Virginia Tech® home

Ph.D. in Operations Research

Operations Research (OR) is a scientific, mathematical modeling-based approach to problem solving and management. OR is used for the efficient design and management of systems, usually seeking to determine an optimal or effective utilization and allocation of scarce resources. OR is widely used in many diverse application areas, e.g., the design and management of service and manufacturing systems, supply chain management, humanitarian logistics, healthcare and public policy.  The curriculum provides a methodological foundation, and is flexible, allowing students to focus on methodological research or applications.  More information about OR can be obtained from the Institute for Operations Research and the Management Sciences (INFORMS), the main professional society for OR, and also from the Institute of Industrial & Systems Engineers (IISE), another professional society that includes OR.

Plan of Study Requirements

A student's plan of study must include a minimum of 90 credits of coursework and graduate research.  At least 39 credits of coursework (of post BS, taken for grade) is required, including the 21 credits for the OR core courses, and at least one primary and one secondary emphasis areas.  Coursework should include at least 24 ISE credits, with at least 9 of those credits at the 6000-level. The plan of study should be designed in consultation with the student’s PhD committee. (All courses listed below are 3 credits, unless specified otherwise.)

Number Title Credits
ISE 5024 ISE Seminar 0
ISE 5405 Optimization I 3
ISE 5406 Optimization II 3
ISE 5414 Random Processes 3
ISE 5424 Simulation 3
MATH 4225 Elementary Real Analysis I 3
ISE 5034 or
STAT 5104
Probability & Distribution Theory 3
STAT 5114 Statistical Inference 3

OR Emphasis Areas

Below are some pre-defined emphasis areas.  At least 4 classes are required for a primary emphasis area, and at least 2 classes for a secondary emphasis.  Some emphasis areas have required classes. Because OR works well with methodologies traditionally from other disciplines (e.g., computer science, statistics, mathematics), and can be applied to application areas beyond those represented in the following emphasis areas, students can develop customized emphasis areas, subject to the approval of their Ph.D. committee.

Number Title Credits
ISE 6414 Integer Programming, Required 3
ISE 6404 Graph Theory and Network Flows 3
ISE 6514 Advanced Topics in Math Programming 3
ISE 6424 Dynamic Programming 3
CS 5114 Theory of Algorithms 3
MATH 4226 or MATH 5226 Elementary Real Analysis II 3
MATH 5454 Graph Theory 3
MATH 5464 Combinatorics 3

CS = Computer Science; MATH = Mathematics

Number Title Credits
ISE 5464 Queueing Theory 3
ISE 6444 Inventory and Operations Management 3
ISE 6474 Reliability Theory 3
ISE 6494 Advanced Simulation 3
ISE 6504 Markov Renewal and Related Processes 3
ISE 6xxx Random Processes II 3
ISE 6xxx Healthcare OR 3
STAT 5204
Experimental Design & Analysis I
STAT 5404 Nonparametric Statistics 3
STAT 5434 Markov Chain & Renewal Theory 3
STAT 5444 Bayesian Statistic
STAT 5504 Multivariate Statistical Methods
STAT 5544 Spatial Statistics 3
STAT 5574 Response Surface Design and Analysis I 3
STAT 6105 Measure and Probability 3
STAT 6404 Advanced Topics in Nonparametric Statistics 3
STAT 6424 Multivariate Statistical Analysis and Analytics 3
STAT 6504 Experimental Design II 3
STAT 6574 Response Surface Design and Analysis II 3
STAT 6984 Response Surface Methods & Computer Experiments 3

STAT = Statistics

Number Title Credits
ISE 6XXX Healthcare and public Policy OR 3
BMVS 6554 Advanced Epidemiology 2
HNFE 5724 Epidemiology 3
MATH 5415 Continuous Models in Biological Applications 3
MATH 5416
Continuous Models in Biological Applications 3
PAPA 5014 Concepts and Approaches in Public Administration 3
PAPA 6214 Public Policy Processes and Analytical Approaches 3
PAPA 6224 Design, Implementation, and Evaluation of Public Policy Programs 3
STAT 5674 Methods in Biostatistics 3
STS 5444 Issues in Bioethics 3

BMVS = Biomedical and Veterinary Sciences; HNFE = Human Nutrition, Foods, and Exercise; MATH = Mathematics, PAPA = Public Administration/Public Affairs, STAT = Statistics, STS = Science and Technology Studies

Number Title Credits
ISE 4424 Logistics Engineering 3
ISE 4434 Supply Chain and Operations Engineering 3
ISE 5024 Production System Analysis 3
ISE 5204 Manufacturing Systems Engineering 3
ISE 5244 Facilities Planning and Material Handling 3
ISE 5264 Modeling and Analysis of Semiconductor Manufacturing 3
ISE 5454 Production Planning and Control 3
ISE 6444 Inventory and Operations Management 3
ISE 6XXX Logistics 3
ISE 6434 Scheduling and Sequencing Theory 3
ISE 6474 Reliability Theory 3

Supporting Faculty Members