A linear programming model for long-term mine planning in the presence of grade uncertainty and a stockpile

The complexity of an open pit production scheduling problem is increased by grade uncertainty. A method is presented to calculate the cost of uncertainty in a production schedule based on deviations from the target production. A mixed integer linear programming algorithm is formulated to find the min- ing sequence of blocks from a predefined pit shell and their respective destinations, with two objectives： to maximize the net present value of the operation and to minimize the cost of uncertainty. An efficient clustering technique reduces the number of var/ables to make the problem tractable. Also, the parameters that control the importance of uncertainty in the optimization problem are studied. The minimum annual mining capacity in presence of grade uncertainty is assessed. The method is illustrated with an oil sand deposit in northern Alberta.

The Roles of Spatial Locations and Patterns of Initial Errors in the Uncertainties of Tropical Cyclone Forecasts

In this study, a series of sensitivity experiments were performed for two tropical cyclones （TCs）, TC Longwang （2005） and TC Sinlaku （2008）, to explore the roles of locations and patterns of initial errors in uncertainties of TC forecasts. Specifically, three types of initial errors were generated and three types of sensitive areas were determined using conditional nonlinear optimal perturbation （CNOP）, first singular vector （FSV）, and composite singular vector （CSV） methods. Additionally, random initial errors in randomly selected areas were considered. Based on these four types of initial errors and areas, we designed and performed 16 experiments to investigate the impacts of locations and patterns of initial errors on the nonlinear developments of the errors, and to determine which type of initial errors and areas has the greatest impact on TC forecasts. Overall, results from the experiments indicate the following： （1） The impact of random errors introduced into the sensitive areas was greater than that of errors themselves fixed in the randomly selected areas. From the perspective of statisticul analysis, and by comparison, the impact of random errors introduced into the CNOP target area was greatest. （2） The initial errors with CNOP, CSV, or FSV patterns were likely to grow faster than random errors. （3） The initial errors with CNOP patterns in the CNOP target areas had the greatest impacts on the final verification forecasts.