ORF 411

Operations and Information Engineering

Professor Warren B. Powell and Dr. Hugo Simao

ORF 411 serves as the capstone course for the Department of Operations Research and Financial Engineering, and as such, helps to define the teaching mission of ORFE at the undergraduate level

This course could easily have several names: Dynamic Resource Management, Information and Decision Engineering, or Stochastic Systems Analysis would be equally appropriate. The students in this course at Princeton have already had courses in statistics, probability and linear programming.

Major themes of the course

First half - Resource management

Second half - Information as an active resource

Course lectures (new!)


Major themes of the course

In its current form, the course focuses on the following themes:


First half - Resource management

The first half of the course develops skills in the modeling and solution of fundamental resource management problems, including

The theme of "resource allocation" makes it possible to illustrate these ideas using a variety of applications of current importance. Today these include energy systems, health services, finance, human resource planning and supply chain management. But the material in the course is easily adapted to other applications.


Second half - Information as an active resource

Most of this material is presented in the context of information as a passive resource, which is the classical model of information as an exogenous process. In the second half of the course, students learn that they can control information (information as an active resource). This theme is developed with the following topics:

Guest speakers from industry are used to highlight challenges in the real world. Recent speakers have included the CEO of PSE&G, the project lead at IBM on a human resource allocation model, and the head of the operations research group at UPS who is responsible for process change using information technology and modeling. During these presentations, students prepare brief summaries of the problems the speaker is presenting by defining the state variable (the information being used), the decisions being made, exogenous information, and goals/objectives.

Lectures (from fall, 2013)

Each lecture is a pdf of a powerpoint presentation (let me know if you would like the original powerpoint files, and I will make these available), which serves as the book for this course.

The course focuses on basic building-block problems that arise in a wide range of resource allocation problem. In the process, we emphasize the modeling of information, transitioning from deterministic models, to stochastic models (information is a purely exogenous process), and finishing with the second half of the course which focuses on information as an active (endogenously controllable) resource.


Introduction - Resource allocation arises in a wide variety of settings. This lecture provides a few examples.

What is a resource? - There are six classes of resources: three active classes (physical, financial and informational) and three passive classes (time, energy and "targets").

Deterministic resource allocation problems

The budgeting problem - Basic problem of allocating resources over time with deterministic forecasts.

Deterministic inventory problems - Students learn how to optimize an infinite horizon problem by minimizing average cost per time period, producing the classic EOQ formula.

Stochastic resource allocation (single resource type)

The newsvendor problem - First introduction to decisions under uncertainty

Modeling stochastic, dynamic problems - Students learn the five core components of any stochastic, dynamic system: states, actions, exogenous information, the transition function and the objective function. Students are taught to model problems before finding a policy.

The four classes of policies - There appear to be four fundamental classes of policies: policy function approximations (PFAs), cost function approximations (CFAs), policies based on value function approximations (VFAs), and lookahead policies.

Modeling storage processes (two lectures) - This set of lectures describes four classes of "storage" problems of increasing complexity.

Substitutable resources (linear programming review)

Substitutable resources I - Students are assumed to have a background in linear programming. We use the basic "transportation problem" to revisit the simplex method where we emphasize graphical methods, while still making the link to the linear algebra of linear programming.

Substitutable resources II - Extending the first lecture, we show how to use the basis to understand the economics of substitutable resources through an understanding of the basis.

Demand as a resource

Demand management - Demand is a resource too. We use a popular example from airline yield management to illustrate booking profiles, which are optimized using a simple stochastic gradient algorithm (carefully illustrated).

Midterm review

Midterm review

The Orange Juice Game - Introduction to the team competition known as the OJ game. The spreadsheet-based handbook is here. The OJ game is a major competition - students have to fill in a spreadsheet with 600 cells. Click here for an example.

Information as an active resource

What is information? - We contrast common concepts of data, information and knowledge, and illutrate five classes of information.

Optimal learning I - Concepts and heuristic policies - Click here for more information on optimal learning. This lecture introduces the basic idea of actively collecting information for the purpose of learning.

Optimal learning II - The knowledge gradient - The knowledge gradient is basically a derivative, where we collecting information that offers the highest marginal value.

The Princeton beer game - This is a highly streamlined version of the classic beer game. This is best done in a class with continuous tables joining students.

Beer game analysis

The two agent newsvendor problem I - This is a nice exercise in the manipulation of information. Students use a simple two-player game to learn how to manage roles of field agent (high cost of underage) and central agent (balanced attitude toward underage and overage) through careful misinformation.

The two agent newsvendor problem II - Spreadsheet for summarizing results is available here.

Information exchange and IPO pricing - Based on the summer internship of an undergraduate, this lecture develops the concept of optimal lying.