Optimization and Quantitative Decision Science

Program Offerings

Offering type

The Certificate Program in Optimization and Quantitative Decision Science (OQDS) is focused on developing quantitative skills for optimal decision-making in complex and uncertain environments. Through this certificate program, students will learn to quantify risk and uncertainty, and to view any complex decision through the lens of mathematical optimization. This outlook will give them a more structured understanding of the decision itself, as they learn to rigorously formulate their constraints, objective functions(s) and the uncertainties involved. It will also lead students to the proper algorithmic tools that are needed to arrive at an optimal decision.

The certificate program may be of interest to students in engineering, the sciences and the liberal arts who are interested in analytical thinking and quantitative reasoning for the purpose of decision-making under uncertainty. Emphasis is placed on rigorous modeling and analysis, taking advantage of the vast flow of data and ubiquitous computing power available today.

The OQDS certificate program complements the certificate program in applied and computational mathematics, and the minors in statistics and machine learning, computer science, and finance.

Goals for Student Learning

The OQDS program requires one core course in optimization, one core course in uncertainty analysis, three elective courses on applications to quantitative decision-making, and a thesis that demonstrates a command of the core disciplines of uncertainty analysis and/or optimization. Some more specific learning goals for the program are the following:

  1. Ability to model any real-world complex decision-making process as a mathematical optimization problem by formulating appropriate decision variables, constraints and objective function.
  2. Ability to quantify uncertainty and risk using the tools of probability theory.
  3. Ability to incorporate uncertainty into formulation of optimization problems with modeling paradigms such as robust optimization, stochastic optimization, chance constraints, etc.
  4. Ability to formulate multistage or dynamic optimization problems that capture the effects of uncertainty changing through time.
  5. Ability to recognize tractable and intractable optimization problems.
  6. Ability to formulate relaxations of intractable optimization problems to compute efficient lower or upper bounds on the optimal value.
  7. Ability to use appropriate optimization software and analyze the output.
  8. Familiarity with basic algorithms in optimization theory and their relative merits.
  9. Ability to go directly from data to optimal decisions, e.g., by learning uncertainty sets or distributions from data as input to robust/stochastic optimization problems.
  10. Ability to design numerical experiments that test the benefits of quantitative decision-making in real-world scenarios.
  11. Ability to formulate the simplest mathematical models that capture the complexities of our societal challenges (e.g., privacy, fairness, diversity, etc.), and to draw policy insights from these models.

Admission to the Program

The OQDS certificate program is open to both B.S.E. and A.B. students. B.S.E. students are required to take math through Math 201 and 202, which will satisfy the math prerequisites of any of the core courses. However, there is flexibility in the choice of core courses, and the math prerequisites depend on the electives that a student chooses. For A.B. students, it is their responsibility to take the necessary prerequisites for their program of study; students are encouraged to take Math 202 (and preferably Math 201) prior to the certificate program's core course requirements.

To be admitted, interested students should email the director of the program at [email protected]. The email should state the student's request to participate in the program, and should include the following information: the student's class year, major, and whether the student has placed out of any course requirements.

Program of Study

The program for each student is worked out by the student and the departmental adviser. The OQDS certificate program does not have a GPA requirement and students may elect to take one requirement on a pass/fail grading basis. Certificate program students may double-count no more than two courses for both their major and the certificate. The program allows double-counting with other certificate programs, but it is the student’s responsibility to check the double-counting constraints of the other certificate program(s) of interest. The program requirements are as follows:

Course Requirements

All students must take five courses from the following three areas:

  1. One core course in optimization
  2. One core course in uncertainty analysis
  3. Three elective courses on applications to quantitative decision-making

Students may choose to take more than one course from category (1) or (2) and count the additional course(s) toward category (3) as long as they take at least one course from category (3).

For the most current course requirements, please refer to the program website.

Independent Work

A senior thesis or project must be completed and submitted to the program director ([email protected]) that demonstrates a command of some portion of the core disciplines of uncertainty analysis and/or optimization. Students in engineering departments that require a one-semester project can typically use a suitably designed project to satisfy the requirement.

Acceptable theses can be on a wide range of topics, but they must demonstrate a command of the core disciplines of the OQDS certificate program, including stochastics and/or optimization. The thesis must demonstrate, in appropriate mathematics, the ability to model a problem and perform analysis that leads to some conclusion or scientific result. A thesis with minimal or no mathematical modeling is not acceptable.

Theses that are not allowed include "soft" topics such as the history of a nation’s economy, and hard-science theses (laboratory-based theses) that do not have a significant modeling or data-analysis component (for example, collecting observations and computing basic statistics is not sufficient).

Certificate of Proficiency

Students who fulfill the requirements of the program receive a certificate of proficiency in Optimization and Quantitative Decision Science upon graduation.

Additional Information

For the most current program requirements, please refer to the program website.


  • Director

    • Amir Ali Ahmadi
  • Executive Committee

    • Matias D. Cattaneo, Oper Res and Financial Eng
    • Elad Hazan, Computer Science
    • Alain L. Kornhauser, Oper Res and Financial Eng
    • Peter J. Ramadge, Electrical & Comp Engineering
    • Clarence W. Rowley, Mechanical & Aerospace Eng
    • Robert J. Vanderbei, Oper Res and Financial Eng

For a full list of faculty members and fellows please visit the department or program website.