Introduction

The Ph.D. program in Management Science is designed to prepare students for research and teaching related to the application of mathematical tools in decision making. The curriculum is set up with two main objectives.

The first goal is to provide a thorough knowledge of fundamental Management Science/Operations Research mathematical models and their uses. This is accomplished through coursework provided directly by the Management Science Program.

The second objective is to develop the student's ability to carry out original research. This is achieved through participation in seminars, joint research with faculty members, and the student's own Ph.D. dissertation. The research may be either of a theoretical or an applied nature. In the latter case, the student can apply Management Science techniques in a chosen field such as, finance, transportation/business logistics, health care, forestry, or computer science.

Admission requirements

To be considered for admission, an applicant must have a bachelor's degree from an accredited four year college or university. Candidates must have a strong mathematical background or equivalent, such as the completion of at least two years of college calculus and proficiency in a computer language. In addition to the Graduate School requirements, the Ph.D. program requires three recommendation forms/letters. Candidates should complete the aptitude portion of the GMAT or GRE.

Degree requirements

A student's program of study is individually tailored to fit prior background as well as present goals. The Management Science Committee must approve individual student curricula. Students may enter the Ph.D. program either with or without a master's degree, and must accumulate 49 semester hours of coursework (not including master's thesis hours or Ph.D. dissertation hours) taken for graduate credit, of which at least 24 hours must be completed at the University of Tennessee. The courses listed below form a typical program for a Ph.D. candidate without prior graduate work.

Course requirements

Required examinations

Qualifying Examination -  All Ph.D. students must take a qualifying examination (on the course material from Management Science 531 and Management Science 532) at the beginning of the second year.  However, Ph.D. students who have earned a Masters degree at the University of Tennessee Management Science Program are exempt from this requirement.

Comprehensive Examination - A Management Science Comprehensive Examination is normally after 2 years of study. The subject matter will be dealing with 600-level coursework.  Ph.D. comprehensive examinations will be based on four 600-level courses, two of which must be from the Management Science 600-level courses. The student is also expected to be able to integrate such material beyond artificial course content boundaries and to extend knowledge beyond his/her prior exposure.

Upon completion of the comprehensive examination requirement, he or she will be admitted to the candidacy, and thus he or she will be referred to as Ph.D. candidate.

Ph.D. dissertations

Once the student has determined an area for dissertation research, he or she forms a dissertation committee, which must include at least two members of the Management Science faculty. The committee will conduct a preliminary examination to provide a critical review of the student's proposed research and to assess the student's ability to complete the research. The student prepares for the preliminary examination by providing the committee with a written proposal which outlines the topic and proposed direction of the research. The student is required to present an oral defense of the proposed research to the dissertation committee.

The student must also complete 24 semester hours of Management Science 600: Doctoral Research and Dissertation, through which he  or she is expected to make a significant contribution to the field. A final oral examination is conducted over the dissertation and such other segments of the program that the dissertation committee deems appropriate.

Description of graduate courses

531  Mathematical Programming (3) Linear programming solutions procedures including duality and sensitivity, and parametric analysis. linear-fractional, piecewise-linear, separable and integer programming, transportation linear programs. Prerequisite (s): Fundamentals of matrix algebra and differential calculus; proficiency in a computer language.

532 Stochastic Models in Management Science (3) Discrete-time Markov chains, Poisson processes Continuous-time Markov Chains, Renewal Theory and Queueing Theory. Prerequisite (s): Statistics 563 and Mathematical analysis course or permission of instructor.

533 Computational Mathematical Programming (3) Computational aspects of mathematical programming models, in particular for large systems. Prerequisite (s): Management Science 531 and proficiency in computer language.

534 Management Science Methods in Business (3) Application of methods from Management Science 531, 532, and 533 to real world problems in business or industry.

551 Leveraging Information Through Descriptive and Prescriptive Modeling (3) Concepts and tools for emulating business operations (descriptive modeling) and for determining optimal operational or tactical strategies (prescriptive modeling).  Visualization, optimization and simulation concepts, reinforced through hands-on experience with technologies:  geographic information systems (GIS), spreadsheet-based models, simulation packages, and supply chain optimization software. 

593 Management Science Problems (1-6) Directed study on subject of mutual interest.  Repeatability:  May be repeated.  Maximum 9 hours.

631 Integer Programming (3) Theoretical and computational aspects of linear programming with integer variables, branch and bound, cutting plane, and group theoretic algorithms. Prerequisite (s): Management Science 531 or equivalent.

651 Nonlinear Optimization (3) Kuhn-tucker theory in nonlinear programming, solution procedures for constrained and unconstrained non-linear programs, search techniques, quadratic programming, duality and sensitivity analysis (Same as Industrial Engineering 602.) Prerequisite: Management Science 531 or equivalent and proficiency in computer language.

681 Special Topics (3) Prerequisite: Management Science 531, Management Science 532 and consent of instructor. Topic may be one or more of Vehicle Routing, Scheduling, Production/Operations Management, Interior Methods, and others. May be repeated. Maximum 9 hours.

691-2 Management Science Seminar (1-1) Subjects selected from current management science literature.