The Optimum Contours Of An Open Pit Mine: An Application Of Dynamic Programming

In 1961 Lerchs and Grossman presented a method, based on graph theory, to determine the optimum ultimate pit limits for an open-cast mine. At the same time they demonstrated a dynamic programming algorithm for the optimum pit limits for a two-dimensional open-cast mine. Since then many methods for determining optimum limits for three-dimensional mines have been programed, and even more have been reported in the literature. The methods include computer "simulation" of the manual methods used by engineers, the development of sets of conic sections and fitting to exclude overlap, integer linear programming (and its equivalent network flow model), and dynamic programming. Many of the methods do not guarantee optimal solutions but seem to satisfy the user. Other reported methods have never been applied, partly because they did not yield optimal solutions. We have developed a three-dimensional dynamic programming algorithm which requires a single pass through the data. Large problems can be solved on a small computer because only a small part of the data is required at any time. In this paper we will review the state of the art and to demonstrate the connection between linear programming (and network flow) models and the dynamic programming method.