A polynomial algorithm for the earthwork allocation problem with borrow and waste site selection

Abstract

In road construction projects, earthwork is planned together with horizontal and vertical alignments. This study focuses on earthwork operations that basically include cutting the hills and filling the holes on the road path. The candidate borrow and waste sites can also be used to obtain or heap earth when the available cut and fill amounts are not balanced or operating these sites reduces the total earthwork cost. Total earthwork cost contains the transportation cost and the overall cost related to opening the candidate sites. The problem is to determine which borrow and waste sites to operate, and the earth flows between cut, fill, waste, and borrow sites such that the total cost is minimized. It is shown that the problem is a generalization of the well-known lot-sizing problem. A fixed charge network flow problem formulation is presented, and a polynomial time dynamic programming algorithm is developed for solving the problem.