# OPRE (OPRE)

**OPRE 207. Statistics for Business and Management Science I. 3 Units.**

Organizing and summarizing data. Mean, variance, moments. Elementary probability, conditional probability. Commonly encountered distributions including binomial. Poisson, uniform, exponential, normal distributions. Central limit theorem. Sample quantities, empirical distributions. Reference distributions (chi-square, z-, t-, F-distributions). Point and interval estimation: hypothesis tests.
Prereq: MATH 121 or MATH 125.

**OPRE 301. Operations Research and Supply Chain Management. 3 Units.**

Operations research (OR) or management science, is the discipline of applying advanced quantitative methods to make better decisions. Techniques covered include linear programming, queuing models and simulation. The second part of the course focuses on how OR tools are used in managing various aspects of Supply Chain. Topics covered include demand forecasting, design of distribution systems, capacity planning, and inventory management. Recommended preparation: one semester of statistics or consent of instructor.
Prereq: STAT 207 or OPRE 207.

**OPRE 332. Computer Simulation. 3 Units.**

Computer Simulation is a process of designing and creating a computerized model that mimics an existing or proposed system so as to better understand the behavior of the system. Many studies have shown that in Industry, simulation is most frequently used Operations Research tool due to its ability to deal with complex systems. The first half of this course is designed to give students a basic idea of simulation methodology with the aid of population simulation software. The emphasis of the course is in simulating business processes, however, the versatility of the technique will be demonstrated with applications from finance, health care, etc. The second half of the 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.
Offered as OPRE 332, OPRE 432, and MSOR 432.
Prereq: OPRE 301.

**OPRE 402. Stochastic Models with Applications. 1.5 Unit.**

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.
Offered as OPRE 402 and MSOR 402.
Prereq: OPRE 433 and not available to MSM-Operations Research & Supply Chain students.

**OPRE 411. Optimization Modeling. 3 Units.**

The first half of the course provides a practical coverage of linear programming, a special type of mathematical model. The art of formulating linear programs is taught through the use of systematic model-building techniques. The simplex algorithm for solving these models is developed from several points of view: geometric, conceptual, algebraic, and economic. The role and uses of duality theory are also presented. Students learn to obtain and interpret a solution from a computer package and how to use the associated output to answer "What-happens-if..." questions that arise in post-optimality analysis. Specific topics include: problem formulation, geometric and conceptual solution procedures, the simplex algorithm (phase 1 and phase 2), obtaining and interpreting computer output, duality theory, and sensitivity analysis. The second half of this course provide a practical approach to formulating and solving combinatorial optimization problems in the areas of networks, dynamic programming, project management (CPM), integer programming, and nonlinear programming. The art of formulating problems, understanding what is involved in solving them, and obtained and interpreting the solution from a computer package are shown. A comparison with formulating and solving linear programming problems is provided as a way to understand the advantages and disadvantages of some of these problems and solutions procedures. Recommended preparation: Knowledge of Excel, one semester each of undergraduate linear algebra and undergraduate calculus (derivatives); or consent of instructor.
Offered as MSOR 411 and OPRE 411.

**OPRE 427. Convexity and Optimization. 3 Units.**

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.
Prereq: MATH 223 or consent of instructor.

**OPRE 432. Computer Simulation. 3 Units.**

Computer Simulation is a process of designing and creating a computerized model that mimics an existing or proposed system so as to better understand the behavior of the system. Many studies have shown that in Industry, simulation is most frequently used Operations Research tool due to its ability to deal with complex systems. The first half of this course is designed to give students a basic idea of simulation methodology with the aid of population simulation software. The emphasis of the course is in simulating business processes, however, the versatility of the technique will be demonstrated with applications from finance, health care, etc. The second half of the 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.
Offered as OPRE 332, OPRE 432, and MSOR 432.
Prereq: Enrollment in a program other than MSM Operations Research.

**OPRE 433. Foundations of Probability and Statistics. 3 Units.**

Data of many kinds are typically available in practice, but the challenge is to use those data to make effective professional decisions. This software-intensive course begins with useful descriptions of data and the probability theory foundation on which statistics rests. It continues to statistics, including the central limit theorem, which explains why data often appear to be normally distributed, and the Palm-Khintchine theorem which explains why data often appear to have a Poisson distribution. The remainder of the course focuses on regression and forecasting, including detecting and overcoming some of the deadly sins of regression, and the surprising flexibility of regression models. Recommended preparation: One semester of undergraduate calculus or consent of instructor.
Offered as MSOR 433, OPRE 433 and MSBA 433.

**OPRE 435B. Integrated Problem Solving in OR and SC. 1.5 Unit.**

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.
Offered as OPRE 435B and MSOR 435B
Prereq or Coreq: OPRE 411 or requisites not met permission.

**OPRE 454. Analysis of Algorithms. 3 Units.**

This course covers fundamental topics in algorithm design and analysis in depth. Amortized analysis, NP-completeness and reductions, dynamic programming, advanced graph algorithms, string algorithms, geometric algorithms, local search heuristics.
Offered as EECS 454 and OPRE 454.
Prereq: OPRE 435A and OPRE 435C.

**OPRE 490. Independent Study in Operations Research. 1 - 15 Units.**

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

**OPRE 501. Special Problems and Topics. 1 - 36 Units.**

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