Department of Operations

This course surveys fundamental methods and models in operations research and operations management that incorporate random elements. Topics discussed will include basic results from the theory of stochastic processes, especially Markov chains; an introduction to stochastic dynamic programming; and models in the control of queues and inventories. Prereq: OPRE 425A and OPRE 425B.

This course enhances the ability to use mathematics in advanced studies. In addition to learning such elementary ideas as the difference between closed-form and numerical-method solutions, a systematic approach is used to learn how to read, understand, think about, and do proofs. Specifically, it is shown how all proofs, regardless of subject area, can be explained as a sequence of individual proof techniques. The following mathematical skills are also taught: translating visual images to symbolic form using quantifiers; classifying mathematical objects into groups having similar properties; creating and working with mathematical definitions; unification; generalization. Prereq: Linear Algebra (equivalent of 1 semester undergrad course) and Calculus (equivalent of 3 semesters of undergrad studies) or consent of instructor.

The objective of this course is to enable the student to formulate deterministic (linear, nonlinear, integer and network) models. The simplex algorithm for solving linear programming problems is presented geometrically, algebraically and economically. The role of duality theory is also discussed. Case studies are used to teach the student how to interpret computer output obtained from the simplex algorithm and how to use that output to answer "What happens if..." questions. Recommended preparation: One semester of undergraduate linear algebra or consent of instructor.

Case studies are used to teach the student how to formulate, use computer packages, and prepare managerial reports for solving deterministic (linear, nonlinear, integer, network, and goal programming) problems that arise in business operations as well as project management problems (using PERT/CPM techniques). Conceptual and mathematical ideas of the various methods for solving such problems are presented.

This course presents the theory of linear programming, including the formal development and proofs of (a) the geometry of linear programming problems (convex sets, extreme points and extreme rays), (b) the steps of the simplex algorithm and their relationship to the geometry, and (c) duality theory and its uses in sensitivity and post-optimality analysis. Prereq: OPRE 410 and OPRE 411A or consent of instructor.

This course presents the algorithms and theory for solving nonlinear programming problems. Problems that do not have constraints include: (a) solving nonlinear systems of equations with Newton's method, (b) finding fixed points of functions using the Brouwer and contractive fixed-point theorems, and (c) optimizing nonlinear functions of a finite number of variables using gradient and conjugate-gradient algorithms with line searches. Problems that have constraints include: (a) solving the linear complementarity problems, (b) solving optimization problems with methods of feasible directions that use the Karush-Kuhn-Tucker conditions and also with methods that use penalty functions. Throughout, the role of convexity in establishing convergence of algorithms is explained.Prereq: OPRE 412A or consent of instructor.

The objective of this course is to expose the students to situations from various business disciplines (e.g., Finance, Marketing, Information Systems, Supply Chain Management, etc.) where quantitative models effectively address the decision problems. This course will also integrate these business disciplines. The course will also prepare students for actionlearning projects where quantitative tools may be appropriate. The course will apply tools and techniques learned in MBAC 414. Other quantitative tools will be introduced "just-in-time" in context to particular application area.Prereq: MBAC 414 or QUMM 414.Coreq: MBAC 425 or OPMT 405.

Most of this course is an introduction to game theory; the remainder is a brief introduction to Bayesian analysis of decision problems including decision trees and conjugate pairs of distributions. The game theory portion consists of an axiomatic approach to utility theory, noncooperative solution concepts emphasizing equilibrium points, and cooperative solution concepts. Examples are drawn from economics, marketing, and operations research. Prereq: Linear Algebra and Calculus. Coreq: Linear Programming.

This course introduces the basic tools of probability. Topics include combinatorial analysis, basics of random variables and distributions, and correlation. Emphasis is placed on business applications in production and inventory planning, reliability and maintenance and finance.Prereq: A semester of calculus or consent of instructor.

This course introduces the fundamental concepts of probability theory. Topics include probability spaces and events, conditional probability and Bayes theorem, joint distributionsof random variables, moment generating functions, laws of large numbers and the central limit theorem.Prereq: OPRE 425A or consent of instructor.

This course analyzes probabilistic models of phenomena which evolve over time. Modules include birth-and-death processes (including the Poisson process), renewal theory, renewal-reward and regenerative processes, Markov chains (discrete- and continuous-time), semi-Markov processes, system properties of queueing models, martingales, and Brownian motion. The course frequently explores the queueing theory consequences of general stochastic processes. Prereq: OPRE 425A and OPRE 425B.

Introduction to the theory of convex sets and functions and to the extremes in problems in areas of mathematics where convexity plays a role. Among the topics discussed are basic properties of convex sets (extreme points, facial structure of polytopes), separation theorems, duality and polars, properties of convex functions, minima and maxima of convex functions over convex set, various optimization problems. Offered as MATH 327, MATH 427, and OPRE 427.

This course covers the modeling and analysis of business systems using computer simulation. The focus of the course is the introduction of simulation as a modeling tool with emphasis on understanding the structure of a simulation mode and how to build such models with the help of popular simulation software(s). Some fundamental statistical concepts behind simulation modeling will also be discussed. Coreq: A course in basic statistics (QUMM 414 or OPRE 428A and OPRE 428B) or consent of instructor.

This course covers the statistical design and analysis of simulation models. The topics include random number generation, input data analysis, statistical analysis of simulation outputs, variance reduction techniques, and design of simulation experiments. Prereq: OPRE 432A. Coreq: OPRE 428A and OPRE 428B or consent of instructor.

The objective of this course is to provide the student with the ability to write object-oriented computer code in C++ for solving problems that do not involve complex data structures. Topics include the use of variables and pointers, built-in functions, input and output, selection statements, loops, functions, and classes. Prereq: Programming experience with one of the following programming languages: Pascal, FORTRAN or C, or permission of the instructor.

This project-oriented course uses a variety of software to involve the student in the complete problem-solving process in OR and OM. This process includes problem definition and formulation, data collection, and storage in a database, connecting the database to the solution algorithm, designing and implementing an appropriate user interface, and presenting the final solution. Prereq or Coreq: OPRE 411B or consent of instructor.

The objective of this course is to provide the student with the data structures (arrays, files, linked lists, trees, and so on) and the numerical methods (differentiation, integration, and solving linear equations) needed for implementing algorithms that solve operations research and operations management problems. These topics are illustrated with C++ and object-oriented programming. Emphasis is given to ensuring that the programs are robust and usable by nontechnical people. Prereq: OPRE 435A or consent of instructor.

This course provides an understanding of the principles, basic concepts, and methodology of engineering economics. It develops proficiency with these methods and with the process for making rational decisions regarding situations likely tobe encountered in professional practice.

This course is an introduction to contemporary portfolio management. In addition to introductory material on securities, options and security markets, topics include contemporary equity and debt management models, hedging strategies, program trading, portfolio insurance, arbitrage programs, mergers and acquisitions, international investing and intermarket influences, and other contemporary factors driving stock and bond prices. Prereq: BAFI 402 or equivalent or consent.

This course presents and analyzes a number of efficient algorithms. Problems are selected from such problem domains as sorting, searching, set manipulation, graph algorithms, matrix operations, polynomial manipulation, and fast Fourier transforms. Through specific examples and general techniques, the course covers the design of efficient algorithms as well as the analysis of the efficiency of particular algorithms. Certain important problems for which no efficient algorithms are known (NP-complete problems) are discussed in order to illustrate the intrinsic difficulty which can sometimes preclude efficient algorithmic solutions. Prereq: OPRE 435A, OPRE 435C and OPRE 410.

This course is offered, with permission, to students undertaking reading in a field of special interest.

The course introduces the basic principles of discrete time financial markets. The focal points are the method of no arbitrage asset pricing, its relationship with equilibrium investment strategies of individuals in a market of financial securities, and its applications in valuation of contingent claims. Specific topics include basic utility theory, single and multiple period investment models, complete and incomplete markets, risk neutral probability measures, pricing of European and American stock options, and introduction to bonds and interest rate derivative models. Prereq: OPRE 411A, OPRE 425A, and OPRE 425B.

This course concerns optimization of stochastic models, it emphasizes models of sequential decisions, and it includes some topics in stochastic processes. It includes the formulation of Markov decision processes and their optimization with various algorithms (often called dynamic programming). Other topics include stochastic order relations and other aspects of lattice programming, adaptive control, and stochastic programming. General results are employed to elicit the structure of optimal policies in areas such as inventory, finance, maintenance, and queueing. Prereq: OPRE 411A. Coreq: OPRE 426.

This course provides the ability to recognize, formulate, and solve (or determine how difficult it is to solve) combinatorial optimization problems. Mathematical programming and network/graph-theory problems are used to illustrate the art of problem formulation. The individual components of combinatorial optimization are identified and presented in a unified framework. The two standard search strategies for finding an optimal solution--namely, the greedy approach and the finite-improvement approach--are illustrated with numerous examples. Conditions are presented under which these search strategies provide an optimal solution. Prereq or Coreq: OPRE 410 or consent.

This course provides the ability to use graph theory as a problem-solving tool. The student is taught to recognize, formulate, and solve graph theory problems. Numerous examples from Operations Research, Computer Science, and related areas are used to illustrate the art of problem formulation. Appropriate theory and algorithms are then developed for solving these problems using the two basic search strategies of the greedy algorithm and the finite-improvement algorithms. Prereq: OPRE 515A or consent.

This course is an introduction to optimization problems involving a finite number of alternatives. Applications include problems in network flows (distribution systems, project scheduling, production planning, routing etc.) and integer programming (scheduling, location, sequencing, capital budgeting, etc.). Numerous algorithms and heuristics are presented for solving these problems (shortest path, maximum flow, cutting plane, enumerative and partitioning algorithms). Computational complexity of these algorithms is also emphasized. Prereq: OPRE 411A, OPRE 412A or consent.