Analysis of some cutting plane algorithms of integer programming

Discrete optimization models and methods, in particular, the apparatus of integer programming, are often used for solving and analysis of many decision-making problems in computers design, productions planning and management, information technologies, engineering. In this paper we investigate some cutting plane algorithms for solving the set packing problem, which has a lot of applications in the mentioned above areas. We give previously obtained estimates on the number of iterations (cutting planes) of these algorithms. We study one class of the problems with random input data. This paper presents an original method for construction of families of set packing problems, which are polynomially solvable on average. Upper bounds on the average iterations number for the problems of these families are built.