Optimum Location of an Oil Storage Facility

by Giovanni Quiel

Submitted : Fall 2010

This project focused on optimizing the distance between three points on an (x,y) Cartesian Coordinate system.  The goal of the project was to find an (x,y) position that would minimize the total pipeline length, or distance between all three points in a specific case. Each position in a case represents an oil well, and the point to be determined is the location of a storage facility in which will minimize the total distance between all three points and the storage facility.  Therefore, the ultimate goal is to minimize the total distance, in which will minimize total pipeline length, between these three points and the storage facility position. With this in mind, we derive a formula to represent the total distance or ‘length’ of piping, and we determine this formula to be the sum of the individual distances between the storage facility and each oil well. From calculus, we can determine the optimal distance by use of the First Partial Derivative along with the Second Partial Derivative Test. The First Partials Test determines critical points of a function of x and y, and then the Second Partials Test determines whether this critical point occurs at a relative minimum, maximum, saddle point, or an indeterminate position. By use of both the First and Second Partials Test, the position of the storage facility, with the intent to reduce the distance between the oil wells to a minimum, can be found.

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