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( There will likely be differences in the instructor, textbook, and/or outline the next time the course is taught.)
Instructor: Dr. Halit Üster
Textbook: R.K. Ahuja, T.L. Magnanti and J.B. Orlin, Network Flows: Theory, Algorithms, and Applications, 1993, Prentice-Hall, NJ.
References:
- D. Solow, How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, John Wiley & Sons, 2004.
- V. K. Balakrishnan, Network Optimization, 1995, Chapman and Hall, London, UK.
- D. P. Bertsekas, Network Optimization: Continuous and Discrete Models, 1998, Athena Scientic, Belmont, Mass.
- J. R. Evans and E. Minieka, Optimization Algorithms for Networks and Graphs, 1992, Marcel Dekker, NY.
- D.T. Phillips and A. Garcia-Diaz, Fundamentals of Network Analysis, Prentice-Hall, Inc., Englewood Cli s, New Jersey, 1981 (Waveland Press, Inc., Prospect Heights, Illinois, 1990.)
Course Description and Objectives:
Network flow problems appear as integral components of large-scale and realistic network design models for tactical and strategic decision-making in a wide range of industrial applications involving movement of raw materials, work-in-process, nished products, parcels/packages, information or passengers over geographical areas. Furthermore, various decision problems that are not on networks, such as production/inventory planning, manufacturing and workforce scheduling problems and project management, can be perceived and formulated as network flow problems. In this course, we will review several such applications with a focus on their mathematical modelling and solutions on networks. We will cover well-known network ow problems including the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem. Our goals are to provide a sound and applicable knowledge of theory and practice of solving network flow problems with an emphasis on network flow algorithms and to help students in developing a good understanding of algorithm development and analysis. Upper level undergraduate students with adequate background can also enroll in the course.
Course Topics
- Introduction, Definitions, Applications,
- Shortest Path Problem
- Maximum Flow Problem
- Minimum Cost Flow Problem
- Minimum Spanning Trees
- Generalized Flows
- Multi-commodity Flows
- Network Design Applications
