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This model is based on the problem B in the Mathematical Modeling Contest of North China Electronic Power University in 2015. It works out solutions for non-overlapping box arrangement with load-bearing limits and without bearing limits, which can finally solve the practical loading problem of overlapping of multi-type boxes considering bearing limits. About the mentioned practical problem, it is actually a two-dimensional layout problem. In this paper, models for integer layout in unified direction are established by integer programming. First, select an area-undetermined rectangle in the lower-left corner of the pallet and pack boxes X in it in unified direction. Then divide the residual area into two pars, B and C, and pack boxes Y in each part in unified direction. The layout of the residual area is concerned with the size of the lower-left corner. To reduce discussions, the maximum area utilization of B and C is set as constraint which will be considered comprehensively, the minimum of the whole oddments of three areas be set as objective function, thus four layout methods can be obtained. Then exchange the box types in the selected rectangle and the residual area, there comes another four layout methods. By analyzing the packing and division methods of the eight layout, the optimal solution can be concluded.

Based on the first question of problem B in the National Undergraduate Mathematical Modeling Contest of the Higher Education Cup in 2015, this model would quantify some relevant indexes to analyze the degree of supply and demand for taxicab resources. In view of this question, this paper would estimate the distribution of taxi resource according to the analysis of the supply and demand, and establish the model of the Time and Neural Network. The assumed space-time condition is different periods and districts in one city. The supply quantity could be available through statistics, so the question is to work out the taxi demand and measure the degree of allocation of demand and supply according to the ratio of demand and actual supply (the arithmetic product of supply quantity and the rate of attendance) in the specific time and space. Firstly, to prove selecting indexes relevant to the demand for taxicabs through relativity analysis. The dimensionality of the variable could be reduced by filtering the main factors through principal component analysis. Secondly, to predict the data of principal components during 2009~2015 according to Time Series Analysis. Since the indexes would increase to the upper limit, the three Exponential Smoothing is more adoptable. The Neural Network prediction model would be established due to its high precision, and then the principal index during 2009~2015 could be input into it and the demand would be output. Finally, to estimate the demand in specific time and space and calculate the allocation degree of demand and supply on the ground of the population ratio in different periods and districts. The relativity analysis proves selected indexes relevant to the demand quantity. The principal component analysis filtered the population in downtown and operating distance. The time sequence predicts the principal component data, and the Neural Network forecasts the demand quantity. the distribution degree of demand and supply is a equilibrium value at 70%. it would be not difficult for people to catch taxis if it is within 60% to 75%. The selected indexes were based on dual analysis, and the prediction dual prediction, which reflects the high precision of this model.