AS/SC/MATH4170.06

Operations Research II

This course deals with deterministic and probabilistic models based on optimization. The following topics will be discussed: 1) game theory (how to find the best strategies in a confrontation between two players with opposite interests); 2) decision theory (how to act in order to minimize the loss subject to the available data); 3) simulation (how to sample from a probability distribution and accurately approximate multiple integrals using random numbers); 4) reliability theory (how to evaluate the lifetime of a system consisting of many interacting subsystems); 5) queueing theory (how to assess what may happen in a system where the customers arrive randomly, wait in line, and then get served); 6) measures of uncertainty and nonlinear optimization (how to measure uncertainty in probabilistic modelling, applications to pattern-recognition and classification, nonlinear optimization techniques). Each chapter contains specific optimization problems and methods and algorithms for solving them. The course is rich in examples.

There is no textbook and the lecture notes are essential. Useful books are: (a) F. S. Hillier and G. J. Liberman, Introduction to Operations Research, 4th ed. (Holden-Day); (b) H. A. Taha, Operations Research, An Introduction, 4th ed. (MacMillan).

There are three prerequisites: (i) some background in probability and statistics such as MATH2030.06 or MATH1132.03 or MATH2030.03; (ii) some background in calculus of several variables such as MATH2010.03, MATH2310.03 or MATH2015.03 (ACMS2030.06); and (iii) some knowledge of linear programming, perferably from MATH3170.06. Students who have not taken these courses need the permission of the course coordinator.

The final grade is based on four one-hour tests worth 15% each and a final examination worth 40%.