Earthwork allocations with nonconstant unit costs

Existing linear programming methods of earthwork allocations in road construction assume that the unit costs of earthwork activities are constant. This paper investigates the factors that affect the variations of unit costs and presents a model of earthwork allocations that incorporates nonconstant unit costs. The unit costs may vary with the total quantity of materials moved from cut to fill sections or disposal sites and from borrow pits to till sections. For earthwork from cut sections, the unit costs can be established from the known quantities of cut sections (and other operating conditions) and can then be treated as constants in the model. For earthwork from borrow pits, the unit costs also vary with the total quantity to be moved from a borrow pit to till sections, but this quantity is unknown. These unit costs are formulated as three-component stepwise functions. The solution of the model is explored and a computer program, EARTHN, which solves the model quite efficiently, is developed. The model is applied to a numerical example to illustrate its use, and possible extensions of the model are examined.