leads to implementation success. 48 The Methodology of Simulation 49 Simulation Types Simulation model consists of relationships that present the real-world operations. Simulation results depend on the set of parameters given as inputs. There are various simulation paradigms such as Monte Carlo simulation, discrete event, agent based, or system dynamics. The level of abstraction in a problem can determine simulation technique. Discrete events and agent based models are used for low levels of abstraction. They consider individual elements such as people in the simulation models, whereas systems dynamics is more appropriate for aggregate analysis. Here we introduce the major types of simulation: probabilistic simulation, time- dependent and time-independent simulation, and visual simulation. 50 Simulation Types Probabilistic Simulation: One or more independent variables are probabilistic. They follow probability distributions, which can be discrete or continuous: o Discrete involves situations with limited event numbers and finite values. o Continuous distributions are situations with unlimited numbers of possible events that follow density functions, such as the normal distribution. Time-dependent Versus Time-independent Simulation: o Time-independent refers to situations where time of event occurrence is unimportant. For example, we may know that the demand for a product is 3 units/day, but do not care when during the day the item is demanded. o However, in waiting-line problems applicable to e-commerce, it is important to know the precise time of arrival. This is a time-dependent situation. 51 Monte Carlo Simulation In business decision problems, we employ probabilistic simulations. The Monte Carlo simulation is commonly used. This method begins with building a model of the decision problem without having to consider the uncertainty of any variables. Then we recognize that certain variables are uncertain or follow an estimated probability distribution. This estimation is based on analysis of past data. Then we begin running sampling experiments. This consists of generating random values of uncertain parameters and then computing values of the variables that are impacted by such parameters or variables. We then analyze the behavior of these performance variables by examining their statistical distributions. 52 Discrete Event Simulation Discrete event simulation refers to building a model of a system where the interaction between different entities is studied. An example of this is modeling the customers arriving at various rates and the server serving at various rates, we can estimate the average system performance, waiting time, number of waiting customers, etc. Such systems are viewed as collections of customers, queues, and servers. There are thousands of documented applications of discrete event simulation models in engineering, business, and so on. Tools for building discrete event simulation models have been around for a long time, but these have evolved to take advantage of developments in graphical capabilities for building and understanding the results of such simulation models. 53 8.10 Visual Interactive Simulation Visual Interactive Simulation Visual Interactive Models and DSS 54 Visual Interactive Simulation Visual interactive simulation (VIS), visual interactive modeling (VIM) and visual interactive problem solving, is a simulation method that lets decision makers see what a model is doing, how it interacts with made decisions. Users employ knowledge to try different decision strategies while interacting with the model. Decision makers can contribute to model validation. VIS uses animated computer graphic displays to present the impact of different managerial decisions. It differs from regular graphics in that the user can adjust the decision-making process and see results of the intervention. VIS can represent static or dynamic systems. Static models display a visual image of the result of one decision alternative at a time. Dynamic models display evolving systems over time. The evolution is represented by animation. 55 Visual Interactive Models (VIM) and DSS VIM in DSS has been used in several operations management decisions. The method consists of priming a visual interactive model of a company with its current status. Waiting-line management is a good example of VIM. Such a DSS usually computes measures of performance for the various decision alternatives. Complex waiting-line problems require simulation. VIM can display the size of the waiting line as it changes during the simulation runs and can graphically present the answers to what-if questions regarding changes in input variables. The VIM approach can be used with AI. Integration of the two techniques adds several capabilities that range from the ability to build systems graphically to learning about the dynamics of the system. 56 Main Reference  Chapter 8 (sections 8.2 to 8.4 and 8.6 to 8.10: Modeling in LP: An Example): “Prescriptive Analytics: Optimization and Simulation” from “Analytics, Data Science, & Artificial Intelligence: Systems for Decision Support”. Week self-review exercises  Application Case 8.5 to Application Case 8.9 from ““Analytics, Data Science, & Artificial Intelligence: Systems for Decision Support”. 57 Thank You 58

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