Mathematical modeling of oil pipeline layout MATLAB, mathematical model of oil pipeline layout

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topic study investigate — m ⋯ One One Zokor | Mattress I'm sorry Epicarboxylic acid ◎ Li Yin Sensitive Wang zuoshun Liu Just. ( Guigang, Guangxi 75130 forces 537100)

【 Abstract 】 This paper studies investigate Lost Oil pipeline laying Set the most Small expenses problem , Yes problem 1 build Set up optimization mold type , shipment use The extremum of a function Theory and MATLAB Software seek Find the optimal solution and give Out The corresponding The laying of Fang case ． The first Let's transport first Using machine The reason is The analysis shows that the public pipeline must be connected with the railway vertical , simplify The problem of , Through research The most One General laying scheme Minimum cost problem , After strict Secret reasoning , have to Out laying There are public pipelines in the scheme The control of Conditions , Last have to It's time strip Piece control Under control And , respectively, seek Get the best layout Fees and standing Point location , through too MATLAB Programming requirements Find the optimal solution and give Laying plan ．

【 key word 】 Extreme value theory ; Minimum cost ; Pipeline laying

1． Restatement of the problem Some oil Tian plans to be on the railway Line side build two Home refining factory , Same as Time is on the iron Build an additional station on the route , Used to transport Product oil ． Because of this mold The formula has One set Universality of , oil Tian design Yuan Xi Hope to establish pipeline Building The cost is the most province Of One General mathematical models and methods ． Ask for Establish reasonable Mathematical module of type , to Out Consider the cost of shared pipelines and non shared pipelines The cost is the same or not The same situation Next , Save two refining oil-extracting mill and vehicle Stand Jianjian state fee use Most economical The loss of oil network Collateral Line chart ．

2． Analysis of the problem 『 Feng 】 Yu Shi Refining in the world Oil factory to railway Route Distance of Cannot leave Same as , oil refining Factory between Distance of Cannot leave Same as , The area where the pipeline passes Different, etc factors , the In order to Establish the most province cost Our pipeline needs comprehensive Consider each Kind of factors ． Refining Oil plants can In total Use a tube Line Can also be With share pipeline , When sharing pipeline Take the exam Consider sharing pipeline cost And The cost of non shared pipelines The relationship between ． When there is sharing Pipeline time , common Pipelines need Hang Youtong To the railway , The station is built on the shared pipeline and railway At the intersection of roads , here share pipeline To the railway The cost of is Most economical Of ． Yes In question 1, Don't consider Area problem bring The addition of cost , Refining oil-extracting mill 、 The railway Bit Set unknown , Need to be Same as When considering two person ． For questions 2, Because the two refineries are located in the suburbs and urban areas respectively , layout In the city Pipelines in the area need to be added A surcharge ． problem 3 Than problem 1 Connect more Near real Occasion , The cost of pipelines varies , The length of expensive pipelines should be reduced as much as possible ．

3． model Type false Setting and symbol description i model Type hypothesis ：

(1) Suppose the railway is straight ．

(2) iron The width of the road Negligible , And put two refineries And the station become quality spot ．

(3) Suppose the tubing is at a non turning perfectly straight layout ．

(4) Ignore the pipe connection Mouth Of Mouth welding cost ．

(5) For questions 2 Engineering in Consulting company Our estimate is Objective ii Symbol description ： { Lay pipelines The cost of ／ Suburbs The cost of laying pipelines in the area Laying pipelines in urban areas The cost of A The line from the factory to the suburb Straight distance C1 Transport per kilometer A Chang Cheng Refined oil Pipeline price ( Ten thousand yuan ／ km ) C2 Public pipelines per kilometer The price of Pave the city Zone pipeline The additional cost of Cd Transportation Kouchangcheng Refined oil Pipeline price ( Ten thousand yuan ／ km ) ( ,y) Shared pipeline and non shared pipeline The coordinates of the intersection point of (0,n) A factory Of coordinate (1,6) B The coordinates of the factory (c, ) city District tube Line And Suburbs District pipeline Of Occupy mark 4． model The establishment of type And solving First, establish such a chart 1—1 Shown Plane right angle coordinate system ,P Express Two tubes Line junction ;P Express A Refineries , coordinate by P (0,0);P Express B Refining oil-extracting mill , Coordinate for P,(z,6);E Express Station , Coordinate for E( ,0); from A towards The railway line is perpendicular , To hang The foot is the coordinate origin spot , The earth The plane of the face by xOy flat Noodles ． Line segment PE And The axis is vertical , Hang Enough for ． Because the two refineries are on the same side of the railway ,

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