MIT Subject Listing for 15.053
Introduces optimization methods with a focus on modeling, solution techniques, and analysis. Covers linear programming, network optimization, integer programming, nonlinear programming, and heuristics. Applications to logistics, manufacturing, statistics, machine learning, transportation, game theory, marketing, project management, and finance. Includes projects in which student teams solve optimization problems of practical interest.
J. Orlin,T. Magnanti
Course Content and Goals
Optimization is an important subfield of operations research and business analytics (see below). The field of optimization is often referred to as "prescriptive analytics." Its purpose is to determine the best possible solutions for an organization. This contrasts with "predictive analytics" whose purpose is to identify the likelihood of future outcomes based on historical data.
Optimization models have been of great value within business, engineering, as well as science. In 15.053, students will see applications of optimization modeling in logistics, manufacturing, statistics, machine learning, transportation, game theory, marketing, project management, and finance. Optimization models also form the basis of neural net technologies as applied to machine learning.
In 15.053, students learn how to express optimization models conceptually (on paper) and then translate these models to a computer using either spreadsheet software (such as Excel) or an algebraic modeling language (such as JuMP, which is written in the Julia language.) After translating the model so that it can be understood by a computer, students can use state-of-the-art solvers such as Gurobi to obtain an optimal solution.
Students learn several types of optimization modeling, including linear programming, network optimization, integer programming, nonlinear programming, and dynamic programming. Students also learn basic solution methodologies for these optimization models.
There are two group projects for 15.053. These projects vary from year to year.
Our goal in 15.053 is to help students develop an "optimization mindset". We want students to look out at the world and see optimization problems everywhere, and to recognize when these problems can be modeled, analyzed, and solved.
The Game of Fiver
The game of Fiver (also known as Lights Out) begins with a grid of circles, green on one side and red on the other. Starting with all green, each move flips a circle and its four adjacent circles. The goal is to minimize the number of flips needed to turn all of the circles red.
James Orlin is the E. Pennell Brooks (1917) Professor in Management and a Professor of Operations Research at the MIT Sloan School of Management.
Thomas Magnanti is an Institute Professor and a Professor of Operations Research at the MIT Sloan School of Management.