Prescriptive analytics: CHAPTER Optimization 6 and simulation Learning Objectives for Chapter 6 Understand the applications of prescriptive analytics techniques in combination with reporting and predictive analytics Understand the basic concepts of analytical decision modeling Understand the concepts of analytical models for selected decision problems, including linear programming and simulation models for decision support Describe how spreadsheets can be used for analytical modeling and solutions Explain the basic concepts of optimization and when to use them Describe how to structure a linear programming model Explain what is meant by sensitivity analysis, what-if analysis, and goal seeking Understand the concepts and applications of different types of simulation Understand potential applications of d iscrete event simulation Copyright C2018 Pearson Education, Inc
1 Copyright © 2018Pearson Education, Inc. Prescriptive Analytics: Optimization and Simulation Learning Objectives for Chapter 6 ▪ Understand the applications of prescriptive analytics techniques in combination with reporting and predictive analytics ▪ Understand the basic concepts of analytical decision modeling ▪ Understand the concepts of analytical models for selected decision problems, including linear programming and simulation models for decision support ▪ Describe how spreadsheets can be used for analytical modeling and solutions ▪ Explain the basic concepts of optimization and when to use them ▪ Describe how to structure a linear programming model ▪ Explain what is meant by sensitivity analysis, what-if analysis, and goal seeking ▪ Understand the concepts and applications of different types of simulation ▪ Understand potential applications of discrete event simulation CHAPTER 6
CHAPTER OUTLINE 6. 1 Opening Vignette: School District of Philadelphia Uses Prescriptive Analytics to Find Optimal Solution for Awarding Bus Route Contracts 6.2 Model-Based Decision Making 6.3 Structure of Mathematical Models for Decision Support 6. 4 Certainty, Uncertainty, and risk 6.5 Decision Modeling with Spreadsheets 6.6 Mathematical Programming Optimization 6.7 Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking 6.8 Decision analysis with Decision Tables and Decision Trees 6.9 Introduction to simulation 6.10 Visual Interactive simulation ANSWERS TO END OF SECTION REVIEW QUESTIONS Section 6.1 Review Questions What decision was being made in this vignette? The school district of Philadelphia was searching for private bus vendors to outsource some of their bus routes to locations in this scenario? predictive)might one need to make the best The vendors were evaluated based on five variables: cost, capabilities, reliance financial stability and business acumen 3. What other costs or constraints might you have to consider in award ing contracts for such routes? Add itionally you might look at minimizing the total number of vendors, the quality of service provided, the potential longevity of the contract, and the vendor s capacity 4. Which other situations might be appropriate for applications of such models Copyright C2018 Pearson Education, Inc
2 Copyright © 2018Pearson Education, Inc. CHAPTER OUTLINE 6.1 Opening Vignette: School District of Philadelphia Uses Prescriptive Analytics to Find Optimal Solution for Awarding Bus Route Contracts 6.2 Model-Based Decision Making 6.3 Structure of Mathematical Models for Decision Support 6.4 Certainty, Uncertainty, and Risk 6.5 Decision Modeling with Spreadsheets 6.6 Mathematical Programming Optimization 6.7 Multiple Goals, Sensitivity Analysis, What-If Analysis, and Goal Seeking 6.8 Decision Analysis with Decision Tables and Decision Trees 6.9 Introduction to Simulation 6.10 Visual Interactive Simulation ANSWERS TO END OF SECTION REVIEW QUESTIONS Section 6.1 Review Questions 1. What decision was being made in this vignette? The school district of Philadelphia was searching for private bus vendors to outsource some of their bus routes to. 2. What data (descriptive and or predictive) might one need to make the best allocations in this scenario? The vendors were evaluated based on five variables: cost, capabilities, reliance, financial stability, and business acumen. 3. What other costs or constraints might you have to consider in awarding contracts for such routes? Additionally you might look at minimizing the total number of vendors, the quality of service provided, the potential longevity of the contract, and the vendor’s capacity. 4. Which other situations might be appropriate for applications of such models?
There are a large number of other situations that might be applicable to this methodology. Some examples might include for construction work, or making advertising decisions Section 6.2 Review Questions List three lessons learned from modeling Models can be used for a wide array of applications. Some examples include making efficient purchasing decisions, making cost-effective travel plans, and efficiently managing a workforce 2. List and describe the major issues in modeling Two major issues in modeling focus on model management and knowledge-based modeling Model management focuses on the use and reuse of existing models in construction of solvable/usable models and predictive analysis techniques or the a fashion that maintains their integrity. Knowledge-based modeling allows 3. What are the major types of models used in DSS? DSS uses mostly quantitative models, whereas expert systems use qualitative, knowledge-based models in their applications 4. Why are models not used in industry as frequently as they should or could be? Models may not be used as often in industry as possible because users see them as being too difficult to create, the software too difficult to use, or fear of making mistakes in the creation of the model itself What are the current trends in modeling? These trends include o the development of model libraries and solution technique libraries o developing and using cloud-based tools and software to access and even run software to perform modeling, optimization, simulation o making analytics models completely transparent to the decision maker o build ing a model of a model to help in its analys Copyright C2018 Pearson Education, Inc
3 Copyright © 2018Pearson Education, Inc. There are a large number of other situations that might be applicable to this methodology. Some examples might include for construction work, or making advertising decisions. Section 6.2 Review Questions 1. List three lessons learned from modeling. Models can be used for a wide array of applications. Some examples include making efficient purchasing decisions, making cost-effective travel plans, and efficiently managing a workforce. 2. List and describe the major issues in modeling. Two major issues in modeling focus on model management and knowledge-based modeling. Model management focuses on the use and reuse of existing models in a fashion that maintains their integrity. Knowledge-based modeling allows for the construction of solvable/usable models and predictive analysis techniques. 3. What are the major types of models used in DSS? DSS uses mostly quantitative models, whereas expert systems use qualitative, knowledge-based models in their applications. 4. Why are models not used in industry as frequently as they should or could be? Models may not be used as often in industry as possible because users see them as being too difficult to create, the software too difficult to use, or fear of making mistakes in the creation of the model itself. 5. What are the current trends in modeling? These trends include: o the development of model libraries and solution technique libraries o developing and using cloud-based tools and software to access and even run software to perform modeling, optimization, simulation o making analytics models completely transparent to the decision maker o building a model of a model to help in its analysis
Section 6.3 Review Questions What is a decision variable? Decision variables describe alternative courses of action The decision maker controls the decision variables 2. List and briefly discuss the major components of a quantitative model Result(outcome) variables reflect the level of effectiveness of a system; that is, they ind icate how well the system performs or attains its goal(s) Decision variables describe alternative courses of action The decision maker controls the decision variables Uncontrollable Variables in any decision-making situation, there are factors that affect the result variables but are not under the control of the decision maker Intermed iate result variables reflect intermed iate outcomes in mathematical model Explain the role of intermed iate result variabl Intermediate result variables reflect intermed iate outcomes in mathemat models Copyright C2018 Pearson Education, Inc
4 Copyright © 2018Pearson Education, Inc. Section 6.3 Review Questions 1. What is a decision variable? Decision variables describe alternative courses of action. The decision maker controls the decision variables. 2. List and briefly discuss the major components of a quantitative model. • Result (outcome) variables reflect the level of effectiveness of a system; that is, they indicate how well the system performs or attains its goal(s). • Decision variables describe alternative courses of action. The decision maker controls the decision variables. • Uncontrollable Variables in any decision-making situation, there are factors that affect the result variables but are not under the control of the decision maker. • Intermediate result variables reflect intermediate outcomes in mathematical models. 3. Explain the role of intermediate result variables. Intermediate result variables reflect intermediate outcomes in mathematical models
Section 6.4 Review Questions Define what it means to perform decision making under assumed certainty, risk and uncertaint In decision making under certainty, it is assumed that complete knowledge is available so that the decision maker knows exactly what the outcome of each course of action will be a decision made under risk is one in which the decision maker must consider several possible outcomes for each alternative, each with a given probability of occurrence In decision making under uncertainty, the decision maker considers situations in which several outcomes are possible for each course of action How can decision-making problems under assumed certainty be handled? Decision-making problems under assumed certainty are hand led as if there is only one possible outcome How can decision-making problems under assumed uncertainty be handled? Decision-making problems under assumed uncertainty are handled as if multiple outcomes are possible How can decision-making problems under assumed risk be handled? Decision-making problems under assumed risk are handled as if multiple outcomes are possible, but the probability of each outcome is known Copyright C2018 Pearson Education, Inc
5 Copyright © 2018Pearson Education, Inc. Section 6.4 Review Questions 1. Define what it means to perform decision making under assumed certainty, risk, and uncertainty. In decision making under certainty, it is assumed that complete knowledge is available so that the decision maker knows exactly what the outcome of each course of action will be. A decision made under risk is one in which the decision maker must consider several possible outcomes for each alternative, each with a given probability of occurrence. In decision making under uncertainty, the decision maker considers situations in which several outcomes are possible for each course of action. 2. How can decision-making problems under assumed certainty be handled? Decision-making problems under assumed certainty are handled as if there is only one possible outcome. 3. How can decision-making problems under assumed uncertainty be handled? Decision-making problems under assumed uncertainty are handled as if multiple outcomes are possible. 4. How can decision-making problems under assumed risk be handled? Decision-making problems under assumed risk are handled as if multiple outcomes are possible, but the probability of each outcome is known
Section 6.5 Review Questions What is a spreadsheet? Spread sheet packages are easy-to-use implementation software for the development of a wide range of applications in business, engineering, mathematics, and science. Spreadsheets include extensive statistical, forecasting, and other modeling and database management capabilities, functions, and routines What is a spreadsheet add-in? How can add-ins help in DSS creation and use? Add-in packages for spread sheets are add itional software items that can be integrated into an existing spreadsheet application in order to expand and enhance the type of calculations that can be performed Explain why a spreadsheet is so conducive to the development of Dss Spreadsheets are very conducive to the development of dss because they are easy to implement and use for a large base of users. Out of the box they have a wide array of functions and tools. These abilities can be easily augmented through add-in packages and templates 6 Copyright C2018 Pearson Education, Inc
6 Copyright © 2018Pearson Education, Inc. Section 6.5 Review Questions 1. What is a spreadsheet? Spreadsheet packages are easy-to-use implementation software for the development of a wide range of applications in business, engineering, mathematics, and science. Spreadsheets include extensive statistical, forecasting, and other modeling and database management capabilities, functions, and routines. 2. What is a spreadsheet add-in? How can add-ins help in DSS creation and use? Add-in packages for spreadsheets are additional software items that can be integrated into an existing spreadsheet application in order to expand and enhance the type of calculations that can be performed. 3. Explain why a spreadsheet is so conducive to the development of DSS. Spreadsheets are very conducive to the development of DSS because they are easy to implement and use for a large base of users. Out of the box they have a wide array of functions and tools. These abilities can be easily augmented through add-in packages and templates
Section 6.6 Review Questions 1. List and explain the assumptions involved in LP. a limited quantity of economic resources is available for allocation The resources are used in the production of products or services There are two or more ways in which the resources can be used. Each is called a solution or a program Each activity (product or service) in which the resources are used yields a return in terms of the stated goal The allocation is usually restricted by several limitations and requirements called constraints List and explain the characteristics of LP measured by a common unit (e.g, dollars, utility/!at is, they can be Returns from different allocations can be compared The return from any allocation is independent of other allocations The total return is the sum of the returns yielded by the different activities All data are known with certainty The resources are to be used in the most economical manner Describe an allocation problem a typical allocation problem focuses around the most efficient use of a scarce resource Define the product-mix problem A typical product-mix problem focuses around the most efficient ratios of two or more products to be produced Define the blend ing problem a typical blending problem combines the issues of an allocation problem (scarcity) with the issues of a product-mix problem(ratios) Copyright C2018 Pearson Education, Inc
7 Copyright © 2018Pearson Education, Inc. Section 6.6 Review Questions 1. List and explain the assumptions involved in LP. • A limited quantity of economic resources is available for allocation. • The resources are used in the production of products or services. • There are two or more ways in which the resources can be used. Each is called a solution or a program. • Each activity (product or service) in which the resources are used yields a return in terms of the stated goal. • The allocation is usually restricted by several limitations and requirements, called constraints. 2. List and explain the characteristics of LP. • Returns from different allocations can be compared; that is, they can be measured by a common unit (e.g., dollars, utility). • The return from any allocation is independent of other allocations. • The total return is the sum of the returns yielded by the different activities. • All data are known with certainty. • The resources are to be used in the most economical manner. 3. Describe an allocation problem. A typical allocation problem focuses around the most efficient use of a scarce resource. 4. Define the product-mix problem. A typical product-mix problem focuses around the most efficient ratios of two or more products to be produced. 5. Define the blending problem. A typical blending problem combines the issues of an allocation problem (scarcity) with the issues of a product-mix problem (ratios)
L ist several on optimization models A (best matching of objects) Dyna programming Go Investment(maximizing rate of return) LI nd integer programming Network models for planning and scheduling Nonlinear programming Replacement(capital bud geting) Simple inventory models(e.g, economic order quantity) Transportation(minimize cost of shipments) Copyright C2018 Pearson Education, Inc
8 Copyright © 2018Pearson Education, Inc. 6. List several common optimization models. • Assignment (best matching of objects) • Dynamic programming • Goal programming • Investment (maximizing rate of return) • Linear and integer programming • Network models for planning and scheduling • Nonlinear programming • Replacement (capital budgeting) • Simple inventory models (e.g., economic order quantity) • Transportation (minimize cost of shipments)
Section 6.7 Review Questions List some difficulties that may arise when analyzing multiple goals In situations where multiple goals exist, it may be difficult to analyze and optimize for each of these goals. This is because the goals may be conflicting, hey may be more complex than they initially appear, and the importance of goals may vary depend ing on the stakeholder List the reasons for performing sensitivity analysis Sensitivity analysis is extremely important in prescriptive analytics because it allows flexibil ity and adaptation to changing conditions and to the requirements of different decision-making situations, provides a better understand ing of the model and the decision-making situation it attempts to describe, and permits the manager to input data to increase the confidence in the model 3. Explain why a manager might perform what-if analysis Managers may elect to perform a what-if analysis because they are very approachable and simple to run. They provide immediate feedback, and can be used over a wide variety of scenarios to get a general idea of what possible outcomes may be Explain why a manager might use goal seeking Managers may elect to perform a goal-seek analysis to find a specific numeric answer given a known set of variables and equations. This type of analysis is easy to perform and provides immediate feed back Copyright C2018 Pearson Education, Inc
9 Copyright © 2018Pearson Education, Inc. Section 6.7 Review Questions 1. List some difficulties that may arise when analyzing multiple goals. In situations where multiple goals exist, it may be difficult to analyze and optimize for each of these goals. This is because the goals may be conflicting, they may be more complex than they initially appear, and the importance of goals may vary depending on the stakeholder. 2. List the reasons for performing sensitivity analysis. Sensitivity analysis is extremely important in prescriptive analytics because it allows flexibility and adaptation to changing conditions and to the requirements of different decision-making situations, provides a better understanding of the model and the decision-making situation it attempts to describe, and permits the manager to input data to increase the confidence in the model. 3. Explain why a manager might perform what-if analysis. Managers may elect to perform a what-if analysis because they are very approachable and simple to run. They provide immediate feedback, and can be used over a wide variety of scenarios to get a general idea of what possible outcomes may be. 4. Explain why a manager might use goal seeking. Managers may elect to perform a goal-seek analysis to find a specific numeric answer given a known set of variables and equations. This type of analysis is easy to perform and provides immediate feedback
Section 6.8 Review Questions What is a decision table? Decision tables conveniently organize information and knowledge in a systematic tabular manner to prepare it for analysis What is a decision tree? a decision tree shows the relationships of the problem graphically and can handle complex situations in a compact form 3. How can a decision tree be used in decision making? Decision trees can be used in decision making to help graphically display the different options that may be selected from so that the results of those decisions can be evaluated in isolation 4. Describe what it means to have multiple goals a multiple goals situation is one in which alternatives are evaluated with several sometimes conflicting, goals Section 6.9 Review Questions 1. List the characteristics of simulation The major characteristics of a simulation are that it is a model used to approximate reality, that it is used to conduct experiments, and that it is used for problems that are too complex to be evaluated using numerical optimization techniques 2. List the advantages and d isadvantages of simulation The theory is fairly straightforward a great amount of time compression can be attained, quickly giving a manager some feel as to the long-term(1-to 10-year) effects of many policies Simulation is descriptive rather than normative. This allows the manager te pose what-if questions. Managers can use a trial-and-error approach to problem solving and can do so faster, at less expense, more accurately, and with less risk A manager can experiment to determine which decision variables and which parts of the environment are really important, and with different alternatives An accurate simulation model requires an intimate knowledge of the problem, thus forcing the model builder to constantly interact with the manager. This is Copyright C2018 Pearson Education, Inc
10 Copyright © 2018Pearson Education, Inc. Section 6.8 Review Questions 1. What is a decision table? Decision tables conveniently organize information and knowledge in a systematic, tabular manner to prepare it for analysis. 2. What is a decision tree? A decision tree shows the relationships of the problem graphically and can handle complex situations in a compact form. 3. How can a decision tree be used in decision making? Decision trees can be used in decision making to help graphically display the different options that may be selected from so that the results of those decisions can be evaluated in isolation. 4. Describe what it means to have multiple goals. A multiple goals situation is one in which alternatives are evaluated with several, sometimes conflicting, goals. Section 6.9 Review Questions 1. List the characteristics of simulation. The major characteristics of a simulation are that it is a model used to approximate reality, that it is used to conduct experiments, and that it is used for problems that are too complex to be evaluated using numerical optimization techniques. 2. List the advantages and disadvantages of simulation. • The theory is fairly straightforward. • A great amount of time compression can be attained, quickly giving a manager some feel as to the long-term (1- to 10-year) effects of many policies. • Simulation is descriptive rather than normative. This allows the manager to pose what-if questions. Managers can use a trial-and-error approach to problem solving and can do so faster, at less expense, more accurately, and with less risk. • A manager can experiment to determine which decision variables and which parts of the environment are really important, and with different alternatives. • An accurate simulation model requires an intimate knowledge of the problem, thus forcing the model builder to constantly interact with the manager. This is
