Linear programming model for finding optimal roadway grades that minimize earthwork cost

The cost of earthwork involved in road construction can vary widely based on the roadway grades chosen by the designer. There is almost an infinite number of feasible grades available to the designer to choose from, all of which satisfy the geometric specification of the road. For every feasible grade selected, a transportation problem must be solved, which is a very tedious task. The roadway grade selection is usually considered as a stage and the earthwork (transportation) is another stage. These two stages have always been treated separately in the literature. The model presented here combines the roadway grade selection stage and the earthwork transportation stage in a single linear programming problem, thus guaranteeing global optimality.