This part of the course applies Linear Programming to the study of matrix game theory and to a number of flow problems on graphs and networks. Network flow problems are linear programming problems of special structure which are important because they represent broad areas of applications arising frequently and because their associated theory provides important insight and suggest new general developments. The problems considered include: the transportation problem (interpreted in terms of graph theory), the assignment problem, the minimum cost flow problem, the transhipment problem, the maximal flow problem. For these problems, we will provide many solution techniques.
- Course lecture notes.
- R. Dorfman, P. A. Samuelson, R. M. Solow, Linear programming and
economic analysis, Dover Publications, Inc., New York, 1987, reprint of
the 1958 edition.
- D. Gale, The theory of linear economic models, McGraw-Hill Book Co.,
Inc., New York-Toronto-London, 1960.
- F. S. Hillier, G. J. Lieberman, Introduzione alla ricerca operativa, Ottava
edizione, McGraw-Hill, Milano, 2006.
- D. G. Luenberger, Linear and nonlinear programming, Second edition,
Springer, New York, 2003.
- R. J. Vanderbei, Linear progamming: Foundations and Extensions.