Abstract
Traditional mining selection methods focus on local estimates or loss functions that do not take into account the potential diversification benefits of financial risk that is unique to each location. A constrained efficient set model with a downside risk function is formulated as a solution. Estimates of this nonlinear mixed-integer combinatorial optimization problem are provided by a simulated annealing heuristic. A utility framework that is congruent with the proposed efficiency model is then used to choose the optimal set of local mining selections for a decision-maker with specific risk-averse characteristics. The methodology is demonstrated in a grade control environment. The results show that downside financial risk can be reduced by around 33% while the expected payoff is only reduced by 1% when compared to ore selections generated by traditional cut-off grade techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Baumol, W. J., 1963, An expected gain-confidence limit criterion for portfolio selection: Manage. Sci., v. 10, p. 174-182.
Bawa, V. S., and Lindenberg, E. B., 1977, Capital market equilibrium in a mean-lower partial moment framework: J. Finan. Econ., v. 5, p. 189-200.
Bienstock, D., 1996, Computational study of a family of mixed-integer quadratic programming problems: Math. Programming, v. 74, p. 121-140.
Borchers, B., and Mitchell, J. E., 1997, A computational comparison of branch and bound and outer approximation algorithms for 0—1 mixed integer non-linear programs: Comput. Oper. Res., v. 24, p. 699-701.
Cardozo, R. N., and Smith, D. K., 1983, Applying financial portfolio theory to product portfolio decisions: An empirical study: J. Marketing, v. 47, p. 110-119.
Cerny, V., 1985, Thermodynamical approach to the travelling salesman problem: An efficient simulation algorithm: J. Optim. Theory Appl., v. 45, p. 41-51.
Chang, T.-J., Meade, N., Beasley, J. E., and Sharaiha, Y. M., 2000, Heuristics for cardinality constrained portfolio optimisation: Comput. Oper. Res., v. 27, p. 1271-1302.
Chirinko, R. S., Guill, G. D., and Herbert, P., 1991, Developing a systematic approach to credit risk manangement: J. Retail Banking, v. 13, no. 3, p. 29-36.
Deutsch, C. V., 1992, Annealing techniques applied to reservoir modeling and the integration of geological and engineering (well test) data: Unpublished Doctoral Dissertation, Stanford University, Stanford, CA, 304 p.
Deutsch, C. V., and Journel, A. G., 1997, GSLIB: Geostatistical software library and user's guide, 2nd edn.: Oxford University Press, New York, 369 p.
Domar, E. V., and Musgrave, R. A., 1944, Proportion income taxation and risk-taking: Quart. J. Econ., v. 58, p. 389-422.
Edwards, R. A., and Hewett, T. A., 1993, Applying financial portfolio theory to the analysis of producing properties: SPE Paper No. 26392, 12 p.
Farmer, C., 1991, Numerical rocks, in Fayers, F., and King, P., eds., The mathematical generation of reservoir geology: Oxford University Press, New York.
Fishburn, P. C., 1977, Mean-risk analysis with risk associated with below-target returns: Amer. Econ. Rev., v. 67, no. 2, p. 116-126.
Goovaerts, P., 1997, Geostatistics for natural resources evaluation: Oxford University Press, New York, 491 p.
Hightower, M. L., and David, A., 1991, Portfolio modeling: A technique for sophisticated oil and gas investors: SPE Paper No. 22016.
Ingersoll, J. E., 1987, Theory of financial decision making: Rowman & Littlefield, Savage, NJ, 474 p.
Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P., 1983, Optimization by simulated annealing: Science, v. 220, no. 4598, p. 671-680.
Lane, K. F., 1988, The economic definition of ore: Cut-off grades in theory and practice: Mining Journal Books Limited, London, 149 p.
Mao, J. C. T., 1970, Models of capital budgeting, E-V vs E-S: J. Finan. Quant. Anal., v. 4, no. 5, p. 657-675.
Markowitz, H. M., 1952, Portfolio selection: J. Finance, v. 7, no. 1, p. 77-91.
Markowitz, H. M., 1959, Portfolio selection: Efficient diversification of investments: Wiley, New York, 344 p.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E., 1953, Equation of state calculations by fast computing machines: J. Chem. Phys., v. 21, no. 6, p. 1087-1092.
Orman, M. M., and Duggan, T. E., 1999, Applying modern portfolio theory to upstream investment decision making: J. Petrol. Technol., March, p. 50-53.
Richmond, A. J., 2001, Incorporating financial risk attitudes in ore selection decisions from probabilistic models: Min. Res. Eng., v. 10, no. 1, p. 39-51.
Sortino, F. A., and van der Meer, R., 1991, Downside risk: J. Portfol. Manage., v. 18, no. 4, p. 27-31.
Speranza, M. G., 1996, A heuristic algorithm for a portfolio optimization model applied to the Milan stock market: Comput. Oper. Res., v. 23, p. 433-441.
Srivastava, R. M., 1987, Minimum variance or maximum profitability: CIM Bull., v. 80, no. 901, p. 63-68.
Stone, B. K., 1973, A general class of three-parameter risk measures: J. Finance, v. 28, p. 675-685.
von Neumann, J., and Morgenstern, O., 1953, Theory of games and economic behaviour, 3rd edn.: Princeton University Press, Princeton, NJ, 648 p.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Richmond, A. Financially Efficient Ore Selections Incorporating Grade Uncertainty. Mathematical Geology 35, 195–215 (2003). https://doi.org/10.1023/A:1023239606028
Issue Date:
DOI: https://doi.org/10.1023/A:1023239606028