The students enrolled in the IE PhD program must obtain a passing grade in 4 subject areas in order to successfully complete the written part of the qualifying exam.

For students admitted in Spring 2016-2017 or before, three of these exams must belong to the set of topics below. The fourth exam may either be in Engineering Mathematics or in an area in one of the FENS PhD programs (including IE).

Students admitted in Fall 2017-2018 or after, should take Deterministic Models in Operations Research and Stochastic Models in Operations Research topics. The third exam should belong to the topics below. The fourth exam may either be in Engineering Mathematics or in an area in one of the FENS PhD programs (including IE).

**Deterministic Models in Operations Research**

*Topics*

- Mathematical programming modeling
- Elementary Convex Analysis
- Linear Programming, Certificates, Duality, Sensitivity Analysis
- Dantzig Wolfe Decomposition and Column Generation
- Shortest Path Problems and Algorithms
- Maximum Flow Problems and Algorithms
- Minimum Cost Flow Problems and Algorithms
- Minimum Spanning Tree and Algorithms

*Reference Books*

- Linear Programming and Network Flows. Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali.
- Operations Research: Applications and Algorithms. Wayne L. Winston.
- Introduction to Operations Research. Frederick S. Hillier and Gerald J. Lieberman.
- Network Flows: Theory, Algorithms and Applications. Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin.
- IE 501 lecture notes available in Pdf format.

**Stochastic Models in Operations Research**

*Topics*

- (Conditional) Probabilities and (Conditonal) Expectations
- Markov Chains
- Poisson Processes
- Continuous Time Markov Chains
- Renewal Processes
- Queueing Models (those that can be handled as Markov processes)

*Reference Books*

- Introduction to Probability Models. Sheldon M. Ross. (Chapters 1–8)
- An Introduction to Stochastic Modeling. Howard M.Taylor, Samuel Karlin. (all chapters except Chapter 8)

**Production and Service Operations Planning and Control**

*Topics*

- Deterministic and Stochastic Inventory Models
- Lot Sizing Algorithms
- Assembly Line Balancing
- Transfer Lines
- Scheduling
- Flexible Manufacturing Systems

* *

*Reference Books*

- Modeling and Analysis of Manufacturing Systems. R. G. Askin, C. R. Standridge. (Chapters 2-5)
- Manufacturing Planning and Control Systems. T. E. Vollmann, W. L. Berry, D. C. Whybark.
- Production and Operations Analysis. S. Nahmias.
- Planning and Scheduling in Manufacturing and Services. M.L. Pinedo.
- Scheduling : theory, algorithms, and systems. M.L. Pinedo.

**Logistics and Supply Chain Planning and Design**

*Topics*

- Facility Location Problems
- Short-Haul Transportation (Vehicle Routing) Problems
- Long-Haul Transportation Problems
- Inventory Management and Risk Pooling
- Supply Chain Contracts
- The Value of Information
- Supply Chain Integration
- Distribution Strategies

*Reference Books*

- Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies. Simchi-Levi, D. Kaminsky, P., Simchi-Levi, E., 2007. (Chapters 2-7)
- Supply Chain Management: Strategy, Planning and Operation. Chopra, S., Meindl, P., 2013.
- Modeling the supply chain. Shapiro J.F.
- Facilities Design. Heragu S. (Chapters 11-12)
- Introduction to Logistics Systems Planning and Control. G. Ghiani, G. Laporte, R. Musmanno. (Chapters 3, 6, 7)

**Manufacturing Processes**

*Topics*

- Fundamentals and Parameters of Manufacturing Processes
- Manufacturing Equipment and Tools
- Machining
- Additive Manufacturing
- Biomanufacturing

*Reference Books*

- Manufacturing Processes and Equipment. Jiri Tlusty.
- Manufacturing Engineering and Technology. Serope Kalpakjian.

**Decision Theory**

*Topics*

- Modeling Decisions
- Subjective Probability and Inference
- Decision Making Heuristics and Biases
- Measurement Theory
- Expected Utility Theory
- Multi Criteria Decision Making

*Reference Books*

- Making Hard Decisions with DecisionTools. Cengage Learning. Clemen, R., & Reilly, T. (2013)
- Judgment in Managerial Decision Making.
- Judgment Under Uncertainty: Heuristics and Biases.
*Science*,*185*(4157), 1124-1131. Tversky, A., & Kahneman, D. (1974). - Measurement Theory. Roberts, F. S. (1985).
- Models, Methods, Concepts and Applications of the Analytic Hierarchy Process. International Series in Operations Research and Management Science, Volume 34. Thomas L. Saaty, L. G. Vargas.

**Computer Integrated Manufacturing**

*Topics*

- Computational Geometry for Curves and Surfaces
- Solid Modelling
- Computer-Aided Design
- Computer-Aided Process Planning
- Computer-Aided Machining
- Automation

* *

*Reference Books*

- Computer-Aided Manufacturing. Chang, T-C. Wysk, R.A. Wang, H-P,
- Automation, Production Systems, and Computer-Integrated Manufacturing. Groover, M.P.
- Principles of CAD/CAM/CAE. Lee, K.