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In order to solve the layout NP complete problem, this paper analyzes the layout optimization model and algorithm, This kind of problems involved in operational research, data structures, algorithm analysis, artificial intelligence, computer network, etc. multi-discipline knowledge. Layout problems widely exist in practice, the main research rectangular optimal layout, Rectangular optimal layout is a series of rectangular parts reasonably emissions in raw material, make the highest utilization of raw material, And the optimization mathematical model is established, and the use of heuristic algorithm to solve the rectangular optimal layout problem. Simulation experiment showed that the optimization algorithm is effective.

Operations research theory of stochastic service at fast food restaurants, banks, video-on-demand, and web access should be extensive. This paper is a study of the design of its video-on-demand system model. We design and built a specific mathematical model, and analysis of algorithms and test results. We propose video stream control method based on popularity, and the popularity of the program is divided into two types of popular and unpopular, analysis of the system instantaneous transition probability, and designs the popularity of video streaming bandwidth prediction formula. The results show that this method can effectively save server resources, and improve the level of service of video. This queuing analysis method can also be applied in other similar random service system.

In order to make the matrix theory of matrix partial order in multivariate analysis and linear model parameter estimation plays an important application, this paper mainly discusses matrix partial order and its application in linear model to compare. Firstly introduces estimation and model comparison the basis knowledge, then use the matrix partial order theory comparison of generalized ridge estimation and LS estimation. Under the mean square error criterion, discusses the ridge estimation superior to LS estimation problem, On this basis, using Lowner partial order generalized ridge estimators are discussed relative to the LS estimate of good properties, popularize the previous conclusions.