Research On The Application Of Mixed Integer Programming In Engineering

Mixed integer programming (MIP) problem is a special math programming(MP) problem which include integer or discrete variables, and the type of problems was apllyed broadly in engineering. The algorithm of mixed integer programming problem is also an important problem in math programming. After Land and Doig put forward the branch and bound algorithm for solving mixed integer programming problem, the research on algorithm that used to solve mixed integer programming problem have made a big progress. In this paper, the theory and algorithm of mixed integer programming was combined with engineering practice, and some helpful attempt have been made on modeling and solving the MIP problem. Some improvements have been made on modeling and algorithm aimed at concrete problem, and the process of modeling was analysised detailedly, and some new method was introduced during the process. All these made the problem access the reality of engineering problem more closely. Based on the branch and bound algorithm, the mathematical model of optimization of portfolio under CVaR measurement and the model of transportation problem which includes interval number variables were established. Combined with Monte Carlo scenarios simulation method, if the number of scenarios is fixed, mathematical model of optimization of portfolio under CVaR risk measurement can be converted to an optimization of a convex function problem. These techniques allow optimizing portfolio that includes large numbers of instruments. Based on the model, integer constraint was introduced, which make the model reflect the market closely. Transportation problem is a problem which was researched by using math programming method at the begining. For the characteristic of transportation problem, it was an integer programming problem naturally. By introducing a new algorithm, a transportation problem which includes interval number variables can be converted into two ordinary linear programming problems. It's a more efficient method, and a simple result can be gained. This technique has changed the condition that the result can be only expressed in an interval number. The results of experiential analysis of two models have shown that the model and the algorithm were efficient. Large scale problem can be solved efficiently.