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• Power and Energy Systems

This course is concerned with modeling of decisions and analysis of models to develop a systematic approach to making decisions. This course introduces probability theory as the fundamental mathematical basis for the development of techniques for solving typical problems faced in making engineering decisions in industry and government. The aim of this course is to teach students to think structurally about decision-making problems. Extensive use of case studies gets students involved in real world situations.

1. Nature of engineering decisions; structuring of decisions; role of models; interplay of economics and technical/engineering considerations; decision making under certainty and uncertainty; good decisions vs. good outcomes; tools
2. Resource allocation decision making using the linear programming framework; problem formulation; duality; economic interpretation; sensitivity analysis; interpretation of results
3. Scheduling and assignment decisions using network flow concepts; transshipment problem formulation and solution; application to matching decisions; network optimization; scheduling application
4. Sequential decision making in a dynamic programming framework; nature of dynamic programming approach; problem formulation; solution procedures
5. Probability theory; random variables; probability distributions; expectation; conditional probability; moments; convolution
6. Statistical concepts; data analysis; statistical measures; estimation
7. Application of probabilistic concepts to the modeling of uncertainty in decision amking; modeling of the impacts of uncertainty; application to siting, investment and price volatility problems
8. Decision making under uncertainty; decision trees; value of information; uses of data; sensitivity analysis and statistics

Decision topics include research allocation, logistics, scheduling, sequential decision making, siting of facilities, investment decisions and other problems for decision making under uncertainty.

• Resource allocation decision making using the linear programming framework: problem formulation; basic approach; duality; economic interpretation; sensitivity analysis; interpretation of results
• Scheduling and assignment decisions using network flow concepts: trans-shipment problem formulation and solution; application to matching decisions; network optimization; scheduling applications
• Sequential decision making in a dynamic programming framework: nature of dynamic programming approach; problem formulation; solution procedures; key limitations
• Probability theory: random variables; probability distribution; expectation; conditional probability; moments; convolution
• Statistical concepts: data analysis; statistical measures; estimation
• Application of probabilistic concepts to the modeling of uncertainty in decision making: modeling of the impacts of uncertainty; applications to siting, investment and price volatility problems
• Decision making under uncertainty: decision trees; value of information; uses of data; sensitivity analysis and statistics
• Case Studies

1. Nature of engineering decisions; structuring of decisions; role of models; interplay of economics and technical/engineering considerations; decision making under certainty and uncertainty; good decisions vs. good outcomes; tools
2. Resource allocation decision making using the linear programming framework; problem formulation; duality; economic interpretation; sensitivity analysis; interpretation of results
3. Scheduling and assignment decisions using network flow concepts; transshipment problem formulation and solution; application to matching decisions; network optimization; scheduling application
4. Sequential decision making in a dynamic programming framework; nature of dynamic programming approach; problem formulation; solution procedures
5. Probability theory; random variables; probability distributions; expectation; conditional probability; moments; convolution
6. Statistical concepts; data analysis; statistical measures; estimation
7. Application of probabilistic concepts to the modeling of uncertainty in decision amking; modeling of the impacts of uncertainty; application to siting, investment and price volatility problems
8. Decision making under uncertainty; decision trees; value of information; uses of data; sensitivity analysis and statistics

   Topics:

   Decision topics include research allocation, logistics, scheduling, sequential decision making, siting of facilities, investment decisions and other problems for decision making under uncertainty.
   • Resource allocation decision making using the linear programming framework: problem formulation; basic approach; duality; economic interpretation; sensitivity analysis; interpretation of results
   • Scheduling and assignment decisions using network flow concepts: trans-shipment problem formulation and solution; application to matching decisions; network optimization; scheduling applications
   • Sequential decision making in a dynamic programming framework: nature of dynamic programming approach; problem formulation; solution procedures; key limitations
   • Probability theory: random variables; probability distribution; expectation; conditional probability; moments; convolution
   • Statistical concepts: data analysis; statistical measures; estimation
   • Application of probabilistic concepts to the modeling of uncertainty in decision making: modeling of the impacts of uncertainty; applications to siting, investment and price volatility problems
   • Decision making under uncertainty: decision trees; value of information; uses of data; sensitivity analysis and statistics
   • Case Studies and Presentations

This course is an elective for both electrical and computer engineering majors. The goals are to provide the students with systematic approaches to making decisions, exposes students to the requisite analytical tools and approaches and provides illustrative examples and team projects of case studies for application of these tools and methodologies.

1. After the first six weeks of class, the students will be able to do the following:

1. Perform fundamental resource allocation analysis using linear programming (1, 2, 6)

2. Make scheduling and assignment decisions using network flow concepts (1, 2, 6)

3. Model the decision process in a mathematical programming framework (1, 4, 6)

4. Understand the insights that the duality framework provides and deploy its application to help solve the primal problems making use of duality information (1, 2, 4, 6)

B. After the first nine weeks of class, the students will be able to to do all of the items listed under A above, plus the following:

5. Model problems in matching jobs and people, scheduling and project management as network flow problems and apply the shortest path algorithm to solve resource allocation problems (1, 2, 4, 6)

6. Perform sequential decision making in a dynamic programming environment (1, 2, 4, 6)

7. Use deterministic programming techniques to solve a broad range of deterministic decision making problems (1, 2, 4, 6)

8. Participate in Team Project 1 to showcase the solution of a deterministic decision making problem, preparation of a written report and the presentation of the results to the class (1, 2, 3, 4, 5, 6)

C. After the first 12 weeks of class, the students should be able to do all of the items listed under A and B above, plus the following:

9. Review the concepts of combinations and permutations and the basic axioms and theoems of probability and solve Bayesian analysis problems for relatively complex problems (1, 2, 4, 6)

10. Review specific parametric discrete and continuous probability distribution functions and their application to the representation of uncertainty in realistic models for decision making under uncertainty (1, 2, 6)

11. Perform basic statistical analysis including estimation (1, 2, 6)

12. Apply Monte Carlo simulation to analyze uncertainty representation in situations in which the probability distributions are unknown (1, 2, 4, 6)

13. Apply conditional probability to evaluate the worth of perfect and imperfect information (1, 2, 6)

14. Participate in Team Project 2 to showcase the solution of a decision making problem under uncertainty, preparation of a written report and the presentation of the results to the class to convince others of the soundness of recommended actions (1, 2, 3, 4, 5, 6)

15. Understand the concept of financial derivative, including forward contracts, futures and options and their application to engineering problems (1, 2, 6)

16. Understand the value at risk concept and apply it to study its use for a portfolio of investments (1, 2, 4, 5, 6)