Program Overview

The Operations Research (OR) Program at the University of Delaware is designed to provide the student with a strong foundation in the theories and methods of economics, engineering, mathematics and statistics in order to analyze problems from a systems approach. Valid applications (case studies) bridge the gap between pure theory and methods. The rigorous core courses provide the student with methodological tools in recognizing, analyzing and solving problems. The program strives to educate w ell-rounded individuals who are able to compete in the market places of academia as well as public institutions and private enterprises.

Programs of Study

The Operations Research Program at the University of Delaware is an interdisciplinary graduate program, drawing its faculty and students from the following: College of Agriculture and Natural Resources (Bioresources Engineering, Food and Resource Economics ), College of Business and Economics (Business Administration and Economics), College of Engineering (Civil Engineering and Electrical Engineering), College of Arts and Science (Computer and Information S ciences, Mathematical Sciences and Statistics), and the College of Marine Studies and Urban Affairs. Programs of study are tailored to student and faculty interests and emphasize research. Course work includes a core in operations research, optimization, statistics, an d applied probability, in addition to supporting courses related to areas of application.

The student is encouraged to select an adviser among the relevant faculty as soon as possible. The director of the program will assist in the search. After the first semester but no later than during the second semester, the student should have an advis er for course selection and thesis/dissertation purposes. Changes in the adviser are possible with special justification, but all concerned including the Director of the Program must agree. The program encourages co-advisers for students if it is in the ir interest.

Master's programs allow students to take either the thesis or non-thesis option. The thesis option requires a research-oriented thesis (six credits) and course work about equally divided between OR-related courses, and course offerings in the area of application, for a total of 33 credit hours. A thesis committee consisting of at least four members, two of which are OR faculty, should be formed after the first year of study to advise the candidate and administer the final oral exam. The non-thesis option requires an internship and a related research report in lieu of the thesis. Two semesters of seminar attendance is required for all masters students. Students are also encouraged to pursue internship oppurtunities with local companies during regular semesters besides summer session.

The Ph.D. program is intended to prepare well-qualified students for management, research or teaching careers in industry, government or academia. Dissertations for the Ph.D. degree are a blend of empirical and theoretical research combining OR methodolo gies with application from a particular discipline. A dissertation committee consisting of at least five members, three of which are OR faculty, should be formed after the second year of study to advise the candidate and administer the comprehensive and final oral exam. The degree requires at least 51 credits hours with nine credits fulfilling the dissertation requirement and the remainder equally divided among OR-related courses and course offerings from the area of application. Ph.D. candidates must take the ORES 800 level course sequence and register for four semesters of seminar attendance. Comprehensive exams are administered in three areas (OR and two other areas of concentration) after a majority of the course work has been successfully complet ed.

Core Courses

ORES 803 Operations Research Survey III (1 credit hour)

PhD students are required to present a survey paper as part of the Operations Research Seminar Series. The paper should be on a topic not covered in the student's chosen course work or thesis requirement and of mutual interest to the student and faculty member willing to serve as a special problem advisor. This requirement entails surveying the relevant literature, summarizing the current state of research and providing a proposal for further research.

Topics suitable to survey are to be chosen from a list provided by faculty interested in serving as special problem advisors. The list will be compiled each year by the director of the program from interested faculty, mailed to OR students and posted at the Operations Research office.

MATH 630 Probability Theory and Applications (3 credit hours)
An introduction to probability theory to serve as a background for further work in statistics or stochastic processes. Course contents: sample spaces and the axioms of probability, discrete sample spaces having equally likely events, conditional probabi lity and independence, random variables and describing their distributions, the classical discrete and continuous random variables, mathematical expectation and the moments of a distribution, the distribution of a function of a random variable, Chebyshev' s inequality, the law of large numbers, the central limit theorem.

MATH 631 Introduction to Stochastic Processes (3 credit hours)

Classical stochastic processes with emphasis on their properties, which do not involve measure theory. Course contents: Markov chains in discrete and in continuous time with examples from random walk, birth and death processes, branching processes and q ueuing theory. Renewal and Markov renewal processes. Basic notions of Brownian motion and second-order processes. Prerequisite: MATH 630.

MATH 694 Non-Linear Mathematical Optimization (3 credit hours)

Introduction to the various branches of non-linear optimization and their applications. Most topics have evolved since World War II in the quest for solutions to contemporary problems in economics, engineering and Operations Research. Likely topics incl ude: basic concepts of calculus and linear programming review, Kuhn-Tucker Theory, geometric programming, dynamic programming, reductions to linear form, piecewise linearization of non-linear functionals, search methods, and calculus of variations.
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Requirements for Degree

Master's Degree

• All Master's degree students must register for two semesters of OR seminars and attend at least 80% of the seminars in any semester.
• A minimum of 33 (recommended 36) credits is required for the Master of Science degree. About 40 percent of the program is comprised of Operations Research core courses; another 40 percent involves course work in the student's subject area. The rema ining 20 percent of the program is devoted to the preparation of the thesis.
• One year in residence (i.e. course taking) and six thesis credits are required.

OR core required courses (in addition to those required by the student's chosen unit of concentration):

Highly recommended Courses:

Microeconomic Theory
For those with no economics background	ECON 801
Advanced	ECON 811

Mathematical Sciences
Introduction to Stochastic Processes	MATH 631

Recommended for students terminating graduate studies in OR:

1. Non-thesis option: Of the standard 6 credit hours toward the Masters Thesis, 3 credit hours could be used for an elective applications course or internship. The second 3 credit hours would consist of project work associated with the internship expanding on the applications course. If an internship cannot be arranged, ideally an applications course and 3 credit hours of project work can substitute for the 6 credit hours of Master's Thesis.

DOCTORAL DEGREE

• All Ph.D. candidates must register for four semesters of OR seminars and attend 80% of the seminars in any semester.
• Work toward the doctoral degree is divided about equally among the supporting mathematical sciences, the student's subject area, and the dissertation.
• Two years in residence (i.e. course taking) and a minimum of nine dissertation or research credits are required.

Required courses:

One of the following, as appropriate:

For students with minimal (Masters OR) level of statistics and some economics:

Econometric Theory ECON 822

For students with two to four undergraduate courses in statistics and some economics:

Seminar in Econometrics ECON 823 or 824

For students with several graduate level statistics courses and no economics:

Microeconomic Theory ECON 801 or 811

PROCEDURE FOR THE DOCTORAL PRELIMINARY QUALIFYING EXAMINATION

The preliminary qualifying exam consists of 2 to 3 written exams and an oral dissertation proposal defense after all or most of the course work has been completed. The written portion is composed of 1 to 2 exams given by the "home" department (see curren t Graduate Handbook for details and consult with your advisor or the Graduate coordinator from that unit). The following procedure applies only to the Operations Research preliminary exam, not the other two qualifiers given by the home department.

The Operations Research Preliminary Exam is administered once a year in August/September and covers the following courses: ORES 601, 602, 801, 802 , MATH 630, 631, 694 and Econometrics.

Procedure:

• The student seeking to be formally examined notifies his/her advisor in April that he/she wishes to take qualifying examinations the following fall.
• When the student notifies the advisor, he/she must submit a list of courses taken and to be taken before the examination is to be given with the names of the instructors.
• Within two weeks of notification, the student will be provided: (1) a copy of the Ph.D. reading list, i.e., a list of readings upon which the qualifying examinations are to be based and (2) the list of topics to be covered by the qualifying examinat ion for both the required and optional areas of study.
• The advisor informs the chair of the OR Curriculum Committee about the student's declaration to stand for examination. The chair, in turn, contacts the examiners for the areas to be covered by the exam. The examiners should be the instructors of th e courses taken by the students. If any initially selected examiners are unavailable or unwilling to serve, then a substitute should be chosen jointly by the advisor and the chair of the Curriculum Committee.
• The selected examiners shall write questions for the student. In so doing, the examiner shall stipulate the conditions of the examination regarding the length, content, number of questions and nature of the examination, i.e., open or closed book.
• The examination questions should be forwarded to the chair of the Curriculum Committee by June 30. A copy of the examination should be placed in the OR office.
• The student shall take the examination in the first week of September, and it should be administered by either his/her advisor and/or the chair of the Curriculum Committee.
• The examinations should be completed according to the conditions of the examination and then returned to the OR office. The chair of the Curriculum Committee will then distribute the examinations to the appropriate examiners.
• The examinations should be read and graded by the examiners within two weeks after the examination is returned by the student. (It is the prerogative of any OR program member to read and comment upon the examinations.) The examination and the grade s should be transmitted to the chair of the OR program who will inform the advisor of the student's performance.
• After the chair informs and consults with the advisor, the student will be informed of his/her performance by the advisor. If a passing grade is not rendered, then the student shall meet with his/her advisor so that remedial action can be undertaken .

Exit Interview

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Operations Research Program
232 Townsend Hall
University of Delaware
Newark, DE 19717