625.623.81 - Introduction to Operations Research: Probabilistic Models

Expanded Course Description

Prerequisites: Multivariate calculus and a course in probability and statistics (such as 625.603).

Course Structure

The course materials are divided into modules. The Modules can be accessed by clicking Course Modules on the left 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. All modules run for a period of seven (7) days. Students should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Introduction to Probability Theory
• Conditional Probability
• Markov Chains
• Markov Processes and Birth-Death Processes
• Renewal Theory
• Queueing Theory 
• Scheduling Theory
• Reliability Theory
• Bayesian Networks
• Monte Carlo Simulation

Course Goals

To develop a fundamental understanding of several important probability models in the field of operations research, and to gain experience with the application of these models to real-world problems.

Course Learning Outcomes (CLOs)

• Understand the probability theory that is the foundation of the models
• Derive many fundamental concepts associated with the models.
• Apply the models to real-world applications.

Textbooks

Sheldon Ross, Introduction to Probability Models 10th edition, Academic Press, 2010. Supplemental references will be provided as needed.

ISBN-10: 0123756863

ISBN-13: 978-0-12-375686-2

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website at http://ep.jhu.edu/bookstore.

Required Software

Some homework assignments will require the use of a computer. Facility with a program like MATLAB will be useful. MATLAB can be obtained through the JHU MATLAB TAH (Total Academic Headcount) license, which is free to WSE faculty, staff, and students for use on Hopkins owned machines or personal machines. You can contact software@jhu.edu to request your license file/code.

Student Coursework Requirements

It is expected that each module will take approximately 10–12 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts as well as some outside reading (approximately 2–3 hours per week), listening to and studying the audio annotated slide presentations (approximately 2 hours per week), participating in the online discussion forum (approximately 1 hour per week), taking quizzes (approximately 1 hour every other week), and homework assignments (approximately 4-5 hours per week).

Grading is based on a combination of homework, discussion forum participation, quizzes, and a class project.

All assignments are due in their entirety according to the dates in the Calendar. Late submissions will not be accepted (no exceptions without prior coordination with me). I will endeavor to grade and return to you, as quickly as possible, all materials that you submit.

This course will consist of four basic student requirements:

Homework Assignments

Each student is responsible for carefully reading all assigned material. The majority of readings are from the course text. Supplemental reading is assigned for some topics.

Quantitative problem sets will be assigned weekly. A random subset of them will be graded (see below for criteria). Please include your name on each page of your submission. If you need to insert extra pages please include your name and an extra page number indicator (i.e., extra page x of y). Your writing should be clear and legible – I recommend that you use a black or blue ball point pen. Solutions should be presented in a logical order that is easy to follow. Grading will consist of both checking to see if the assignment is completed and detailed grading of selected problems.

Note: The lowest homework grade will be dropped.

Quantitative homework problems are evaluated by the following grading elements:

• Each part of problem is answered (20%)
• The course content is correctly applied to arrive at the solutions (40%)
• Intermediate derivations and calculations are provided (20%)
• Solution is technically correct and is clearly indicated (20%) Quantitative homework problems are graded as follows:

100–90%—All parts of problem are addressed; The course material is correctly applied to arrive at the solution; All intermediate derivations and calculations are provided; Solution is technically correct and is clearly indicated.

89–80%—All parts of problem are addressed; The course material is correctly applied; Some intermediate derivations and calculations are provided; Solution is technically correct and is indicated.

79–70%—Most parts of problem are addressed; Some course material is not correctly applied; Few intermediate derivations and calculations are provided; Some solutions are not technically correct but are indicated.

<70%—Some parts of the problem are addressed; Some course material is not correctly applied; Intermediate derivations and calculations are not provided; Some answers are incorrect or missing.

Discussion Forums

Online forum participation is an important component of mastering the course material. For most of the course modules, topics will be posted for discussion by all students. In general, each topic will require a thoughtful response and not simply a regurgitation of what was covered in the associated module. In addition, there will be opportunities to discuss the lesson content during the weekly office hours.

Posting a response to the discussion question is part one of your grade for participation in the discussion forums (Timeliness).

Part two of your grade for discussion forum participation is your interaction (i.e., responding to classmate postings with thoughtful responses) with at least two classmates (Critical Thinking). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.

I will monitor class discussions and will respond to some of the comments as they are posted. Participation in the discussion forums is evaluated by the following grading elements:

• Timeliness (50%)
• Critical Thinking (50%) Participation is graded as follows:

100–90—Timeliness [regularly participates; all required postings; early in discussion; throughout the discussion]; Critical Thinking [rich in content; full of thoughts, insight, and analysis].

89–80—Timeliness [frequently participates; all required postings; some not in time for others to read and respond]; Critical Thinking [substantial information; thought, insight, and analysis has taken place].

79–70—Timeliness [infrequently participates; all required postings; most at the last minute without allowing for response time]; Critical Thinking [generally competent; information is thin and commonplace].

<70—Timeliness [rarely participates; some, or all required postings missing]; Critical Thinking [rudimentary and superficial; no analysis or insight is displayed].

Quizzes

There will be bi-weekly quizzes in the course. Quizzes may include both short-answer questions and quantitative problems.

Short answer questions will be evaluated based on the correctness of the responses. Quantitative problems are evaluated by the following grading elements:

• Each part of problem is answered (20%)
• The course content is correctly applied to arrive at the solutions (40%)
• Intermediate derivations and calculations are provided (20%)
• Solution is technically correct and is clearly indicated (20%) Quantitative quiz problems are graded as follows:

100–90—All parts of problem are addressed; The course material is correctly applied to arrive at the solution; All intermediate derivations and calculations are provided; Solution is technically correct and is clearly indicated.

89–80—All parts of problem are addressed; The course material is correctly applied; Some intermediate derivations and calculations are provided; Solution is technically correct and is indicated.

79–70—Most parts of problem are addressed; Some course material is not correctly applied; Few intermediate derivations and calculations are provided; Some solutions are not technically correct but are indicated.

<70–-Some parts of the problem are addressed; Some course material is not correctly applied; Intermediate derivations and calculations are not provided; Some answers are incorrect or missing.

Class Project

As a final project, each student will identify a real-world application related to the models studied in the course and write a report describing the application, the models applied, and the insight provided by the models into the behavior of the applications. In addition, each student will produce a short video about his or her project, and will critique project videos submitted by other students. More details are provided in the project description.

The project is evaluated by the following grading elements:

• A project proposal for studying the modeling of a real-world application, submitted at least four weeks before the project report is due.
• A project report describing the application, models, and results.
• A video summarizing the project to be viewed by fellow course mates.
• Critiques of videos submitted by other students in the course.

The project is graded as follows:

100–90—Project proposal well written, focuses on significant application, provides clear description of the application, models, and project goals; Final report well-prepared, demonstrates that student understanding of application and models is rich in content, thought, insight, and analysis, reflects extensive research; Project video well organized, engaging, and informative regarding motivation and results; Critiques reflect thoughtful viewing of the videos, describe personal insights gained, provide balanced, constructive feedback.

89–80 — Project proposal well written, focuses on significant application, provides clear description of the application, models, and goals; Final report provides sufficient details to demonstrate that student understanding of the application and models is substantial in content, thought, insight, and analysis, reflects adequate research; Project video well organized and informative regarding motivation and results; Critiques reflect thoughtful viewing of the videos, provide balanced, constructive feedback.

79–70 —Project proposal provides adequate description of the application and models; Final report results are thin, demonstrate student understanding of application and models generally competent, reflects minimal research; Project video provides sufficient information to understand problem and results; Critiques demonstrate videos were viewed, provide some useful feedback.

<70—Project proposal provides weak description of application, models, and project goals; Final report results are thin, demonstrate that student understanding of problem and models is poor, reflect little to no research. Project video lacks clarify regarding problem and results; Critiques suggest cursory viewing of videos, no useful feedback provided.

Grading Policy

Student assignments are due in their entirety according to the dates in the Calendar and Assignments items in the corresponding modules. I will post grades one week after assignment due dates.

Homework, discussion forum participation, quizzes, and the class project will be graded on a scale from 0 to

100. Final grades will be determined by the following weighting:

All parts of the course are mandatory. A student cannot get a grade of B- or better without contributing to the online discussions and completing the quizzes. Students who do not contribute to at least 60% of the online discussions or turn in 60% of the quizzes will have 10% automatically deducted from their overall grade. The final grade will be translated into a letter ranging from A+ to F. Here is a grading curve for the overall course score:

100–97 = A+

96.9–93 = A

92.9–90 = A−

89.9–87 = B+

86.9–83 = B

82.9–80 = B−

79.9–70 = C

<70 = F

It is possible that the grading curve for the overall course score will be relaxed, but it won’t be made tougher.

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.