# ME402: Design Decisions in Engineering

Unit 4: Mathematical Tools For Decision Making   An engineering designer should always validate decisions with mathematical data and analysis.  Accordingly, Unit 4 will cover the mathematical concepts and tools needed to make design decisions.  You will learn various operational research/optimization tools, including the linear and dynamic programming method.  You also will learn how to develop algorithms and techniques for analyzing project path and how to conduct supply chain and transportation analysis.  These tools and techniques will help you make sound design decisions supported by mathematical data.

This unit will take you approximately 52 hours to complete.

☐    Subunit 4.1: 20 hours

☐    Subunit 4.2: 8 hours

☐    Subunit 4.3: 8 hours

☐    Subunit 4.4: 12 hours

☐    Subunit 4.5: 4 hours

Unit4 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Explain the principles of constrained optimization, linear optimization, and dynamic optimization. - Use optimization algorithms to support decision making. - Conduct probabilistic risk assessment. - Explain the principles and perform decision tree analysis. - Explain utility theory and calculate utilities of decisions. - Perform real options analysis.

4.1 Optimization Algorithms   4.1.1 Introduction to Constrained Optimization   - Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 3: Introduction to Constrained Optimization” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 3: Introduction to Constrained Optimization” (PDF)

Instructions: Please download the PDF file for “Chapter 3: Introduction to Constrained Optimization” and read the entire file.  This reading gives a general overview of constrained optimization.  This reading will take approximately 4 hours to complete.

4.1.2 Linear Programming   - Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 5: Linear Programming” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management:Chapter 5: Linear Programming” (PDF)

Instructions: Please download the PDF file for Chapter 5 and read the entire file. You will learn how to use linear programming for constrained optimization.  Make sure that you understand the concepts of objective function and decision variables.  You may want to refresh your knowledge of linear algebra before reading this chapter.  This reading will take approximately 3 hours to complete.

• Assessment: Management Science with Spreadsheets by William Stevenson, Rochester Institute of Technology, and Ceyhun Ozgur, Valparaiso University: “Multiple Choice Quiz for Chapter 3” Link: Management Science with Spreadsheets by William Stevenson, Rochester Institute of Technology, and Ceyhun Ozgur, Valparaiso University: “Multiple Choice Quiz for Chapter 3” (HTML)

Instructions: Please click on the link above and answer all questions in the quiz.  Select your answer from choices given for each question.  Click on “Submit Answers” at the bottom of the webpage when you have answered all the questions.  The webpage will tell you whether your answer is correct and what the correct answer is.  This assessment will take 1 hour to complete.

4.1.3 Dynamic Programming   - Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 7: Dynamic Programming” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 7: Dynamic Programming” (PDF)

Instructions: Please download the PDF file for Chapter 7 and read the entire file.  This chapter discusses the basic concepts of dynamic programming, which is designed to overcome the major disadvantages of linear programming, including its inability to handle nonlinear problems or discontinuous variables.  Work through the example provided in Section 7.4.  This reading will take approximately 4 hours to complete.

4.1.4 Sensitivity Analysis   - Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 6: Sensitivity Analysis” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 6: Sensitivity Analysis” (PDF)

Instructions: Please download the PDF file for Chapter 6 and read the entire file. This chapter will introduce you to the basic principles of performing sensitivity analysis to determine the dependency of the optimal solutions on the formulation of the problem and the pertinent assumptions.  This reading will take approximately 4 hours to complete.

4.1.5 Multi-Objective Optimization   - Assessment: The Saylor Foundation’s “Constrained Optimization” Link: The Saylor Foundation’s “Constrained Optimization” (PDF)

Instructions: Complete the linked assessment. When you are done -- or if you are stuck! -- check your work against the Saylor Foundation’s “Constrained Optimization Answer Key” (PDF). Consult the tutorials suggested in the assessment.

• Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 8: Multiobjective Optimization” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 8: Multiobjective Optimization” (PDF)

Instructions: Please download the PDF file for Chapter 8 and read the entire file. In previous subunits, we are mostly concerned with optimization with respect to a single objective.  This chapter discusses the basic concepts of multi-objective optimization, which aims to achieve optimum over several objectives at once.  This reading will take approximately 4 hours to complete.

4.2 Risk Assessment and Management   4.2.1 Probabilistic Risk Assessment   - Reading: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 7: RPRA: Probabilistic Risk Assessment” Link: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 7: RPRA: Probabilistic Risk Assessment” (PDF)

• Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 15: Risk Assessment” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 15: Risk Assessment” (PDF)

Instructions: Please download the PDF file for “Chapter 15: Risk Management” and read the entire file.  This reading will provide a more in-depth discussion of probabilistic risk assessment, including the use of Bayes’ theorem and likelihood ratios.  This reading will take you approximately 4 hours to complete.

4.2.2 Risk Management   - Reading: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 9: RPRA 7: Risk Management” Link: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 9: RPRA 7: Risk Management” (PDF)

Instructions: Please click on the link above, which will take you to the website for the course, “Engineering Risk-Benefit Analysis.”  Download the PDF file for “Lecture 9: RPRA 7: Risk Management” and read the entire file.  In the previous subunit, you learned about how to assess the risk of a particular design or a decision.  In this subunit, you will learn about risk management, including important concepts like risk tolerance, safety goals, and risk mitigation.  This reading will take you approximately 2 hours to complete.

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4.3 Decision Analysis   - Web Media: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—1” Link: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—1” (YouTube)

Instructions: To view this video (5:42), click on the link above.  In this video, you will learn about nonprobabilistic decision rules, Min-Max algorithms, and opportunity loss matrix.

• Web Media: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—2” Link: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—2” (YouTube)

Instructions: To view this video (6:56), click on the link above.  In this video, you will learn how to construct a decision tree, calculate expected monetary values, and calculate the expected value of perfect information.

• Web Media: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—3” Link: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—3” (YouTube)

Instructions: To view this video (6:04), click on the link above.  In this video, you will learn about Bayes’ revision of conditional probabilities in decision analysis.

• Web Media: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—4” Link: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—4” (YouTube)

Instructions: To view this video (9:01), click on the link above.  In this video, you will continue to learn how to construct and expand a decision tree.

• Web Media: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—5” Link: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Decision Analysis—5” (YouTube)

Instructions: To view this Lecture 13: DA 1: The Multistage Decision Model video (3:07), click on the link above.  The last video in this series will introduce you to Expected Value of Sample Information (EVSI).

• Reading: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: Link: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 13: DA 1: The Multistage Decision Model” (PDF)

Instructions: Please click on the link above, which will take you to the website for the course, “Engineering Risk-Benefit Analysis.”  Download the PDF file for Lecture 13 and read the entire file.  This reading will illustrate the use of decision trees and Bayes’ theoremin decision analysis.  This reading will take you approximately 2.5 hours to complete.

• Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 16: Decision Analysis” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management:Chapter 16: Decision Analysis” (PDF)

Instructions: Please download the PDF file for “Chapter 16: Decision Analysis” and read the entire file.  This reading will provide a more in-depth discussion on mathematical foundations and applications of decision analysis.  This reading will take you approximately 4 hours to complete.

• Assessment: MIT: Professor Richard de Neufville’s “Engineering System Analysis for Design: Final Exam 2004” Link: MIT: Professor Richard de Neufville’s “Engineering System Analysis for Design: Final Exam 2004” (PDF)

Instructions: Please download the PDF file for “Final Exam 2004” and work on problem 3 of the midterm.  Check your answers against the “Solutions” file on the same webpage.  This reading will take you approximately 1 hour to complete.

• Assessment: The Saylor Foundation’s "Risk Assessment and Decision Analysis" Link: The Saylor Foundation’s "Risk Assessment and Decision Analysis" (PDF)

Instructions: Please complete the linked assignment.  When you are done--or if you are stuck!--consult the tutorials suggested in the assignment.

4.4 Utility Theory   4.4.1 Introduction to Utility   - Web Media: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Stochastic Utility Assessment” Link: YouTube: Production Operations Management (POM) and Supply Chain Management (SCM): “Stochastic Utility Assessment” (YouTube)

Instructions: To view this video (6:04), please click on the link above.  This video will explain how to evaluate utility.

• Reading: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 15: DA 3: The Axioms of Rational Behavior”, “Lecture 16: DA 4: Introduction to Utility,” and “Lecture 16: DA 5: Risk Aversion” Link: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 15: DA 3: The Axioms of Rational Behavior” “Lecture 16: DA 4: Introduction to Utility,” and “Lecture 16: DA 5: Risk Aversion” (PDF)

Instructions: Please click on the link above, which will take you to the website for the course, “Engineering Risk-Benefit Analysis.”  Download the PDF files for “Lecture 15: DA 3: The Axioms of Rational Behavior”, “Lecture 16: DA 4: Introduction to Utility,” and “Lecture 16: DA 5: Risk Aversion,” and read them.  In these readings, you will be introduced to the basic concepts of utility theory.  These readings will take approximately 6 hours to complete.

• Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 18: Value and Utility Functions” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 18: Value and Utility Functions” (PDF)

Instructions: Please download the PDF file for “Chapter 18: Value and Utility Functions” and read the entire file.  It will supplement the information provided in Professor George Apostolakis’s Lecture Notes.  This reading will provide a more in-depth discussion of utility and value functions and take approximately 2 hours to complete.

4.4.2 Multi-Attribute Utility   - Reading: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 17: DA 6: Multiattribute Utility Theory” Link: MIT: Professor George Apostolakis’s Lecture Notes on “Engineering Risk-Benefit Analysis”: “Lecture 17: DA 6: Multiattribute Utility Theory” (PDF)

Instructions: Please click on the link above, which will take you to the website for the course, “Engineering Risk-Benefit Analysis.”  Download the PDF file for “Lecture 17: DA 6: Multiattribute Utility Theory” and read the entire file.  This reading will introduce you to multi-attribute utility.  This reading will take approximately 2 hours to complete.

• Reading: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management: “Chapter 20: Multiattribute Utility” Link: Professor Richard de Neufville’s, Applied Systems Analysis: Engineering Planning and Technology Management:Chapter 20: Multiattribute Utility” (PDF)

Instructions: Please download the PDF file for “Chapter 20: Multiattribute Utility” and read the entire file.  This reading will supplement the information provided in Professor George Apostolakis’s Lecture Notes.  This reading will take approximately 2 hours to complete.

4.5 Real Options   - Reading: MIT: Professor Richard de Neufville’s “Real Options” Link: MIT: Professor Richard de Neufville’s “Real Options” (PDF)

Instructions: Please click on the above link, which will take you to course materials prepared by Professor Richard de Neufville.  Download the PDF file titled “Real Options” and read the entire file.  The slide deck will introduce you to real options analysis, a hot area of research in engineering decisions, leveraging the experience of analyzing options in the financial industry.  This reading will take approximately 2 hours to complete.

• Assessment: MIT: Professor Richard de Neufville’s “Engineering System Analysis For Design: Mid-Semester Quiz 2001” Link: MIT: Professor Richard de Neufville’s “Engineering System Analysis For Design: Mid-Semester Quiz 2001” (PDF)

Instructions: Please download the PDF file for “Mid-Semester Quiz 2001” and work on problems 3 and 4 of the midterm.  Check your answers against the “Solutions” file for Mid-Semester Quiz 2001 on the same webpage.  This assignment will take approximately 2 hours to complete.

• Assessment: The Saylor Foundation’s “Unit 4 Quiz” Link: The Saylor Foundation’s “Unit 4 Quiz” (PDF)

Instructions: Please complete the linked assignment.  When you are done--or if you are stuck!--check your work against The Saylor Foundation’s “Answer Key” (PDF).