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

Underground mine access design to maximise the net present value

© 2015 Dr. Kashyapa Ganadithya SirinandaThe current methods of designing underground mine access do not maximise the Net Present Value (NPV) of a mine over its life. Designing the access for underground mines and scheduling its construction is a continual challenge for the mining industry. To date, the scheduling and access design of an underground mine have only been considered as two separate optimisation problems. First, access to the mine is designed and then the scheduling is completed. One drawback of this approach is that the costs of access construction fail to be correctly reflected in the NPV calculation. This research develops fundamental methods and efficient algorithms towards maximising the NPV for an underground mine subject to operational constraints. The NPV is defined by taking the locations of ore bodies and their values, the decline construction costs, the decline development rate and the discount rate into account. The process of constructing the access can be classified according to the number of faces being developed concurrently. An underground mine with a single decline branching at a junction point into two declines is considered. After construction reaches the junction, the two faces of the decline can be developed sequentially or concurrently. Here, two algorithms are proposed for optimally locating a junction point (Steiner point) to maximise the NPV for both cases. The optimal mine access is presented for a range of discount rates. A real mine consists with more junction points. An underground mine with two junction points is considered. The algorithm that has been developed for the single face operation is extended to locate two junction points to maximise the NPV. The optimal locations of the junction points are obtained for a range of discount rates. The gradient constraint defines the safe-climbing limit for mining trucks. A further algorithm is proposed for optimally locating the junction point to maximise the NPV when the gradient constraint is active. This algorithm is applied to a case study where two underground mines are joined using a connector. The aim is to maximise the NPV associated with the connector

Time delayed discounted Steiner trees to locate two or more discounted Steiner points

A discounted Steiner tree is a weighted Steiner tree in which the costs of constructing the edges and values at the nodes are discounted over time. Discounted Steiner points can be located to maximise the sum of the discounted cash flows, known as the net present value, and an algorithm for doing this for a single Steiner point, known as the discounted Steiner point algorithm, was previously established. An application of this problem is underground mine planning. This article proposes an algorithm to optimally locate two junction points, given a surface portal and three ore resource points, for maximum net present value, which includes the value of the ore bodies and the construction costs. The discounted Steiner point algorithm is extended to locate two junction points where time delays may occur at a discounted Steiner point before constructing the adjacent edges. The optimal locations of the junction points are obtained for a range of discount rates. Numerical trials show that this algorithm works well. A generalisation of the algorithm to locate more discounted Steiner points is also discussed. References E. N. Gilbert and H. O. Pollak. Steiner minimal trees. SIAM J. Appl. Math., 16(1):1–29, 1968. doi:10.1137/0116001. F. K. Hwang, D. S. Richards, and P. Winter. The Steiner Tree Problem. Elsevier, 1992. https://www.elsevier.com/books/the-steiner-tree-problem/hwang/978-0-444-89098-6. K. G. Sirinanda, M. Brazil, P. A. Grossman, J. H. Rubinstein, and D. A. Thomas. Optimally locating a junction point for an underground mine to maximise the net present value. ANZIAM J., 55:C315–C328, 2014. doi:10.21914/anziamj.v55i0.7791. K. G. Sirinanda, M. Brazil, P. A. Grossman, J. H. Rubinstein, and D. A. Thomas. Maximizing the net present value of a Steiner tree. J. Global Optim., 62(2):391–407, 2015. doi:10.1007/s10898-014-0246-3