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April  2010, 6(2): 393-400. doi: 10.3934/jimo.2010.6.393

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

Valentin R. Koch 1, and  Yves Lucet 2,

1. 

Mathematics, I. K. Barber School of Arts & Sciences Unit #5, University of British Columbia, 3333 University Way, Kelowna BC, V1V 1V7, Canada
2. 

Computer Science, I. K. Barber School of Arts & Sciences Unit #4, University of British Columbia, 3333 University Way, Kelowna BC, V1V 1V7, Canada

Received  August 2009 Revised  January 2010 Published  March 2010

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 slope constraint may be violated for second- and higher-order splines. In this note we amend the gap constraint, while maintaining the linearity of the model. We also present an improved slope constraint for linear and quadratic splines, and show that it becomes nonlinear for cubic and higher 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.
Keywords: earthwork allocation, roadway grades., Linear programming, transportation.
Mathematics Subject Classification: Primary: 90C05, 90C08; Secondary: 41A15, 90B0.
Citation: Valentin R. Koch, Yves Lucet. A note on: Spline technique for modeling roadway profile to minimize earthwork cost. Journal of Industrial and Management Optimization, 2010, 6 (2) : 393-400. doi: 10.3934/jimo.2010.6.393
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