Quadratic representation for roadway profile that minimizes earthwork cost

Abstract

Roadway design usually involves choices regarding grade selection and earthwork (transportation) that can be solved using linear programming. Previous work considered the road profile as series of interconnected linear segments. In these models, constraints are included in the linear programming formulation to insure continuity of the road, which cause sharp connectivity points at the intersection of the linear segments. This sharp connectivity needs to be smoothed out after the linear programming solution is found and the earth in the smoothed portion of the roadway has to be moved to the landfill. In previous research, the smoothing issue is dealt with after an optimal solution is found. This increases the work required by the design engineer and consequently increases the construction cost; furthermore, the optimal solution is violated by this smoothing operation. In this paper, the issue of sharp connectivity points is resolved by representing the road profile by a quadratic function. The continuity constraints are dropped (unneeded) and global optimality is guaranteed. Moreover, no violation is incurred to implement the optimum results. Although a quadratic function is used to represent the road profile, the mathematical model is purely linear in nature.

Keywords

Linear programming / transportation / earthwork allocation / roadway grades

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