Study On Optimum Of Cutoff Grade In Underground Mine Based On Dynamic Programming Method

Cutoff grade is an important parameter in mining process and is a critical grade used to distinguish ore and waste stone. The selection of cutoff grade affects production scale, production life-span and mining plan of mine and even utilization rate of non-renewable resource through the mine quantity and its grade distribution. As a given deposit, it exist a optimal cutoff grade which could maximize the economic benefits of the entire mine, with the certain technical and economic conditions. To define the cutoff grade is a key decision-making, in mining production. Cutoff grade optimization is one of the major research projects, in the modern mining industry.The dynamic programming is a optimal algorithm in operations research, and is a mathematical method to solve the optimization problem of multistage decision process. The dynamic programming is a gradual improvement method, and it parts the problem into a series of sub-problems which have similar structure. The dynamic programming of cutoff grade optimization divides exploitation process into several stages, considers a number of constraint conditions, and obtains the best cutoff grade of various stages targeting the NPV or profit as optimum objective. Ore-body mining sequence, mine production capacity, ore grade's spatial distribution and other factors were considered, in the dynamic programming of cutoff grade optimization, and the optimal results is in accord with the actual mine.On the base of dynamic programming idea, the mining process is divided into transition mining stages of the before and after, and one state is a optimization unit. A stage includes a number of states, and the state variable of a stage was showed by cumulate mining quantity from start to this stage mining finished. Every state has mining quantity in the stage, and cutoff grade of every state could be obtained from the distribution graph of grade VS mine quantity of optimize unit. Profit of mining quantity could be calculated by the investment of mining process and the mining cost of using the corresponding mining method. Then, the profit could be converted into the NPV of initial stage, according the production time which could be calculated by the annual production capacity of mine. The NPV of this state is equal to that NPV of the former transition state add on NPV obtained by the mining quantity of this stage. The cutoff grade and the NPV of each state were calculated to the final stage (final optimize unit) with similar method. The state whose NPV is maximum is found out, in last stage, and this state is deduced reversely by the transition order. Then, the optimal transition (also called optimal decision-making) of every stage was obtained. The optimal result of this cutoff grade optimization problem was composed of all optimal decision-makings. According to the above optimization ideas, a new dynamic programming model of cutoff grade optimization was established, in which the NPV was targeted as function, and mining method, mine production capacity, ore grade's spatial distribution, impoverishment rate in mining and some main parameters of technical and economic were considered.With actual production of Zambia Chambishi copper mine, optimization target was divided into 12 Optimization units which had their grade distribution. With the parameter values of technical and economic of two mining method(backfill mining method and caving mining method), optimal cutoff grade of Chambishi copper mine was obtained, using the dynamic programming model of cutoff grade optimization. The Optimization result is:On the whole, the cutoff grade of using backfill mining method is higher than using caving mining method, of which cutoff grade of optimization unit-2,3,8,10 are higher than cutoff grade of using caving mining method, and the cutoff grade of other eight optimization units do not change. The NPV of using backfill mining method and caving mining method are 232884409 dollars and 209635929 dollars respectively. Based on maximizing the NPV, using backfill mining method is more economical, in actual production of mine. Finally, parameters sensitivity about the model are analyzed, and result is:discount rate, concentrate grade, recovery rate in ore-dressing, mining costs and fixed cost are more sensitive to cutoff grade of optimizative;and recovery rate in ore-dressing, the price of concentrate, concentrate grade and rate of poverty are more sensitive to the total NPV. Through analyzing the impact characteristics of these parameters, we can adjust parameters values to improve the economic benefits of mining, combining technical and economic parameters indicators and according to the results of sensitivity analysis of parameters.