Syllabus

15.053 is an undergraduate subject in the theory and practice of optimization. We will consider optimization models with applications to transportation, logistics, manufacturing, computer science, E-business, project management, finance as well as several other domains. This subject will survey some of the applications of optimization as well as heuristics, and we will present algorithms and theory for linear programming, dynamic programming, integer programming, and non-linear programming.

One way of summarizing a subject is a lecture-by-lecture description of the subject, or a description of the methodologies presented in the subject. We do list a lecture-by-lecture description, but first we describe several cross cutting themes.

1. Optimization is everywhere. We will present applications of optimization to a wide range of fields including operations management, finance, marketing, engineering, and strategic planning, as well as operations of a university and personal decision-making. We will also present different models and conceptual frameworks for optimization including linear programming, integer programming, non-linear programming, dynamic programming, and heuristics.
2. Algorithms. As is traditional at MIT, we learn the inner workings of algorithms. It is not sufficient to say that Excel contains an algorithm that solves linear programs. We need to know how the algorithm works. Learning algorithms has several important implications. First of all, some problems are easily solved, and others are intrinsically intractable. Learning the algorithms helps to distinguish one from the other. Secondly, understanding the behavior of an algorithm can be an important first step in interpreting the output of the algorithm and applying it to gain insight about the optimization problem. Thirdly, it is only by understanding the inner working of algorithms that we are in a position to design our own algorithms, or modify those that exist.
3. The goal of the models is insight, not numbers. We build models not as a mirror of reality, but only as a partial reflection of reality. The nature of modeling in Management Science and Operations Research is that we approximate reality in order to provide support for decision-making. One useful way that models support decision-making is that they permit managers to explore a range of scenarios in order to help in determining which decisions are robust under a number of assumptions. In a similar manner, one can analyze models to determine which numbers are the most important, and which numbers can be changed with little impact on the decision. A major theoretical tool for aiding insight is sensitivity analysis and its variations. One caveat is the impact of E-business on modeling. In many E-business applications, one needs to solve thousands of models over a short period of time. In this case, there is not time for human assessment of model outputs, and we need to design models that are robust and trustworthy.
   
4. Performance guarantees. One of the hallmarks of optimization (and mathematical programming) is that it provides both an optimal solution, and also provides a succinct certificate (guarantee) of optimality. Even when a problem is intrinsically difficult, optimization-based techniques may provide some guarantees. A particularly useful guarantee is a maximum distance from optimality. Two major theoretical tools for developing bounds on the distance from optimality are "linear programming duality" and "branch and bound."
5. Search techniques and heuristics. It is often the case that problems are too intractable to be solved optimally or even nearly optimally. In such cases, one needs to develop strategies to develop a good solution. Such techniques are often referred to as heuristics. We will discuss a variety of heuristics approaches including neighborhood search, simulated annealing, tabu search, and genetic algorithms.
   

Attendance in 15.053 is not required, but it is strongly encouraged. In past semesters, students attending class regularly found the subject material much easier to learn, and performed better on the midterms and exams. Regardless of whether a student is able to attend a class, he or she is fully responsible for the material covered in the class, some of which may be covered in a different manner than in the book.

Students attending class should do their best to arrive on time. A student arriving late may disrupt the flow of the class, and (depending on his or her attitude) may signal a lack of professional respect. Similarly, students should not leave class early, except when unavoidable. A student who has a conflict at the beginning of a class should E-mail Professor Orlin in advance of the class. Similarly, a student who has a conflict at the end of the class should alert Professor Orlin of his or her need to leave early.

Office hours for the TA and for the Professor will be arranged early in the semester and put on the web site.

Recitations will be held on a weekly basis, and will meet in the classroom from 2:30 to 4:00 on Fridays. Recitations are optional, and are not intended for the presentation of new material.

On the Wednesday prior to each recitation, we will hand out a list of problems to be covered during the recitation, and any other topic to be covered in recitation. In general, the recitation problems will be similar to the ones covered on the assignment for that week, although there may be some additional topics covered as well, for example, the use of Excel Solver plus Ad Ins.

Students may work in groups, but the write-up of the homework should be individual responsibility. Students should not share written answers, and it is not permitted for one student to copy (or nearly copy) the answer of someone else.

A student receiving substantial help from a classmate should list this help on the first page of his or her homework set. (There is no reduction in scores or points for receiving help.)

The MIT Sloan School is committed to creating an environment in which every individual can work and study in a culture of mutual respect. When making individual decisions we must keep in mind the interests of the many other stakeholders.

Consistent with the general goal of mutual respect, faculty, students, and staff are reminded to demonstrate:

• On-time arrival to classes and presentations, with uninterrupted attendance for the duration
• On-time initiation and termination of classes and presentations
• Maintenance of a professional atmosphere. This includes, but is not limited to:
  
  • Using respectful comments and humor
  • Employing appropriate manners and decorum, especially when food and drinks are served
  • Utilizing computers and technology suitably (e.g., silencing wireless devices, no web-browsing or emailing)
  • Refraining from distracting or disrespectful activities (e.g., avoiding side conversations and games)
• Fulfillment of engagements with recruiters and speakers, or timely notification of cancellation
• Courtesy towards all guests, hosts and participants at any activity associated with the Sloan community
• Observance of the most conservative standards when one is unsure about which norms apply

These points offer specific illustrative examples to encourage broader reflection of each individual's impact on the Sloan community.

Upholding these expectations and the standards upon which they are based is a shared right and responsibility for all faculty, students and staff at the Sloan School. As a learning and professional community, we seek and deserve no less.