Doctoral Courses :

B60.4101.20 Applied Probability:

  1. Continuous Time Markov Chains
    a. Birth and Death processes
    b. The Kolmogorov differential equations
    c. Absorption probabilities
  2. Renewal Theory:
    a. Regeneration, recurrence and transience
    b. Wald's equation
    c. The key renewal theorem
  3. Martingales:
    a. Martingales, Supermartingales, and Submartingales
    b. The Optional Sampling Theorem
    c. Martingale Convergence Theorem
  4. Brownian Motion:
    a. Definitions and preliminaries
    b. Path continuity
    c. Hitting times and Maximum values
    d. Reflected Brownian Motion
  5. Stability and Control of Queueing Networks
    a. The sample path approach
    b. Fluid models
    c. Queues in heavy traffic

    All these concepts will be applied throughout the course to examples from reliability theory, flexible manufacturing, inventory management, call centers, and telecommunication networks.

 

Text Books:

  1. Karlin S. and Taylor H., (1975) A First Course in Stochastic Processes, 2nd Edition, Academic Press.
  2. Ross S., (1996) Stochastic Processes, 2nd Edition, John Wiley and Sons.
  3. El-Taha M. and Stidham S., (1999) Sample-Path Analysis of Queueing Systems, Kluwer Academic Publishers.
  4. Dai J., (1998) Stability of Fluid and Stochastic Processing Networks, Author's class notes.

B60.4303 Special Topics in Operations Management: Stochastic Models

This is a doctoral course in Operations Management. The course introduces research topics in OM using published journal papers, book chapters, class notes, and not yet published preprints.

Students are expected to read all the papers, and present two of them to the class during the semester. If one paper is covered in a class, the presentation will be 75 minutes. This will be followed by a 60 minutes discussion. If two papers are presented, each presentation will be 40 minutes long, followed by a 30 minutes discussion. The student who presents will also run the discussion.

All the papers deal with models to real life problems. The introduction of the paper should always start by describing the specific problem the paper deals with. The presentation and discussion should focus both on the modeling aspects of the paper as well as the mathematical tools that are used to analyze this model. Nevertheless, one should always conclude by stating the managerial insights that are suggested by the paper.

In addition to the regular class sessions we will have two (or more) guest speakers (see classes 3, 5 and 6 in the course outline). Two homework assignments will be given during the semester. Both are due the week after they are assigned.

Each student is required to submit and present a project during the last class session. For the project, each student should come up with an OM related question that he or she is interested in. The next step is to write a literature survey on this issue. The last step is to write a research proposal. Both literature review and research proposal will be presented in the last session.

B60.4304 Special Topics in Operations Management:
Supply Chain Management

Operations Management is concerned with the concepts and methods for the management of processes required to produce goods and services. These include product design, process design, capacity and production planning, distribution and logistics, inventory management, quality management, and many others.

This course introduces doctoral students in operations management to some of the
principal model paradigms and methodologies relevant to research in Operations
Management.

The topics include:

  • Inventory management
  • Production scheduling
  • Distribution management and vehicle routing
  • Supply Chain Management - Bullwhip effect, Delayed differentiation, Consumer choice and assortment decisions, Management of short lifecycle products
  • Product Design, and Time to market issues
  • Performance evaluation
  • Interactions with other functions such as Finance, Accounting, and Marketing

The ultimate goal of this course is to equip students to conduct research in this area. We
will study published journal papers, review articles, book chapters, and recent not yet
published preprints. The classes will consist of a combination of lecture, active discussion, and formal student presentations.

Prerequisites:
Basic understanding of Optimization Theory and Probability Theory.

B60.4307 Supply Chain Management - II

This course is designed for Ph.D. students in the areas of operations management, economics (applications of game theory to operations), and econometrics (application of econometrics to operations). The course B60.4304 'Special Topics in Operations Management: Supply Chain Management' is not a prerequisite for this course.

The course delves into three areas of research in the realm of supply chain management:

  1. Econometric models
  2. Supply chain coordination
  3. Application of financial economics in supply chain management: real options, hedging, commodity markets.

Our goal is to learn the methodologies used for research in these areas, and gain familiarity with the existing research models and results. The mode of learning includes a mix of lectures and student presentations. The course content shall include book chapters and published research articles.

B60.4320.20 Stochastic Modeling in Operations Management

  1. Introduction (session 1)
    1. Applications: Flexible Manufacturing, Inventory Management, Call Centers, Telecommunication Networks, Reliability Theory
    2. Discrete time Markov chains (DTMC) - overview of main concepts
    3. Examples of continuous time Markov chains
  2. Continuous time Markov chains (CTMC) (session 2)
    1. Poisson process
    2. Birth and Death Processes
    3. The Kolmogorov differential Equations
    4. Strong Markov Property
  3. Renewal Processes (sessions 3 & 4)
    1. Stopping rules
    2. Wald's equation
    3. Renewal theorems
    4. Regenerative Processes
  4. Brownian Motion (sessions 5 & 6)
    1. Definitions and preliminaries
    2. Path continuity
    3. Hitting times and maximum values
    4. Reflected Brownian Motion
  5. Queueing systems design and control (sessions 7-13)
    1. Queueing systems as an application of CTMCs (session 7)
    2. The sample path approach (session 8)
    3. Stability and Fluid models (sessions 9 & 10)
    4. Control of Queueing systems in heavy traffic using diffusion models (sessions 11 & 12)
    5. Applications (session 13)

Recommended Texts

  1. Karlin S. and Taylor H., (1975) A First Course in Stochastic Processes, 2nd Edition, Academic Press.
  2. Karlin S. and Taylor H., (1981) A Second Course in Stochastic Processes, 2nd Edition, Academic Press.
  3. Ross S., (1996) Stochastic Processes, 2nd Edition, John Wiley and Sons.
  4. El-Taha M. and Stidham S., (1999) Sample-Path Analysis of Queueing Systems, Kluwer Academic Publishers.
  5. Dai J., (1998) Stability of Fluid and Stochastic Processing Networks, Author's class notes.
  6. Glasserman P. (1993) Brownian Models, Author's class notes