Earthwork allocations with linear unit costs

This paper presents a quadratic programming model of earthwork allocations that accommodates linear unit cost functions of purchase and excavation for borrow pits. The unit costs of haul and compaction for borrow pits and the various unit costs for earthwork from cut to fill sections and disposal sites are assumed to be constant (based on an earlier investigation). The solution of the model is explored and it is found that the global minimum cost is guaranteed only when the linear unit cost functions are nondecreasing. Extension of the model to accommodate setup costs for borrow pits and landfills is made and an efficient solution method is devised. This model, which complements existing optimization models of earthwork allocations, provides several capabilities over the commonly used mass-haul diagram. Application of the model to a numerical example is presented.