Steel Pipe Order and Transport

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 Steel Pipe Order and Transport

Abstract: This paper for the sake of the optimization problem of the minimum cost of ordering and transport program of the steel pipe, developed in accordance with the relevant conditions and data analysis of the marginal effect of the steel pipe selling price and production ceiling.
The key to this question is to establish the total cost of steel pipe subscription program and the relationship between transportation planning. First empowering the use of graph theory to map the shortest path for solving ideas, re-numbering the nodes in the graph, first find the minimum transportation costs between the railway any two road adjacent to the point transportation costs, and then integrated into The cost of network "Floyd algorithm is the minimum cost path between any two points in the figure, particularly to obtain the minimum cost of the pivotal point of the steel to the pipe line matrix and the minimum cost route. Then the ordering of steel pipes at minimum cost routes first transported to the pivot point, each hub points again to the adjacent side laying. Then calculated from the costs to both sides of the laying of the pipe node, and then to manufacturers ceiling constraints, the objective of minimizing the total cost of the establishment of a quadratic model. Take into account does not have seven steel mills ordering steel pipe, and the lower limit of production constraints, whereby the introduction of 0-1 variables, to establish an improved model. The two models are consistent, to some extent, validated the accuracy of the model results.
Purchase transport plan and the total cost to consider steel pipe price changes and changes in steel pipe production ceiling, unable to conclude that changes in the total cost and selling price changes, the upper limit changes a function of each steel discussed separately, the increase or decrease in accordance with the production ceiling at 10%, steel selling price in the $ 100,000 range to obtain the total cost of the change and share transport plan, fitting the intuitive graphical carried out relatively, you can get model results.
Using MATLAB software programming solving based on Floyd algorithm, minimum cost matrix of the steel to the pivot point. Then using the LINGO software to solve the various models created to get all ask the model results are as follows:
1, the problem of minimum total cost: 127.8632 million yuan.
2, the steel mills of the selling price changes in the total cost implications; selling price go up, share transport plan affect the selling price down, share transport plan; steel production ceiling changes on the purchase transport plans and the total cost of the greatest impact.
The minimum total cost of the problem: 140.6632 million.
In the case of road transport pricing change and mileage linear draw more savings in cost, total cost: 127.8373 million yuan.
Data and road network maps found in the observation of the question, our model results are in line with the principle of proximity and the principle of minimum spend. This is consistent with the general principles of real-life transport problems, in a sense illustrates the rationality and accuracy of the results of the model.
Keywords: quadratic, Floyd shortest path algorithm, the idea of ​​branch and bound
 Second, the problem restated
    To the laying of a A1-> ... -> the A15 the main channel of transmission of natural gas, such as Appendix IV in the figure below. After the first round of screening to determine the production of such competent Road steel pipe mills. If a steel bear the manufacture of this steel pipe, the need to produce at least 500 units (1km in charge of Road steel pipe is called a unit pipe). Steel can be produced within a specified period of the steel pipe the maximum number of units, steel pipe factory selling price of a unit of steel pipe for the million, the following table:

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