Job Site Optimization Cost Efficiency Problem

by Kenneth Cabana

Submitted : Spring 2012

The problem is an optimization problem using a variation of Newton’s Method to find the minimum distances in three segments of a particular job. Each segment of the job uses one of two methods of inserting an 8 inch water line. The two methods differ in both the process and cost of how the pipe is put into the ground. One of the processes is called Open Cut Trenching, which refers to the use of an excavator to dig the soil to a desired level and inserting the pipe in sections piece by piece. The second method is called Directional Drilling and refers to a machine being able to drill horizontally at a negative slope to reach a desired depth before leveling out. Rod sections are added to continue underneath ground level to a desired length and when that level is reached, the slope is positively increased to pop above ground. The pipe is the attached to the rod and pulled to the rig.

The job is one that would be designed by a Civil Engineer and completed through and through by an Underground Contractor. The student mapped out a job that included three segments in which open cut were used in the beginning and the ending segments and directional drilling used in the middle to cross underneath a highway. With directional drilling costing approximately double of what open cut does, the distances of all segments need to be found to make the job cost at its least. The starting and ending point of the directional drilling portion are two variables that are unknown. To achieve the whereabouts of these variables, the researcher used the distance formula between each segment including all the variables. To be able to solve for these variables the partial derivative is taken.; Once that is achieved, the equations are implemented in a spread sheet where multiple calculations of a guess and check nature are done to then converge at the same set of numbers where none of the values differ from guess to guess. The distances of each of the segments can then be multiplied by the cost of inserting the pipe by linear foot put into the ground. Added altogether, the results equal the bare minimum of that particular job. This information is helpful to any underground contractor as his profit margins can be determined from this data. The information is also helpful to everybody that is involved in the long chain of companies that make jobs like this happen. This data will give them an insight on what it takes to complete a job and what money is on the line if something may go wrong. This process may help in getting an answer to head council men faster than previously before.

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