Optimally locating a junction point for an underground mine to maximise the net present value

A review of the relevant literature identified an opportunity to develop algorithms for designing the access and construction schedule for an underground mine to maximise the net present value (NPV). The methods currently available perform the optimisation separately. However, this article focuses on optimising the access design and construction schedule simultaneously to yield a higher NPV. Underground mine access design was previously studied with the objective of minimising the haulage and development costs. However, when scheduling is included, time value of money has a crucial effect on locating the junction points (Steiner points) in the access network for maximum value. This article proposes an efficient algorithm to optimally locate a single junction, given a surface portal and two ore bodies, for maximum NPV where NPV includes the value of the ore bodies and the construction costs. We describe the variation in the location of the junction for a range of discount rates. References K. F. Lane, The economic definition of ore---cutoff grade in theory and practice. Mining Journal Books Limited, London 1988. F. K. Hwang, D. S. Richards and P. Winter, The Steiner tree problem. Elsevier, 1992. http://www.elsevier.com/books/the-steiner-tree-problem/hwang/978-0-444-89098-6 M. Brazil and D. A. Thomas, Network optimisation for the design of underground mines. Networks 49:40–50, 2007. doi:10.1002/net.20140 M. Brazil, J. H. Rubinstein, D. A. Thomas, J. F. Weng and N. C. Wormald, Gradient-constrained minimum networks (I). Fundamentals. J. Global Optim. 21:139–155, 2001. doi:10.1023/A:101190321029

Gradient-Constrained Minimum Networks, I. Fundamentals

In three dimensional space an embedded network is called gradientconstrained if the absolute gradient of any dierentiable point on the edges the network is no more than a given value m. A gradientconstrained minimum Steiner tree T is a minimum gradient-constrained network interconnecting a given set of points. Such networks can contain extra vertices, known as Steiner points. In this paper we investigate some of the fundamental properties of these minimum networks