A note on: Spline technique for modeling roadway profile to minimize earthwork cost

Abstract

The gap constraint used in A. A. Moreb, Spline technique for modeling roadway profile to minimize earthwork cost, J. Ind. Man. & Opt., 5 (2) (2009), 275-283 introduces unnecessary errors, while the slopeconstraint may be violated for second- and higher-order splines. In this note we amend the gap constraint, whilemaintaining the linearity of the model. We also present an improved slope constraint forlinear and quadratic splines, and show that it becomes nonlinear for cubic andhigher order splines. The improvements also apply to A. Moreb, M. Aljohani, Quadratic representation for roadway profile that minimizes earthwork cost, J. Sys. Sci. & Sys. Eng., 13 (2) (2004), 245-252.