Abstract
Roadway design usually involves decisions regarding the grade selection as the first stage; consequently, it is followed by another stage to solve the resulting earthwork allocation problem. Researchers have resorted to linear programming to solve the earthwork allocation problem using piecewise linear segments to model the road profile. Non linear functions were used to resolve the issue of sharp connectivity points present at the piecewise linear models. However, scaling problem may arise in the computaitonal phase.
In this paper, a one-dimensional (univariate) spline (piecewise polynomials) is used to fit the road profile and solve both the roadway grade selection and the earthwork allocation problem in a single linear programming problem. The mathematical model is purely linear in nature, regardless of the type of spline function used; and it guarantees global optimality. This approach has resolved the scaling problem while preserving the flexibility and smoothness of the road (no sharp connectivity points). The proposed model has exceeded all previous models in terms of efficiency and savings in cost. For illustration, three cases are considered.