OPERATIONS RESEARCH

Department of Mathematics

376 Fretwell Building

704-687-4929

Degree

Interdisciplinary Graduate Minor

The interdisciplinary graduate minor in Operations Research is designed to provide advanced problem solving skills and knowledge in the general areas of operations research and optimization to enable their application to effectively address the present‑day problems of business, management science, engineering and computer science. This program can serve as an effective and focused supplement to existing graduate programs in the participating departments. The required courses are offered by the participating departments of Electrical Engineering, Civil Engineering, Computer Science, Mechanical Engineering, Economics, and Information & Operations Management.

Admission Requirements

Students admitted to graduate degree programs in the participating departments and the M.B.A. program who are in good standing, are eligible for the minor in Operations Research.

Requirements for the Minor

1) Declaration of the minor, preferably by the end of the first semester of graduate study.

2) Formation of a Program Committee: Students who elect to minor in Operations Research will select a participating faculty member as a member of their regular graduate committee. A list of participating faculty will be available from the coordinator of the minor in Operations Research.

3) Fulfill the requirements of a participative degree program and complete OPRS 6101/8101 and one course each from two of the following areas selected with the advice and knowledge of the student's program committee.

Mathematics: OPRS 5111, 5112, 5113, 5114 MATH 5165, 7125, 7177 and topics: reliability theory, queuing models, variational methods.

Computer Science: CSCI 5131, 5150, 6160, 6166

Management Information Systems and Operations Management: MBAD 6121, 6122, 6141

Economics: ECON 4100, 4112

Electrical Engineering: EEGR 6111, 6112, 6115, 6116

Civil Engineering: CEGR 5090, 6181

Students must have a cumulative 3.0 GPA in courses applied to the minor. Course waivers and transfer credit will be considered on an individual basis.

Courses in Operations Research

OPRS 5010. Topics in Decision Mathematics. (2-3) Prerequisite: consent of the department. Topics in decision mathematics selected to supplement regular course offerings in this area of mathematics. May be repeated for additional credit with the approval of the department. Credit for the M.A. degree in mathematics requires approval of the department. (On demand)

OPRS 5111. Linear Programming. (3) Prerequisite: OPRS 3111 and CSCI 1100 or 1201 and 1201L. Mathematical formulation and solution of linear programming problems. Topics include: the simplex method and its variations, sensitivity and parametric analysis, duality, and applications. A project will be required for all graduate students. (On demand)

OPRS 5112. Non-Linear Programming. (3) Prerequisites: CSCI 1100 or 1201 and 1201L, OPRS 3111 and MATH 2241. Basic unconstrained optimization problems, search techniques, some discussion of rates of convergence and an introduction to constrained optimization. Computer implementation and testing of optimization algorithms will be required. A project will be required of all graduate students. (On demand)

OPRS 5113. Game Theory. (3) Prerequisites: OPRS 3111 and one of STAT 2122, MATH/STAT 3122, or OPRS 3113. The theory of zero-sum matrix games, mini-max theorem, optimal strategies, symmetric games, economic models, infinite, separable, polynomial, multi-stage, general-sum and n-person games. A project will be required of all graduate students. (On demand)

OPRS 5114. Dynamic Programming. (3) Prerequisites: CSCI 1100 or 1201 and its lab, OPRS 3111, and one of STAT 2122, MATH/STAT 3122 or OPRS 3113. The identification of dynamic programming problems and their solution in terms of recurrence relations. Elementary path problems, resource allocation, shortest path, traveling salesmen problem, discrete-time optimal control, replacement models and inventory systems. A project will be required of all graduate students. (On demand)

OPRS 6101. Introduction to Operations Research. (3) Prerequisite: STAT 3122. Operations Research approach: modeling, constraints, objective and criterion. The problem of multiple criteria, optimization, model validation. The team approach. Systems design. Examples, or methodology: mathematical programming, optimum seeking, simulation, gaming, heuristic programming. Examples, or applications: theory of inventory, economic ordering under deterministic and stochastic demand. The production smoothing problem, linear and quadratic cost functions. Waiting line problems: single and multiple servers with Poisson input and output. The theory of games for two-person competitive situations. Project management through probabilistic activity networks and deterministic activity network (CPM-PERT). (Fall)

OPRS 7125. Stochastic Processes. (3) Same as MATH 7125.

OPRS 8101. Introduction to Operations Research. (3) See description for OPRS 6101.

OPRS 8125. Stochastic Processes. (3) Same as MATH 7125.