Optimizing the vertical alignment under earthwork block removal constraints in road construction

The road design problem is usually split into the horizontal alignment, the vertical alignment, and the earthwork scheduling problems. Optimizing the vertical alignment assumes a predetermined horizontal alignment and changes the height of the road at different points to minimize overall construction costs, while maintaining the design requirements. The problem gets complicated because of the natural blocks like rivers, mountains, etc., in the road construction area. Existing vertical alignment models deal with the blocks before the beginning of road construction, which sometimes results in a non-optimal solution. A substantial portion of the total construction cost comes from the earthwork operations. As a result, some existing models only find the optimal earthwork schedule for a predetermined vertical alignment. This research extends a recent mixed integer linear programming (MILP) model that considers blocks when optimizing earthwork operations. We propose a novel model of vertical alignment that considers blocks. In the model, we propose a novel way of incorporating side-slopes of the road to improve the accuracy of the model. Our numerical results show a considerable improvement in the accuracy of the model without introducing significant computational burden. Finally, we propose another novel model using concepts from the network flow algorithms that gives more that 75% speedup for 87% of the problems for our test set of 280 problems.