Probabilistic Methods in OR
Department of Mathematical Sciences
WORCESTER POLYTECHNIC INSTITUTE
MA 4327, Probabilistic Methods in OR, Term B03
B. Doytchinov
Office: SH105D
Office hours: TBA
e-mail:bogdand@wpi.edu
TEXT
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F. S. Hillier, G. J. Lieberman, Introduction to Operations Research,
Seventh Edition, McGraw Hill.
COURSE CONTENTS
The course consists of five main parts:
- Dynamic Programming.
Characteristics of Dynamic Programming Problems.
Deterministic and Probabilistic Dynamic Programming.
Hillier and Lieberman, Chapter 11.
- Decision Analysis.
Decision Making with and without experimentation. Decision
trees. Utility theory.
Hillier and Lieberman, Chapter 15.
- Markov Chains
Discrete-time Markov Chains - classification of
states, ergodic properties, Chapman-Kolmogorov equations,
absorption states. Continuous-time Markov Chains.
Hillier and Lieberman, Chapter 16.
- Queueing Theory and Applications.
Queueing systems. Poisson flows and the role of the
exponential distribution. Birth-and-death processes
and queueing models based on such processes. Little's formulas.
Wait-cost functions and decision making in queueing.
Hillier and Lieberman, Chapters 17 and 18.
- Markov Decision Processes.
The model for Markov decision processes. Optimality criteria.
Methods for constructing optimal strategies.
Hillier and Lieberman, Chapter 21.
CLASSES
There are four lectures per week, conducted in
SH203, on Mo,Tu,Th, and Fr, 9:00 - 9:50am.
You are supposed to attend all lectures. If you
miss a class, it is your responsibility to make a copy of the classnotes
from another student and make sure you learn what you have missed.
HOMEWORK
There will be four or five homework assignments throughout the course.
You will have approximately one weak to complete each assignment. The
problems will be taken most often from the book. Each assignment will
be announced in class, and then it will also appear
on the web.
SOFTWARE
Some of the problems assigned might be computationally intensive. You will
need some computing device with the ability to multiply matrices. The text
comes with a compact disk of programs for the PC, called Student CD-ROM.
You are welcome to use it for the purposes of this course, but you are not
obliged to stick to it.
For example, MATLAB and Maple can be used successfully in most cases. A calculator
that can multiply matrices would be sufficient, too.
GRADING POLICY
There will be a take-home Mid-Term Exam, and also a Final Exam
the form of which will be determined later. Your final grade will be
calculated in the following way:
30% of the grade come from the Homework,
30% of the grade come from the Midterm Exam,
40% of the grade come from the Final Exam.
These scores are combined to give a final number of
points, between 0 and 100. The
point ranges for the final grades should be expected to be:
A: 100-90
B: 89-80
C: 79-65
Probabilistic Methods in OR, Term B03
Send me mail:
bogdand@wpi.edu
