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The problem of optimization gas or oil pipelines arrangement can be converted into Fermat problem of “Two points and One Line”. The optimal arrangement of pipelines with the same unit cost of shared or non shared pipeline (OAPSU-Model) is proposed to study the problems of lowest cost of pipelines firstly. The optimal arrangement of pipelines with the different unit cost of shared or non shared pipeline (OAPDU-Model) is established to find the Fermat point and the minimum cost of pipelines. In fact, OAPSU-Model is the special case of OAPDU-Model. Introduction An oilfield company plans to build two refineries on the one side of railway, and built a station in the railway to transport oil products as shown in Fig.1. Some Oilfield Design Institutes hope to establish the general mathematical models and methods to cut pipelines construction costs as much as possible. These kinds of problem are common in oil and gas transportation. Actually, this kind of problem is very complicated because the distance between refineries and the vertical distance between refineries and railway are different in different locations. And some position is not suitable to build refineries or railway stations. And the unit cost of shared or non-shared pipelines is different because the materials or sizes of pipes are different. The problems are interesting for many scholars. For example, Wang Yuchun built a mathematical model based on the correlation method of gray system to study pipelines construction problem [1].And WU Ming set up a running model to long distance heated crude oil pipeline [2]. However, the gas and oil transportation problems require further study in different case. Hence, it is valuable to propose the mathematical model based on Fermat problem to study this kind of transportation problems. Notations k : The unit cost of shared or non-shared pipelines f : The total length of pipelines F : The total cost of pipelines a : The vertical distance from refinery A to the railway b : The vertical distance from refinery B to the railway l : The horizontal distance between refinery A and B

Optimization in Oil Pipelines Arrangement with Fermat Problem