575.608.81 - Optimization Methods for Public Decision Making

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Introduction to linear programming
• Linear programming: standard form and basic assumptions
• Linear programming: geometry
• Linear programming: modeling practice 1
• The simplex method for solving linear programs
• The simplex method extended
• Shadow prices in linear programming
• Linear programming: modeling practice 2
• Introduction to multi-objective linear programming
• The weighting method for multi-objective LP
• Introduction to integer programming
• Integer programming models with binary variables
• Introduction to dynamic programming
• Applications in public sector and environmental policy and management

Course Goals

The goal of this course is to provide a practical familiarity with the application of constrained optimization methods to decision-making in the public sector, with a focus on environmental policy and management. The course aims to provide basic skills in formulating optimization models and in finding and interpreting solutions.  Students will demonstrate and apply skills and knowledge through class discussions, written assignments, and a course project.

Course Learning Outcomes (CLOs)

• Analyze and articulate complex decision problems that arise in environmental engineering, environmental management, public sector resource allocation, and policymaking.
• Formulate basic constrained optimization models for such problems, including the writing of mathematical objective functions and constraints. Models types include linear programs, multi-objective programs, integer and mixed-integer programs, and dynamic programs.
• Apply methodologies for solving optimization problems. Methodologies include the simplex algorithm for linear programming, the weighting method for multi-objective programming, the branch and bound method for integer programming, and a recursive algorithm for dynamic programming, among others.
• Interpret and communicate quantitative solutions, results, and outcomes of the optimization modeling process.

Textbooks

ReVelle, C. S., Whitlach, E. E. & Wright, J. R. (2004). Civil and environmental systems engineering (2nd ed.). New Jersey: Prentice Hall.

ISBN 10: 0130478229
ISBN 13: 9780130478221

Required Software

Linear Programming Solver.  Some of the course work including the course project involves solving mathematical programs using a computer solver. You may wish to use the LP Solver in the Excel Spreadsheet, which typically is a convenient option for students.  Other options for computer LP solvers will be provided during the course, including free solvers that can be used interactively on-line or downloaded at no cost.  Another possibility is to purchase a solver, although it will be possible for you to complete the course requirements using either the Excel Solver or a no-cost option.

Student Coursework Requirements

The amount of time that this course demands will vary, depending on the student and on the module. It is expected that each class module will take approximately 7-9 hours per week to complete, although approximately 3 additional hours per week will be required during the second half of the course to complete the computer assignment and exams.  Here is an approximate breakdown:

• Reading the course notes, listening to audio material, and completing other assigned reading: approximately 3 hours per week
• Participating in the class discussion (Modules 1-12): approximately 1-2 hours per week
• Completing homework problem set assignments (Modules 1-11): approximately 3-4 hours per week
• Completing optimization modeling computer assignment (Modules 7, 9, and 11): approximately 3-5 hours per week
• Midterm Exam (Module 8 only): approximately 2-3 hours
• Critique of published paper (Module 12 only): approximately 3-4 hours
• Final exam (Module 12 only): approximately 2-3 hours

Preparation

Each student is responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are from the course lecture notes and textbook.  Many of the course modules also contain recommended videos that students may wish to watch.  Papers from the literature in applied operations research comprise additional assigned reading, as indicted in the course schedule.

Your grade for the course will be based on your performance in six areas:

1. Participation in class discussions: 20%
2. Homework problem sets: 35%
3. Optimization modeling computer assignment: 20%
4. Critique of published paper: 5%
5. Midterm exam: 10%
6. Final exam: 10%

Important:  Your Assignment submissions, Discussion postings, and submissions of other course material are expected to be on time.  No credit will be given for late submissions, as explained below.  However, exceptions can be made for exceptional situations such as unforeseen travel for work, family emergencies, and medical emergencies including Covid-19.  Please contact the instructor as soon as you know that you will not be able to submit something on time.

1. Participation in Class Discussions (20% of Final Grade Calculation)

Participation in class discussions involves two parts: (1) your initial response to the discussion question; and (2) your replies to the postings of classmates.  The first part is to:

1. Post your initial response to the discussion question by the end of Day 4 for that module week (11:59 PM). There is a 24 hour grace period added to the deadline of 11:59 PM. Postings after the grace period will receive no credit.

In addition to responding to the discussion question yourself, we also want you to interact with the rest of the class.  Therefore, the second part is to:

2. Reply to the postings of (at least) two classmates. Your replies to two classmates must be posted by the end of Day 7 for that module week (11:59 PM). There is a 24 hour grace period added to the deadline of 11:59 PM. Postings after the grace period will receive no credit.

The grade for your initial response to the discussion question will be based on the thoughtfulness, level of detail, and level of critical thinking, insight, and analysis exhibited. The grades for your replies to the postings of classmates also will be based on these same criteria, but in terms of a “value added” aspect.  Do you add new insight to your classmate’s ideas or are you able to extend them in an informative way? Feel free to agree or disagree with your classmates, but please ensure that your postings are civil and constructive.

Justin Williams will monitor class discussions and will respond to some of the student responses as they are posted. In most modules Dr. Williams will post his own response to the discussion question on the last day of the discussion, and may in some cases post a summary of the overall discussion for the class.

Evaluation of your participation in class discussions will be scored as follows.  You will receive a score of 0 to 6 points for your initial response to the discussion question, and scores of 0 to 3 points for each of your replies to another student.  If you respond to the postings of more than two other classmates (which you are encouraged to do), only the two highest scores will be counted.

The maximum of 6 points or 3 points will be awarded for exceptional critical thinking, insight and analysis; exceptional value added aspect.  Fewer points will be awarded for postings that do not fully meet these criteria.  Again, late postings or missing postings will receive no points.

So, your total discussion score for each module will range from 0 to 12 points.  At the end of the course, all 12 of your module discussion scores will be added to determine your cumulative score (out of 144 possible points).

2. Homework problem set assignments (35% of Final Grade Calculation)

Eleven problem sets will be assigned during the course. These problem sets are designed to help you develop skills in formulating mathematical models and in solving problems using the algorithms and other analytical methods covered in the course.

Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the problem statement, assumptions, computations, and conclusions / discussion delineated. All Figures and Tables should be captioned and labeled appropriately. Show your work and clearly indicate you final answer, as appropriate for the problem.

All problem sets are due at the end of Day 7 (11:59 PM) of the module in which the problem set was assigned.  There is a 24 hour grace period added to the deadline of 11:59 PM.  You may submit problem sets, without penalty, during the grace period.  However, no credit will be given for assignments turned in after the grace period has ended.  If you have not finished the problem set when it is due, turn in what you have completed on time for possible partial credit.

Problem set answers will be posted in Canvas soon after the assignment due date. Although you will receive some feedback on your homework along with your score, it will not be practical to provide detailed feedback to every student on every problem. Therefore, students will be expected to compare their answers to the posted answers and to identify any differences. Students should take the initiative to recognize any misunderstandings they have and to ask the instructor questions or request guidance regarding how particular problems can be solved.

Assessment of problem sets: Individual problem sets will be scored relative to a maximum possible score of 20 points. Scores will be based on the completeness and correctness of: (a) your application of a modeling procedure or solution methodology, and (b) your final answer or result. Partial credit may be given, as appropriate. At the end of the course, all 11 of your problem set scores will be added to determine your cumulative score (out of 220 possible points).

3. Optimization modeling computer assignment (20% of Final Grade Calculation)

This course includes an extended optimization modeling / computer assignment that spans five weeks (Modules 7-11).  This assignment supplements the problem sets and is designed to further build your skills in formulating and solving mathematical optimization problems (using a computer solver) in a way that gives you hands-on experience with a real-world problem.  A detailed description of the assignment is available in the Course Information folder.  You should read through the assignment description at the beginning of the course.  You are expected to begin thinking about this assignment prior to Module 7.

The modeling assignment has three deliverable items and is graded out of 100 total points.  A summary of the point allocations and due dates for the deliverable items is shown in the table below.  No credit will be given for submissions received after the 24 hour grace period.  If you have not finished the deliverable item, turn in what you have completed on time for possible partial credit.  Grading of the modeling assignment will be based on the suitability, completeness, and correctness of: (a) your application of the modeling procedure and solution methodology, and (b) your final result, as described in the assignment handout.

When submitting your deliverables, include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. The problem statement, assumptions, computations, results, conclusions, and any discussion must be clearly articulated. All Figures and Tables should be captioned and labeled appropriately. Show your work throughout, as appropriate.

4. Critique of published paper (5% of Final Grade Calculation)

This assignment involves writing a critical review of a paper published in the peer-reviewed literature.  These papers involve applications of mathematical programming to real-world problems in public sector and environmental policy and management.  Students are to choose one of six possible papers to review.  The review is to be based on the optimization modeling process described in Module 3, Part 2, and should be three to four pages long.  The document type that you submit must be either Word or PDF.  Additional details about this assignment are provided in Module 12.

This assignment is due at the end of Day 7 of Module 12 (11:59 PM).  There is a 24 hour grace period added to the deadline of 11:59 PM.  No credit will be given for submissions made after the grace period. If you have not finished the assignment, turn in what you have completed on time for possible partial credit.

Assessment of the critical review paper: This assignment will be graded out of 20 points, based on writing quality, critical insights and evaluations, and the extent to which you have followed the assignment guidelines.

5. Midterm exam (10% of Final Grade Calculation)

The Midterm Exam will be available at the beginning of Module 8.  The Midterm Exam will cover the material in Modules 1 – 6.  In terms of format, the Exam will comprise true/ false, multiple choice, short answer, and problem-solving questions.  Students may use the course notes, textbook, and other material to complete the Exam.  However, students may not consult with other persons regarding exam questions or answers.  All questions or concerns regarding the Exam should be directed toward the course instructor.

6. Final Exam (10% of Final Grade Calculation)

The Final Exam will be available at the beginning of Module 12.  The Final Exam will cover the material in Modules 7 – 11.  In terms of format, the Exam will comprise true/ false, multiple choice, short answer, and problem-solving questions.  Students may use the course notes, textbook, and other material to complete the Exam.  However, students may not consult with other persons regarding exam questions or answers.  All questions or concerns regarding the Exam should be directed toward the course instructor.

Grading Policy

Student assignments are due as indicated above and in the Assignment sections of modules. Justin Williams will post scores within one week following assignment due dates.

I generally do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade.

As explained above, you will receive a point score for each of the five items of the course that are assessed (1 participation in class discussions; 2 homework problem sets; 3 modeling / computer assignment; 4 critique of published paper; and 5 final exam). Your final grade will be based on the weighted average of these five scores using the following weighting:

Graduate students:  Your combined weighted score will be translated into a letter grade, as follows.  Note that grades of C+, C−, D+, D, and D- are not available as final grades for graduate students.

90 -100% = A- / A / A+   (this range may be revised to 87.5% - 100%)

80–89.9% = B- / B / B+  (this range may be revised to 75% - 87.4%)

70–79.9% = C               (this range may be revised to 62.5% - 74.9%)

< 70 % = F                    (this range may be revised to < 62.5%)

Undergraduate students:  Your combined weighted score will be translated into a letter grade, as follows.

90 -100% = A- / A / A+   (this range may be revised to 87.5% - 100%)

80–89.9% = B- / B / B+  (this range may be revised to 75% - 87.4%)

70–79.9% = C- / C / C+  (this range may be revised to 62.5% - 74.9%)

60–69.9% = D               (this range may be revised to 50% - 62.4%)

< 60 % = F                    (this range may be revised to < 50%)

Example grade calculation:  As an example, suppose that a student received the following scores:

The student’s weighted average score and course grade would be:

(0.958 x 0.20) + (0.932 x 0.35) + (0.880 x 0.20) + (0.900 x 0.05) + (0.840 x 0.10) + (0.840 x 0.10) =

0.192 + 0.326 + 0.176 + 0.045 + 0.084 + 0.0800  =  0.903 or 90.3%, which would be awarded an A–.

Course Policies

Note:  As a default, all due dates and times for discussion posts, assignments, and other deliverables appear in the Canvas course Calendar in Eastern Time.  Please take this into account if you live in another time zone. (Note also that Canvas has a feature that allows you to auto-convert Calendar due dates and times to your local time.)

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.