Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Models for representing piecewise linear cost functions
Operations Research Letters
A continuous bi-level model for the expansion of highway networks
Computers and Operations Research
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Selecting an optimal vertical alignment while satisfying safety and design constraints is an important task during road construction. The amount of earthwork operations depends on the design of the vertical alignment, so a good vertical alignment can have a profound impact on final construction costs. In this research, we improve the performance of a previous mixed-integer linear programming model, and we propose a new quasi-network flow model. Both models use a piecewise quadratic curve to compute the minimum cost vertical alignment and take earthwork operations into account. The models consider several features such as side-slopes, and physical blocks in the terrain. In addition to improving the precision, we propose several techniques that speed up the search for a solution, so that it is possible to make interactive design tools. We report numerical tests that validate the accuracy of the models, and reduce the calculation time.