Optimization Methods in Business Analytics

Instructor:   James B. Orlin



15.053 main page (Athena)

Lectures '18

Student projects

Student reviews

OCW website for 15.053 ('13)


Applied Math Programming (book)

This website is for MIT students who are considering whether or not to take 15.053, Optimization Methods in Business Analytics.   It provides an overview of 15.053 beyond what students can find in the subject description and course reviews.   For additional information, see the OCW website for 15.053 in 2013. 

15.053 is an introduction to optimization methods and models.  The course title includes " Business Analytics" in order to emphasize the subject's connection to the 15-2 major and minor in business analytics.  In addition to providing applications to business, 15.053 relates optimization to "analytics" broadly construed.  


Some companies that rely heavily on business analytics

15.053 includes applications to many domains including:  machine learning and statistics (e.g., optimal estimation and classification), sports analytics (e.g., optimal batting orders, as mentioned in the article in Poets and Quants about former 15.053 student Austin Filiere, who was drafted by the Chicago Cubs), finance (e.g., optimal portfolio selection), operations (e.g., optimal inventory control and production planning), marketing (e.g., optimal selection of advertising media), and more (e.g., optimal assignment of MIT freshmen to dormitories).   As one of the students wrote in his or her subject evaluation, "This class is very applicable to all majors, which is great!"  Another wrote " One of the best parts about [Professor Orlin's] lecture style is constantly related everything we learn to practical application."   (Here are other student comments from the 2017 subject evaluations.)

Analytics and model-based thinking

INFORMS, the professional society for Operations Research and Business Analytics, defines Analytics as "the scientific process of transforming data into insights for making better decisions."

A fundamental methodology used in analytics is mathematical modeling.    Model-based thinking is the thought processes involved in creating mathematical models for problems in practice and in using the models to develop insights for making better decisions.

In 15.053, we help students to develop model-based thinking so that they can create effective models as well as insightful analyses.   To paraphrase George Box, "All models are wrong, but if the models are developed using sound principles, many of these models will be quite useful."

Subject content.

15.053 first introduces students to the optimization paradigm:  optimizing a function of decision variables subject to constraints on the decision variables.   We focus on three classes of optimization models, (1) linear optimization, (2) integer optimization, and (3) nonlinear optimization.  For each of these three classes of optimization models, we use algebraic modeling languages to create the models.  The models are then solved using  free state-of-the-art software.   In addition, we discuss approaches for improving models and for carrying out useful analyses even in situation in which we know that the model is not correct.  15.053 also presents "greedy algorithms" and "local search algorithms", which are general purpose optimization approaches that can help to solve a wide range of problems in practice. 

A linear program.


Here is a list of lectures for 15.053 in 2018.


The project in 15.053


15.053 aims to teach students methods for modeling and solving optimization problems.  In order to bring these concepts to life, students prepare group projects to model a real world optimization problem.  The student teams will select an actual situation and use the concepts from class to define the problem, build an optimization model, and solve it.  Here are examples of projects from previous years.