Masters in Operations Research
|Major Code: 8074||Degree Awarded: Master of Science|
|Age Restriction: N||Admission status: graduate, online graduate main campus, Extended Studies|
|Delivery Mode/s: classroom, online|
|Admission Materials: none||Location/s: main campus, Aberdeen, Virtual Site|
Operations research is a scientific approach to analyzing problems and making decisions. It uses mathematics and mathematical and computational modeling to forecast the implications of various choices and identify the best alternatives.
Operations research techniques are applied to a broad range of problems in both the public and private sectors. These problems often involve designing systems to operate in the most effective way. Many problems deal with the allocation of scarce human resources, money, materials, equipment or facilities. Applications include staff scheduling, vehicle routing, warehouse location, product distribution, quality control, traffic light phasing, police patrolling, preventive maintenance scheduling, economic forecasting, design of experiments, power plant fuel allocation, stock portfolio optimization, cost-effective environmental protection, inventory control and university course scheduling.
Operations research is interdisciplinary and draws heavily from the mathematics program. It also uses courses from computer science, systems engineering and other engineering programs.
The Master of Science in Operations Research offers concentrations that emphasize those areas of application most in demand in today's job market. Graduates have skills that include probability and statistics, deterministic and stochastic models, optimization methods, computation and simulation, decision analysis and the ability to effectively communicate with clients and managers. In addition, graduates have a breadth of knowledge that allows them to work in teams, interacting with people who bring different expertise to a problem. All areas involve expertise with standard computer software packages.
An applicant for the master's program in operations research should have an undergraduate major in a science or engineering discipline that requires a significant amount of mathematics. Business majors with strong quantitative backgrounds are also encouraged to apply. A proficiency in mathematics covering topics in calculus, probability theory, statistics, linear algebra, and computer literacy must be demonstrated by testing or suitable coursework.
General admission requirements and the process for applying are presented in the
The master of science degree can be pursued with either a thesis or nonthesis option; each requires 30 credit hours. Under the thesis option, up to six credit hours of thesis may be granted in place of electives toward the required 30 credit hours and an oral defense is required. The nonthesis option requires a final program examination. Courses taken to satisfy admission prerequisites cannot be counted toward the degree requirements.
The program's curriculum is designed to provide breadth with some flexibility to accommodate the diversity of backgrounds typically found in an operations research program. Greater flexibility is provided for the elective courses beyond the core. A student has the choice of developing greater depth in one area of specialization, aiming at eventual research in that area, or continuing to develop breadth across more than one area. By choosing courses in a related field of application, students can prepare for careers in specialty areas such as management science, actuarial science or economic modeling in addition to conventional areas of operations research.
Each student will complete a program plan that satisfies the requirements listed below, subject to approval of the department head. Substitutions are sometimes permitted.
MTH 5411 Mathematical Statistics 1Credit Hours: 3Covers discrete and continuous random variables, generating and moment generating functions, multivariate distributions, covariance and correlation, sums of independent random variables, conditional expectation, Central Limit Theorem, Markov and Chebyshev inequalities and the Law of Large Numbers.
ORP 5001 Deterministic Operations Research ModelsCredit Hours: 3An applied treatment of modeling, analysis and solution of deterministic operations research problems. Includes model formulation, linear programming, network flow and transportation problems and algorithms, integer programming and dynamic programming.
ORP 5002 Stochastic Operations Research ModelsCredit Hours: 3An applied treatment of modeling, analysis and solution of probabilistic operations research problems. Topics chosen from decision analysis, game theory, inventory models, Markov chains, queuing theory, simulation, forecasting models.
ORP 5003 Operations Research PracticeCredit Hours: 3Includes OR methodology, how an OR analyst interacts with clients, and preparation and presentation of oral reports. Students form teams to analyze real cases where each student gets an opportunity to be a team leader and present oral reports.
ORP 5010 Mathematical ProgrammingCredit Hours: 3Surveys popular optimization techniques. Topics chosen from linear, integer, nonlinear, dynamic and network flow programming; combinatorial graph algorithms.Requirement(s):Prerequisite course or instructor approval
MTH 5051 Applied Discrete MathematicsCredit Hours: 3Logic fundamentals, induction, recursion, combinatorial mathematics, discrete probability, graph theory fundamentals, trees, connectivity and traversability. Applications from several fields of science and engineering, including computer science, operations research, and computer and electrical engineering.
MTH 5102 Linear AlgebraCredit Hours: 3Linear algebra, systems of linear equations and Gauss elimination method; inverses, rank and determinants; vector spaces; linear transformations, linear functional and dual spaces; eigenvalues, eigenvectors; symmetric, Hermitian and normal transformations; and quadratic forms.
MTH 5401 Applied Statistical AnalysisCredit Hours: 3Covers statistical distributions, statistical tests for data, least squares and regression, estimations, tests of hypotheses, analysis of variance, planning and designing research experiments, randomized blocks, Latin and Graeco-Latin squares and data reduction, analysis using ANOVA (analysis of variance) and other methods.
MTH 5412 Mathematical Statistics 2Credit Hours: 3Includes maximum likelihood and Bayes estimators, confidence intervals, testing hypotheses, uniformly most powerful tests, nonparametric methods (chi-square and Kolmogorov-Smirnov goodness-of-fit tests) and regression analysis.
ORP 5020 Theory of Stochastic ProcessesCredit Hours: 3Introduces stochastic models, discrete- and continuous-time stochastic processes, point and counting processes, Poisson counting process, compound Poisson processes, nonstationary Poisson processes, renewal theory, regenerative processes and Markov chains.Requirement(s):Prerequisite course or instructor approval
ORP 5021 Queuing TheoryCredit Hours: 3Includes queuing processes; imbedded and continuous time parameter processes; Markov, semi-Markov and semi-regenerative processes; single-server and multiserver queues; processes of servicing unreliable machines and computer applications; and controlled stochastic models.Requirement(s):Prerequisite course or instructor approval
MTH 5301 Numerical AnalysisCredit Hours: 3Includes Gaussian elimination and solution of linear systems of equations, root finding methods, systems of nonlinear equations, interpolation, numerical integration, initial value problems for ODEs and fast Fourier transform.
MTH 5320 Neural NetworksCredit Hours: 3Introduces architectures, algorithms and applications. Includes single and multilayer perceptrons, counterpropagation, Kohonen self-organization, adaptive resonance theory, neocognition, probabilistic neural networks and Boltzmann machines with and without learning, recurrent neural networks.
ORP 5050 Discrete System SimulationCredit Hours: 3Covers the principles of building and using a discrete event simulation; construction and statistical testing of random variate generators; statistical analysis and validation of results; design of simulation projects; and variance reduction methods.Requirement(s):Instructor approval or prerequisite course
Three courses in areas of interest to the student as approved in the student's program plan.
At least one course plus up to six credit hours for a thesis. The thesis should be an in-depth study of some topic and/or problem in operations research, subject to the approval of the thesis committee.