Ph.D. Program

Frequently Asked Questions

What Ph.D. degree options are available in the ISE Department?

  • Ph.D. in Industrial and Systems Engineering. 

What are the main areas of concentration for Ph.D. study?

  • Optimization
  • Nonlinear optimization
  • Discrete optimization and integer programming
  • Convex and conic optimization
  • Numerical method of optimization and software
  • Stochastic and robust optimization
  • Optimization method for learning
  • Applied Probability and Statistics
  • Stochastic processes
  • Queueing networks
  • Simulation
  • Applied Operations Research
  • Supply chain
  • Financial optimization
  • Smart grid and applications in energy
  • Scheduling
  • Healthcare systems

How long will it take to complete a Ph.D. degree in the ISE Department?

  • The Ph.D. program requires a minimum of 48 credit hours if entering with a master’s degree.
  • If entering with a bachelor’s degree, a student must complete at least 72 credit hours. 
  • The usual length of time is about four to six years.  A dissertation is required for the Ph.D. program.

Could I apply directly to the Ph.D. program without having a master’s degree first?

  • Yes; you will need to complete 72 credits of course work. 


The Ph.D. program offered by the Department of ISE involves rigorous study of the Industrial Engineering and Operations Research methodology and practice.  The program is among the highest ranked in the U.S. with world-renowned faculty and a large and diverse group of Ph.D. students.

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Students in the program work with the faculty in a wide range of research fields including

  • optimization modeling and methodology
  • high-performance computing and numerical methods
  • machine learning
  • stochastic processes and queueing systems
  • supply chain modeling and management
  • healthcare systems
  • financial applications

The faculty are actively involved with professional societies such as the

  • Institute of Electrical and Electronics Engineers (IEEE)
  • Institute of Industrial Engineers (IIE)
  • Institute for Operations Research and Management Sciences (INFORMS)
  • Mathematical Optimization Society (MOS)
  • Society for Industrial and Applied Mathematics

and students and faculty regularly publish in journals such as

  • Annals of Operations Research
  • Computational Management Science
  • IEEE Transactions on the Smart Grid
  • Journal of Machine Learning Research
  • Journal of Optimization Theory and Applications
  • Mathematical Models of Operations Research
  • Mathematical Programming
  • Naval Research Logistics
  • Proceedings of the Power Engineering Society
  • Production and Operations Management
  • SIAM Journal on Scientific Computing
  • SIAM Journal on Optimization

and attend various conferences including

  • IIE Annual Meeting
  • INFORMS Annual Meeting
  • Integer Programming and Combinatorial Optimization (IPCO)
  • International Conference on Machine Learning (ICML)
  • International Conference on Stochastic Programming (ICSP)
  • International Symposium on Mathematical Programming (ISMP)
  • Manufacturing and Service Operations Management (MSOM)
  • Modeling and Optimization: Theory and Applications (MOPTA)
  • Neural Information Processing Systems (NIPS)
  • SIAM Conference on Optimization (SIOPT)
  • Workshop in Mixed Integer Programming (MIP)

In fact, the highly-regarded MOPTA conference is held annually at Lehigh University, bringing to campus some of the top scientists in the world working on theoretical and applied aspects of mathematical optimization.

A majority of the Ph.D. students in the program participate in Summer internship programs at top companies and research labs throughout the U.S.  Recent internships have been acquired at institutions such as

  • American Airlines
  • Argonne National Laboratories
  • Bosch Research
  • ExxonMobil Research
  • IBM Research
  • Goldman Sachs
  • SAS
  • Siemens
  • Yahoo! Laboratories

These internships offer students the ability to expand their knowledge and develop contacts both in academia and industry, leading to the receipt of highly competitive job offers after graduation.  Recent graduates from the program have accepted post-doctoral research and faculty positions in academic institutions such as

  • Georgia Institute of Technology
  • Indian Institute of Technology, Bombay
  • Massachusetts Institute of Technology (MIT)
  • Shanghai Jiao Tong University
  • Technical University of Eindhoven
  • University of California, Berkeley
  • University of Tennessee

and have accepted jobs at companies and research institutions such as

  • Air Products
  • Amazon
  • American Airlines
  • Argonne National Laboratories
  • Bosch Research
  • Capital Blue Cross
  • Ernst & Young
  • Goldman Sachs
  • Hospital for Special Surgery
  • Humana
  • IBM Research
  • JP Morgan Chase
  • Marriott
  • Oracle
  • Pivotal
  • Sabre
  • SAS
  • Siemens
  • Turkish Airlines
  • United Airlines

The department benefits from being affiliated with several well-known research establishments including the Laboratory for Computational Optimization Research at Lehigh (COR@L), the Center for Value Chain Research (CVCR), and Lehigh's new multi-disciplinary research cluster on Integrated Networks for Electricity.  The department has been recognized for its academic excellence and ties to industry as a 4-time finalist for the INFORMS-UPS George D. Smith Prize.

The Lehigh University INFORMS Student Chapter, housed in the Department of ISE, is extremely active, recently being recognized by INFORMS by a Student Chapter Award at the Cum Laude level.  The Chapter organizes a weekly seminar series, coffee hours and lunches with visiting scholars, career development workshops, and social events.

General requirements

This section outlines the general requirements for completing a doctor of philosophy (Ph.D.) degree in the Department of Industrial and Systems Engineering (ISE). A summary of the steps is provided below, followed by more details in the subsequent subsections.

  1. Complete a set of common core courses.
  2. Declare a field of concentration within ISE and complete the Ph.D. qualifying exam.
  3. Pass a formal review conducted by the faculty following completion of the first two requirements.
  4. Complete the additional course requirements associated with the field of concentration.
  5. Form a dissertation committee, propose a dissertation topic, and successfully defend this proposal to the committee.
  6. Successfully complete a general exam conducted by the dissertation committee consisting of written and oral parts.
  7. Successfully pass all annual progress reviews.
  8. Complete and successfully defend a doctoral dissertation.
  9. Satisfy any additional Ph.D. degree requirements specified by the P.C. Rossin College of Engineering and Applied Science (refer to Lehigh University Catalog).

I. Course Requirements

The core course requirements for all first-year students are as follows.

Fall Semester 1st year

Course Title

ISE 401

Convex Analysis (3)

ISE 406

Introduction to Mathematical Optimization (3)

ISE 429 

Stochastic Models and Applications (3)

Spring Semester 1st year

Course Title

ISE 417

Nonlinear Optimization (3)

ISE 418

Discrete Optimization (3)

ISE 4xx

Models and Applications of Operations Research (3)

Over the second year additional courses are taken as follows:

Fall Semester 2nd year

Course Title

ISE 407

Numerical Methods of Scientific Computing

Spring Semester 2nd year

Course Title


Course title to be announced

The overall Ph.D. course requirements include:

  • The core courses described above
  • Four additional 400-level courses with two from the list of their chosen field of concentration (described in Section II) and at least two from other fields’ lists.

Students are also encouraged to take relevant 400-level courses outside of the ISE department and these courses can stand in place of some of the four additional courses, with approval of Ph.D. director or Ph.D. advisor. The above minimal Ph.D. course requirements total 12 courses (36 credits). For students who enter Lehigh with a Master’s degree, completion of the degree requires an additional 12 credits (via courses or dissertation), totaling 48 credit hours. Those entering without a Master’s degree need to complete an additional 36 credits, totaling 72 credit hours. All course selections are subject to approval by the student’s academic advisor in consultation with the student’s dissertation committee.

For core courses in ISE, any student who has already completed an equivalent course at another institution may fulfill the course requirement by successfully passing an examination by the instructor of the course in question. Note, however, that this does not reduce the required number of credit hours (except if such a course would qualify as transfer credit per Lehigh’s transfer credit rules)  and the student will not receive formal credit for the course. In exceptional cases a student may, with the permission of the Ph.D. director, replace any core course with another course if sufficient justification is presented.

In the case when a student lacks the background necessary for one or more of the first year core courses, this student may be given permission by the Ph.D. director to take a preparatory course offered by ISE or the Department of Mathematics. In such a case the qualifying exam of the student may be delayed until after the core courses are completed.

II. Declaration of Fields and Course Requirements

At the end of the first year of study, each student must declare a field of concentration, which will be one of the following three:


  • Nonlinear optimization
  • Discrete optimization and integer programming
  • Convex and conic optimization
  • Numerical methods of optimization and software
  • Stochastic and robust optimization
  • Optimization methods for learning

Applied Probability and Statistics

  • Stochastic models
  • Queueing systems and networks
  • Simulation

Applied Operations Research

  • Supply chain management
  • Financial optimization
  • Smart grids and applications in energy
  • Scheduling
  • Healthcare systems

Core course requirements associated with each of these fields of study are discussed in Section V below. Additional custom-designed programs in applied or theoretical fields are also permissible with approval.

III. Qualifying Exam

Immediately following final exams at the end of the first year, all Ph.D. students must take the qualifying exam (unless permission to delay the exam has been granted, as described in this document). The purpose of the exam is to

  1. Test the student’s knowledge and strength in basic topics of Industrial and System Engineering.
  2. Assess the student’s ability to conduct original research.
  3. Assess the student’s ability to communicate, both orally and in writing.

Each student’s exam will be conducted by a panel consisting of three faculty members. Each member of the student’s panel will pose a research question to be studied during the two-week examination period. After the two-week period, the student will present a written report and oral presentation to the panelists, who will each assess the student’s performance using an evaluation form that will be made available to the student ahead of time on request. The results of the exam are either pass or fail. These results are only used as input to the annual review, described below.

NOTE: A student entering the Ph.D. program without a Master’s degree may petition to delay their qualifying exam until the end of their third semester of study. This does not exempt them from a first-year review (see below). The timing of the qualifying exam for part-time students will be determined based on a customized program of study developed in consultation with the Ph.D. director

IV. Annual Reviews

First Year

At the end of the first year, every Ph.D. student will undergo a review consisting of:

  1. Evaluation of grades.
  2. Evaluation of qualifier exam results (if applicable).
  3. Evaluation of research project carried out during the first year.
  4. Other input as deemed relevant by the faculty.

The results of this first-year review are determined by vote of the faculty and may be either pass, conditional pass, or fail. A pass indicates that the student may continue into the second year of the program and should start to form a dissertation committee. A conditional pass indicates that the student may continue, subject to certain stated conditions being fulfilled. These conditions may include, but are not limited to, re-taking the qualifying exam, writing a research report, taking additional coursework, or achieving a minimum GPA during subsequent semesters. Failure of the first-year review will result in a student’s dismissal from the Ph.D. program, after which the student may petition to transfer to a master degree program in order to receive a degree before leaving the department.

In cases in which a student has arranged to delay the scheduling of the qualifying exam, is required to retake it, or has conditionally passed a prior review, a supplemental review will take place directly following any off-cycle offering of the qualifying exam or completion of a required conditional action. When the student feels that the conditional actions have been completed, he or she should notify the Ph.D. director and request a supplemental review. The Ph.D. director may also call for the supplemental review to take place as deemed appropriate. For part-time students whose exam date extends beyond the second year, annual reviews will be conducted by the faculty each year until the qualifying exam is passed successfully.

Subsequent Years

Following successful completion of the qualifying exam and successful fulfillment of conditions imposed as a result of the subsequent review, each student is required to identify a dissertation advisor, identify a dissertation topic, and form a dissertation committee to guide their further study.  In each subsequent year, the student will be required to submit an annual report of progress to be reviewed by the committee who will pass on to the Ph.D. director a brief summary of the committee’s assessment of the student’s progress.

It is expected that most students will present their dissertation proposal to their dissertation committee at its first meeting, which will also serve as the second annual review.  In case when the dissertation proposal is not ready, a presentation of the student’s ongoing research should be scheduled with the dissertation committee. This presentation will serve as the second annual review. In subsequent years the dissertation committee is expected to convene about once a year – for the proposal defense, for the general exam and, finally, for the dissertation defense. If any of these are delayed a meeting with the dissertation committee should be conducted to update the committee on the student’s progress and reasons for delay.

Addendum A: Acceptable Courses in Fields of Concentration

This list of courses is annually updated as approved by the Ph.D. Curriculum Committee.


CORE (Minimum of 2 courses from the following list)

  • CSE 441 Advanced Algorithms
  • ISE 411 Graphs and Network Flows
  • ISE 414 Heuristic Methods in Combinatorial Optimization
  • ISE 416 Dynamic Programming
  • ISE 444 Optimization Methods in Machine Learning
  • ISE 495 Conic Optimization
  • Math 405 Partial Differential Equations I

Applied Probability and Statistics

CORE (Minimum of 2 courses from the following list):

  • ECO 415 Econometrics I
  • ECO 416 Econometrics II
  • ECO 461 Forecasting
  • ISE 404 Simulation
  • ISE 409 Time Series Analysis
  • ISE 410 Design of Experiments
  • ISE 439 Queueing Systems
  • Math 312 Statistical Computing and Applications
  • Math 334 Mathematical Statistics
  • Math 435 Functional Analysis I
  • Math 461 Topics in Mathematical Statistics
  • Math 462 Modern Nonparametric Methods in Statistics
  • Math 464 Advanced Stochastic Processes
  • Math 467 Financial Calculus I
  • Math 468 Financial Calculus II

Applied Operations Research

CORE (Minimum of 2 courses from the following list):

  • CSE 411 Advanced Programming Techniques
  • CSE 432 Object-Oriented Software Engineering
  • CSE 441 Advanced Algorithms ISE 404 Simulation
  • ISE 409 Time Series Analysis
  • ISE 411 Graphs and Network Flows
  • ISE 412 Quantitative Models of Supply Chain Management
  • ISE 414 Heuristic Methods in Combinatorial Optimization
  • ISE 416 Dynamic Programming
  • ISE 419 Sequencing and Scheduling
  • ISE 420 Service Systems Engineering
  • ISE 424 Robotic Systems and Applications
  • ISE 425 Advanced Inventory Theory
  • ISE 439 Queueing Systems
  • ISE 444 Optimization Methods in Machine Learning
  • ISE 447 Financial Optimization
  • ISE 458 Topics in Game Theory
  • ISE 465 Applied Data Mining
  • Math 405 Partial Differential Equations I
  • Math 467 Financial Calculus I
  • Math 468 Financial Calculus II

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