Optimization model of surface mine production rate

J. Changsheng and Z. Youdi

Fil:Fi2 + opt.

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where NPV is the net present value, Res. is the reserves in the mining limits, ANPV is the NPV increment with varied PR difference, AA, is the increment of PR and Fi1:Fi2 is the matching ratio of Factor 1 to Factor 2. These calculations are subject to: A .x 2 (or I )A, where A is the coefficient matrix of constraints; x is a variable; A, is the upper or lower limit of one constraint.
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Introduction
Production rate (PR) is a critical element in surface mine decision making. Many essential operating parameters are functions of the production rate. These include the size of the processing plant, the infrastructure and the amount of capital investment. Because amine's revenue is closely related to the PR, it is very important to optimize the mine's PR during mine planning. Since the 1970s, several coal deposits suitable for surface mining have been discovered in China. Some of these are now in operation, while others are still in the planning stage. However, research on production-rate optimization cannot keep up with the development of coal mines. In some mineplanning programs, production rates can vary significantly, and the selected PR may not be strongly supported by sufficient data. In this paper, a comprehensive optimization model of the surface-mine production rate is proposed. A mine is used to demonstrate the model's application.

Optimization steps
The eight optimization steps are: Step 1: Optimizing mining parameters under certain mining method and limits. Step 2: Estimation of initial capital investment and operating cost in a determined annual production rate. Step 3: Cash-flow analysis in different PR to get NPV. Step 4: Economy-of-scale analysis. Step 5: Constraints analysis. Step 6: Determination of economic PR. Step 7: Optimizing reserves in the mining limits. Step 8: Matching related factors to PR.

Optimization model
The optimization of surface-mine production rate is affected by many factors. Different evaluation methods can reach quite different conclusions. Taking into consideration the influence of various factors, a comprehensive optimization model was developed. The model is based on a systemengineering approach, on the theory of economy of scale and on technical economics. The model is described below. The objective functions of the model are: maximum net present value per ton of reserves NPV/Res.

Example of model
The Anjialing surface coal mine (AJLM) was chosen to illustrate the application of the model as follows: Step 1: Basic mining parameters determination. A shovel and truck system was selected as the mining method with the coal reserves at 1,500 Mt. Because coal seams are shallow-dipping, the overburden can be dumped into the mining void after the pit floor is exposed. The optimized box cut length is about 1,500 m, with the overburden depth of about 160 to 200m.

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maximum NPV increment with the increase of PR ANPVJAAp + max.

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J. Changsheng and Z. Youdi are with the Department of Mining Engineering, China University of Mining and Technology,Xuzhou Jiangsu, P.R. China. Nonmeetingpaper number 98-342. Original manuscript submittedfor review July 1998. Paper accepted for publication March 1999. Discussion of this peer-reviewed paper is invited and must be submitted to SME prior to Sept. 30, 2000.
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Table 1 - AJLM Cash Flow Analysis (US$1.OO = Y8.30).

Step 4: Economy-of-scaleanalysis. The aim is to know if the increment of NPV is more than that of the capital investment. Step 5: Constraints analysis. The coal produced from AJLM can be used in China or exported. The coal is mainly transported by rail. Therefore, the first constraint is the railway capacity from mine to customs, which in recent years cannot be more than 20 Mt/a. The second constraint is the advance speed of the working face, which limits the amount of exposed coal reserves in a shovel and truck mining system. Annual exposed-coal reserves can range from 26 to 39 Mt. Present market demand and investment money are not seen as constraints. From the constraint analysis mentioned above, the maximum annual production rate of AJLM cannot exceed 20 Mt. Step 6: The interval of economy of scale. The upper limit of the production rate is determined by constraint analysis, while the lower limit is dependent on the payback period of the money investedor the internal rate of return. Using a set discount rate of 12%, the minimum production rate of the mine should not be lower than 15.87 Mt/a.

year
300.00 150.00 100.00 75.00 60.00 50.00 42.86 37.50 33.33 30.00 27.27 25.00 23.08 21.43 20.00 18.75 17.65 16.67 15.79 15.00 14.29 13.64 13.04 12.50

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

-1 103.53 -606.86 107.71 943.78 1,858.1 1 2,822.06 3,818.90 4,818.64 5,810.67 6,771.66 7,733.83 8,622.97 9,504.59 10,400.24 11,114.99 12,063.41 12,781.80 13,496.54 14,220.94 14,466.41 15,197.63 15,971.30 16,076.28 16,920.69

45.01 1 17.75 776.22 96.88 51.88 35.32 26.18 20.59 16.54 14.21 1 1.50 10.22 9.42 6.87 8.53 5.96 5.59 5.37 1.73 5.05 5.09 0.66 5.25

450.60 366.00 324.08 297.28 278.03 263.24 251.34 241.47 233.09 225.83 219.47 213.81 208.74 204.15 199.97 196.13 192.60 189.33 186.28 183.43 180.77 178.26 175.90 173.67

Step 2: Capital and operating costs. The capital cost is calculated according to

Step 7: Optimization of reserves in the mining limits. From the first objective function mentioned above, the optimum tonnage in the mining limits is determined to get maximum NPV per ton of reserves (NPVIptr.). Table 2 show that the optimum deposit tonnage should be from 450 to 550 Mt, with an annual PR of from 15.87 to 20Mt.
Step 8: Determine the optimum matching between some essential elements. These elements include:

1 1 3.76 107.55 104.51 102.60 101.25 100.22 99.42 98.76 98.21 97.75 97.35 97.01 96.71 96.45 96.21 96.01 95.82 95.65 95.50 95.37 95.25 95.14 95.04 94.95

where Ki is thecapital investmentofApi (Ch annual production rate); KO is the capital investment at the A (which is known to be 324.08Y/t, US$1.00 ~ 8 . 3 0 y ; Api is the annual production rate (to be determined); ApOis the annual production rate of 15 Mt/a; and n is the empirical index, which is equal to 0.7. The operating cost of unit operations is determined by comparing it with a neighboring mine having the same conditions, i.e., drilling and blasting costs of 1.54Y/m3,excavation costs of 1.74Y/m3,hauling costs of 2. 16Y/m3-km,dumping costs of 0.41Y/t, auxiliary costs of 3.67Y/m3 and a stripping ratio of 5.16 m3/t. Internal dump trucks travel around end walls. Trucks are used to convey the coal from the working faces to the crusher, which is located at the end wall. After crushing, the coal is sent to the processing plant through a conveyer tunnel. The fixed cost is calculated according to the capital investments at different PRs.
Step 3: Cash-flow analysis. Acomputerprogram is formed to calculate cash flow in and out with a discount rate of 12%. The net present values of varied PRs are listed in Table 1.The selling price of the raw coal is set at 169.00Ylt.
T O A h l C A P T l n h l C 1000 \ m l
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the ratio of mine lifetime to discounted years of major mining equipment should be the least common multiple or in its round numbers, mine production rate is exactly divided by mining equipment production and the number of mining equipment is equal or near to that of working benches. Taking into consideration the optimum match of the essential elements listed above, the mining limits should be divided into three pits, with each pit having a deposit tonnage of 500 Mt, an annual PR of 16.67 Mt and a lifetime of about 30 years.

Conclusion
The proposed optimization model of the surface-mine production rate, based on the systems-engineering approach and on the theory of economy of scale, can take into consideration the mine production rate, the deposit tonnage in the mining limits and other important elements related to PR. From the application of the model, it is concluded that deposit tonnage in the mining limits, mine lifetime and
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Table 2 - NPVA of reserves with vaned production rate (US$l .OO = Y8.30).
Reserve, Annual PR, Mt Mt Lifetime, year NPV, MY NPVlptr., Ylt Reserve, Annual PR, Mt M t Lifetime, year NPV, MY NPVlptr., Ylt

annual productionrate should be well matched to maximize net present value per ton of reserves in the open pit.

Cao, E., 1995, Project Evaluation, Publishing House of Wuhan University, 3, pp. 96-98. Cavender, B., 1992, "Determination of the optimum lifetime of a mining project using discounted cash flow and option pricing techniques," Mining Engineering, Vol. 44, No. 10, Oct., pp. 1262-1268.

References
Li, Z., 1989, "A theoretical approachto determination of mine life and design capacity," International J. of Surface Mining,3 , pp. 49-50.

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