Strip mine mining plan optimization method based on boundary grade dynamic change

Abstract

The invention aims to provide a strip mine mining plan optimization method based on boundary grade dynamic change in order to solve the problems of the existing strip mine mining plan optimization method. According to the technical scheme, the method comprises the following steps of 1, generating a decision-making unit, namely generating an alternative mining position; 2, constructing a mining plan optimization mathematical model; and step 3, boundary grade-mining plan collaborative optimization. According to the method disclosed by the invention, the ore rock attributes can be quickly decided along with the change of market conditions and technical conditions, and the ore rock quantity is dynamically adjusted, so that the purpose of maximizing the overall economic benefit of a mine is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of open-pit mining, and in particular relates to an open-pit mining plan optimization method based on dynamic changes in boundary grade. Background Art

[0002] In order to maximize the overall dynamic economic benefits of mining (i.e., the maximum net present value NPV), the determination of the cut-off grade must consider two aspects: one is the dynamic characteristics of the cut-off grade in time; the other is the dynamic characteristics of the cut-off grade in space. In other words, the optimal cut-off grade changes with time and with the mining location, and the two are interrelated.

[0003] To optimize the mining plan within a defined final boundary is to determine the annual ore production and rock stripping volume (production capacity), mining location (mining sequence), and mining life (production life) within this final boundary, so as to maximize the final economic benefits (NPV). For an actual open-pit mine, in theory, there are any number of mining locations each year (each possible mining location is called a decision unit here), and there are many possible production capacities each year, and the corresponding production life will also change accordingly (especially when the boundary grade of each year is also changing). When the total annual mining volume of the mine is constant, if different boundary grades are selected, it means that the amount of ore in the 100 million tons will also be different. For an open-pit mine that has been mined for decades, the technical and economic parameters will change greatly, which will lead to changes in the boundary grade. In other words, the boundary grade of the open-pit mining plan that divides its ore and rock types each year will also change dynamically with the development of time and space. Therefore, it is unreasonable to design a mining plan for decades under a fixed boundary grade according to the traditional method.

[0004] The relevant technologies of existing open-pit mining planning optimization methods are:

[0005] Chinese patent application CN202311324867.8 "A method and system for determining the grade index of low-grade polymetallic ore" is a static determination method for ore body delineation, which does not consider the impact of open-pit production plan. The master's thesis "Dynamic optimization and application of open-pit mine boundary grade based on metal price fluctuations" published in 2022 evaluates the reasonable boundary grade settings in different periods for the established final boundary and mining plan, without considering that changes in boundary grade will also react on the preparation of the plan. The journal paper "Research on Boundary Grade Optimization of Open-pit Mining of a Copper Deposit" published in 2013 optimizes the boundary with a certain boundary grade step size to find the optimal boundary grade under the maximum profit plan, without considering the impact of the mining plan on the optimization plan. Summary of the invention

[0006] The purpose of the present invention is to provide an open-pit mining plan optimization method based on the dynamic change of boundary grade to solve the problems existing in the existing open-pit mining plan optimization method. The method of the present invention can make rapid decisions on the properties of ore and rock as the market situation and technical conditions change, and dynamically adjust the amount of ore and rock to achieve the purpose of maximizing the overall economic benefits of the mine.

[0007] The present invention proposes an open-pit mining plan optimization method based on dynamic changes in cut-off grade, comprising the following steps:

[0008] Step 1: Generate decision-making units, that is, generate alternative mining locations

[0009] The ore rock within the planned final boundary of the open-pit mine is discretized into many blocks. One or some of these discretized blocks are the locations that may be mined in a certain year in the future. These discretized blocks are called decision-making units.

[0010] The decision-making unit is generated as follows:

[0011] Step 1.1: Cut the planned final boundary range on the XY horizontal plane into several rectangular or square modules in the horizontal and vertical directions, and mark the ore grade of each module; and construct a cone shell template with the top of the cone facing upward and the angle between the cone shell and the horizontal plane equal to the working slope angle, which is large enough to cover the current final boundary range on the XY horizontal plane; and set the ore rock increment between adjacent decision units to ΔQ;

[0012] Step 1.2: Take the current final state as the initial decision-making unit, and the first current final state is the planned final state;

[0013] Step 1.3: Set a row of modules in the vertical direction as a module column; set the module column serial number i, i = 1, 2, ..., n;

[0014] Step 1.4: Place the vertex of the cone shell template at the center of the lowest module of module column i in the current decision-making unit, where the lowest module is the first module from the bottom whose center elevation is greater than the side or bottom elevation of the current decision-making unit;

[0015] Step 1.5: Find all modules in the current decision-making unit that fall into the cone shell template, calculate the ore volume, rock volume and average grade of the cone shell template (the average grade is equal to the metal content of the ore divided by the total amount of ore and rock); if the ore volume of the cone shell template is less than or equal to ΔQ, place the cone in a cone array from low to high according to the average grade, and then proceed to step 1.6; if the ore volume of the cone is greater than ΔQ, the cone is discarded and go to step 1.7;

[0016] Step 1.6: Move the cone shell template upward along the module column i by one step. If the top height of the cone shell template is higher than the given distance of the ground elevation at the module column, proceed to step 1.7; otherwise, return to step 1.5;

[0017] Step 1.7: If module column i is not the last module column within the current decision unit, take the next module column, that is, set i=i+1, and return to step 1.4; otherwise, execute the next step.

[0018] Step 1.8: At this point, all the module columns within the current decision-making unit have been "scanned" to obtain a cone array consisting of n cone shell templates sorted from low to high according to the average grade; find the "union" of the first m cone shell templates from the array (the union does not include any overlapping parts between cones) so that the mineral volume of the union is closest to ΔQ;

[0019] Step 1.9: Exclude the cone shell template complex from the current decision unit, that is, raise the bottom elevation of each module column affected by the cone shell template in the complex to the cone shell elevation at the center line of the module column, and a new decision unit is obtained, which is stored;

[0020] Step 1.10: Calculate the ore volume of the new decision-making unit; if its ore volume is greater than ΔQ, use this new decision-making unit as the current decision-making unit and return to step 1.3 to generate the next smaller decision-making unit; otherwise, all decision-making units have been generated and the step ends;

[0021] Step 2: Construction of mathematical model for mining plan optimization

[0022] According to the above decision-making unit generation method, a series of optimal decision-making units {P *} N , the optimization of mining plan is the sequence {P *} N Find the optimal subsequence {P *} m (m≤N); in the sequence {P *} N Find the optimal subsequence {P *} m , is the number of years t (t = 1, 2, ..., m) in the mining plan at {P *} NFind an optimal decision unit as the stope to be mined until the end of the year to maximize the total net present value; the number of decision units m in the optimal subsequence is the optimal mining life of the mine; the tth (t = 1, 2, ..., m) decision unit in the subsequence is the optimal position and shape to which the stope should be advanced at the end of the tth year; the ore and waste rock amount of the first decision unit in the subsequence is the optimal mining and stripping production capacity in the first year, and the ore and waste rock amount between the tth and t-1th decision units is the optimal mining and stripping production capacity in the tth year;

[0023] Step 2.1: Find the optimal subsequence and use dynamic programming to optimize the mining plan:

[0024] Let mining time be the stage variable and decision-making unit be the state;

[0025] The decision unit (i.e., state) P at stage t i * , it can be compared with P from the previous stage t-1 i * The smaller decision-making units are transferred; when P at stage t i * is the decision unit P at stage t-1 j * (t-1≤j≤i-1), the amount of ore mined in the tth stage (i.e., the tth year) is q t,i (t-1,j), unit is tons, the metal content is m t,i (t-1,j), in tons, the amount of waste rock stripped is w t,i (t-1,j), unit is tons, then the state transfer equation in the dynamic programming process can be expressed as:

[0026] q t,i (t-1,j)=Q i * -Q j * (1)

[0027] m t,i (t-1,j)=M i * -M j * (2)

[0028] w t,i (t-1,j)=W i * -W j * (3)

[0029] In the formula, Q i *: After considering the ore recovery rate and waste rock mixing rate during mining, the decision unit sequence {P *} N The i-th decision unit P i * The amount of ore, that is, P i * The amount of ore mined, in tons;

[0030] W i * : After considering the ore recovery rate and waste rock mixing rate during mining, the decision unit sequence {P *} N The i-th decision unit P i * The amount of waste rock, that is, P i * The amount of waste rock mined, in tons;

[0031] M i * :Q i * The amount of metal contained in the waste rock (taking into account the grade of waste rock mixed in), in tons;

[0032] The profit p generated by this state transition t,i (t-1,j), the identity element, is:

[0033]

[0034] Where P p (t): concentrate price in year t, which can be a constant or change with time, in RMB;

[0035] c m (t): unit mining cost of ore in year t, in yuan;

[0036] c w (t): unit stripping and disposal cost of waste rock in year t, in Yuan;

[0037] c p (t): unit beneficiation cost of the beneficiation plant in year t, i.e., the cost of processing 1 ton of ore, in RMB;

[0038] r p : Ore dressing recovery rate;

[0039] g p : Concentrate grade;

[0040] The cumulative net present value (NPV) achieved at the end of year t t,i (t-1,j), the unit element, is

[0041]

[0042] In the formula, NPV t-1,j is the decision unit P that reaches the previous stage t-1 along the best path j * The cumulative net present value of the unit yuan has been calculated when evaluating the various states of the previous stage and is known; starting from the first year, the net present value comparison is made for each additional year, and the path with the largest net present value is retained, that is, the best path;

[0043] Step 2.2: The state transition with the maximum cumulative NPV is the best state transition (i.e. the optimal decision in dynamic programming). Therefore, there is the following recursive objective function:

[0044]

[0045] The starting conditions at time 0 (initial state) are:

[0046]

[0047] Step 2.3: Using the above formulas, starting from stage 1, evaluate all states (decision-making units) at each stage step by step until all states at all stages are evaluated, and then the optimal state transfer and cumulative NPV of all decision-making units at all stages are obtained;

[0048] Step 3: Cut-off grade-mining plan collaborative optimization

[0049] After a series of decision-making units are generated in the final realm, the cut-off grade needs to be dynamically considered each year during the mining plan optimization process to maximize the total net present value;

[0050] Step 3.1: Since the decision unit sequence order {P *} N There are N decision-making units in total. According to the above, one decision-making unit corresponds to one stage, so the number of stages is the number of decision-making units, that is, the number of stages is N; the situation or condition of each stage is called state, and the state is defined as the cumulative ore volume, that is, a state of a stage is the total amount of ore mined from the beginning of mining to the end of the stage; let the state expression be S i,j , i represents the stage, i=1, ..., N, j represents that a state in the i-th stage is j;

[0051] The number of states in each stage depends on the grade distribution of the decision-making units corresponding to this stage and the previous stages, as well as the required calculation resolution; the resolution here is the ore increment of adjacent states at a certain stage, the preset upper and lower limits of the boundary grade [g dn ,g up], and determine the maximum ore quantity Q of each decision unit based on this upper and lower limit up and minimum ore quantity Q dn , and then according to the designed resolution (Δq, that is, the increment of adjacent states), all states corresponding to each stage can be obtained;

[0052] Step 3.2: Take the state S at stage i i,j , when S i,j It is the state S from the previous stage (i-1) i-1,k When it arrives, the amount of ore mined in the decision unit i corresponding to stage i in this state transition is q i,j (i-1,k), in tons, is:

[0053] q i,j (i-1,k)=Q i,j -Q i-1,k (8)

[0054] In the formula, Q i,j For state S i,j The corresponding cumulative ore volume, in tons;

[0055] Q i-1,k For state S i-1,k The corresponding cumulative ore volume, in tons;

[0056] This equation establishes the connection between states at adjacent stages and is called the state transfer equation;

[0057] Step 3.3: Corresponding to the ore quantity q i,j The cut-off grade g of (i-1,k) i,j (i-1, k) can be obtained from the incremental part ΔQ between decision unit i and decision unit i-1 i,i-1 The grade-volume relationship is obtained, that is, g i,j (i-1,k) is the cut-off grade that satisfies the following equation:

[0058]

[0059] Where ΔQ i,i-1 is the total amount when the cut-off grade between decision unit i and decision unit i-1 is 0, in tons;

[0060] g i,i-1 represents the ore grade between decision making unit i and decision making unit i-1;

[0061] f i (g) is the incremental part ΔQ i,i-1 The distribution density function of the internal mineral grade is obtained based on the samples falling into the decision unit; the mineral quantity q can also be obtained based on the grade-ore quantity table i,j(i-1,k) corresponds to the boundary grade; here g i,j (i-1, k) is collectively called the production cutoff grade;

[0062] Step 3.4: In this state transfer, according to the production cut-off grade g i,j (i-1,k) The amount of ore mined q i,j The amount of metal contained in (i-1,k) is denoted as M i,j (i-1, k), in tons, is calculated by the following formula (can also be found in the grade-metal content table):

[0063]

[0064] In this state transition, the rock mass w i,j (i-1,k), unit tons:

[0065] w i,j (i-1,k)=ΔQ i,i-1 -q i,j (i-1,k) (11)

[0066] Step 3.5: So, when state S i,j It is the state S from the previous stage (i-1) i-1,k When transferred, the profit P from the sale of concentrate i,j (i-1,k), the identity element, can be calculated as follows:

[0067]

[0068] In the formula, c m (t) is the unit mining cost of mining stage i in year t, in RMB;

[0069] c p (t) is the unit beneficiation cost of mining stage i in year t, in RMB;

[0070] r m is the recovery rate;

[0071] r p is the mineral processing recovery rate;

[0072] r w is the waste rock mixing rate;

[0073] g p is the concentrate grade;

[0074] P(t) is the selling price of concentrate in mining stage i in year t, which can be a constant, in units of yuan;

[0075] In the above formula, the first item is the sales of mining products, the second item is the mining and beneficiation costs (taking into account the mixing of waste rock and the recovery rate) in the process of extracting ore and sending it to the beneficiation plant to select the concentrate, and the third item is the rock stripping cost (taking into account the mixing of waste rock and the recovery rate);

[0076] Step 3.6: Increment ΔQ i,i-1 Mining volume q i,j The time required for (i-1,k) is t i,j (i-1,k), in years, is:

[0077]

[0078] In the formula, m i is the mining increment ΔQ in stage i i,i-1 The planned mining capacity (in tons / year) can be a constant;

[0079] Step 3.7: When state S i,j From state S i-1,k When arriving, from the beginning to state S i,j The cumulative time required is recorded as T i,j (i-1,k), in years, is calculated using the following formula:

[0080] T i,j (i-1,k)=T i-1,k +t i,j (i-1,k) (14)

[0081] Step 3.8: Pass state S i-1,k To S i,j Transfer, S i,j The cumulative net present value NPV achieved i,j (i-1,k), the identity element, is:

[0082]

[0083] Step 3.9: When state S i,j When different states from stage i-1 (i.e. different k) are taken, the amount of ore mined in stage i (Equation 8) is different, and the corresponding cut-off grade, mining time and metal content are also different; then, state S i,j The cumulative NPV achieved at each state is also different; therefore, for a state S i,j , each state transition has a cut-off grade and cumulative net present value; then, the transition corresponding to the maximum NPV is the best transition, and its corresponding cut-off grade is state S i,j The best cut-off grade, g i,j ; Thus, the recursive function of dynamic programming is:

[0084]

[0085] Where: K i,j It is the state S that can be transferred from stage i-1 to stage i i,j The number of states;

[0086] The above formulas (8) to (14) combine the cut-off grade with the profit P i,j (i-1,k) and time T i,j (i-1, k), so formula (16) implies the optimal production cutoff grade g i,j Choice;

[0087] The initial conditions are:

[0088]

[0089] Step 3.10: Apply the above formulas, starting from the first stage, evaluate the state stage by stage until all states in all stages are completed, and the optimal state transfer and the corresponding optimal cut-off grade and NPV of each state in each stage are obtained;

[0090] Step 3.11: Starting from the state with the maximum NPV in the last stage, trace the optimal state transfer of each stage in reverse until the first stage, and then get the optimal path, that is, the optimal strategy of dynamic programming; this optimal strategy gives the optimal cut-off grade, corresponding ore volume and economic benefits that should be used when mining each decision unit; according to the time cumulative recording function T i,j (i-1,k), with one year as a time length, then the decision unit corresponding to the end of a certain year is the mining position of the mine in that year, and the ore production capacity of the corresponding year is also obtained; in one year's production, multiple decision units may be mined across, which means that different production boundary grades may be used in different mining areas within a year; in this way, the annual production capacity of the mine and the boundary grade, mining sequence and mining life adopted in that year are obtained at the same time.

[0091] The beneficial effects of the present invention are:

[0092] The present invention proposes an open-pit mining plan optimization method based on dynamic changes in boundary grade. In the process of mining plan optimization, when deciding whether to mine a certain area in a certain year, the market situation and technical conditions of the year are comprehensively considered, the best boundary grade in the environment is calculated, and the ore and rock properties are quickly decided, and the ore and rock quantity is dynamically adjusted to maximize the overall economic benefits of the mine. The present invention not only considers the time value of funds, but also considers the mutual influence relationship between different mining periods in the entire mining plan, so that the economic benefits and resource utilization of the mine are comprehensively optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 A schematic diagram of the cone exclusion method for generating candidate mining locations (decision making units) in the present invention;

[0094] Figure 2 Dynamic programming diagram for cut-off grade-plan collaborative optimization;

[0095] Figure 3 A schematic diagram of the ore and rock quantities corresponding to all decision-making units at a cut-off grade of 20%;

[0096] Figure 4 This is a schematic diagram of the cumulative ore and rock volume of the 100th decision-making unit;

[0097] Figure 5 This is the mineral quantity statistics chart for the grade interval of the 100th decision-making unit. DETAILED DESCRIPTION

[0098] The invention will be further described below with reference to the accompanying drawings and specific implementation examples.

[0099] The present invention proposes an open-pit mining plan optimization method based on dynamic changes in boundary grade, such as Figures 1 to 5 As shown, the following steps are included:

[0100] Step 1: Generate decision-making units, that is, generate alternative mining locations

[0101] The internal ore rock of the planned final boundary of the open-pit mine is discretized into many blocks. One or some of these discretized blocks are the locations that may be mined in a certain year in the future. As for which block is the best location for the corresponding year, it is necessary to make an optimized decision, so these discretized blocks are called decision-making units;

[0102] The decision-making unit is generated as follows:

[0103] Step 1.1: Cut the planned final boundary range on the XY horizontal plane into several rectangular or square modules in the horizontal and vertical directions, and mark the ore grade of each module; and construct a cone shell template with the top of the cone facing upward and the angle between the cone shell and the horizontal plane equal to the working slope angle, the size of which is sufficient to cover the current final boundary range on the XY horizontal plane; and set the ore rock increment between adjacent decision units to ΔQ; the smaller the value of ΔQ, the more accurate the result of the decision unit, but it will greatly increase the amount of calculation, so it will be set to about 1 / 10 of the mining capacity in the present invention;

[0104] Step 1.2: Take the current final state as the initial decision unit. The first current final state is the planned final state. Figure 1For example, the black solid line first represents the final state range of a certain section obtained by the above-mentioned final state optimization; the state marked by the black solid line is the planned state, that is, the initial decision unit;

[0105] Step 1.3: Set a row of modules in the vertical direction as a module column; set the module column serial number i, i = 1, 2, ..., n;

[0106] Step 1.4: Place the vertex of the cone shell template at the center of the lowest module of module column i in the current decision-making unit, where the lowest module is the first module from the bottom whose center elevation is greater than the side or bottom elevation of the current decision-making unit;

[0107] Step 1.5: Find all modules (whole and partly whole) in the current decision-making unit that fall into the cone shell template, and calculate the ore volume, rock volume and average grade of the cone shell template (the average grade is equal to the metal content of the ore divided by the total amount of ore and rock); if the ore volume of the cone shell template is less than or equal to ΔQ, place the cone in a cone array from low to high according to the average grade, and then proceed to step 1.6; if the ore volume of the cone is greater than ΔQ, the cone is discarded and go to step 1.7;

[0108] Step 1.6: Move the cone shell template upward along the module column i by one step. If the top height of the cone shell template is higher than the given distance of the ground elevation at the module column, proceed to step 1.7; otherwise, return to step 1.5;

[0109] Step 1.7: If module column i is not the last module column within the current decision-making unit, take the next module column, that is, set i=i+1, and return to step 1.4; otherwise, execute the next step;

[0110] Step 1.8: At this point, all the module columns within the current decision-making unit have been "scanned" to obtain a cone array consisting of n cone shell templates sorted from low to high according to the average grade; find the "union" of the first m cone shell templates from the array (the union does not include any overlapping parts between cones) so that the mineral volume of the union is closest to ΔQ;

[0111] Step 1.9: Exclude the cone shell template complex from the current decision unit, that is, raise the bottom elevation of each module column affected by the cone shell template in the complex to the cone shell elevation at the center line of the module column, and a new decision unit is obtained, which is stored;

[0112] Step 1.10: Calculate the ore volume of the new decision-making unit; if its ore volume is greater than ΔQ, use this new decision-making unit as the current decision-making unit and return to step 1.3 to generate the next smaller decision-making unit; otherwise, all decision-making units have been generated and the step ends.

[0113] Step 2: Construction of mathematical model for mining plan optimization

[0114] According to the above decision-making unit generation method, a series of optimal decision-making units {P *} N , then the optimization problem of mining plan becomes a problem in the sequence {P *} N Find the optimal subsequence {P *} m (m≤N) problem; in the sequence {P *} N Find the optimal subsequence {P *} m , is the number of years t (t = 1, 2, ..., m) in the mining plan at {P *} N The optimal decision-making unit is found as the stope to be mined until the end of the year to maximize the total net present value. An optimal subsequence is found, and the number of decision-making units m in the subsequence is the optimal mining life of the mine. The t-th (t=1, 2, ..., m) decision-making unit in the subsequence is the optimal position and shape to which the stope should be advanced at the end of the t-th year. The ore and waste rock quantities of the first decision-making unit in the subsequence are the optimal mining and stripping production capacity in the first year, and the ore and waste rock quantities between the t-th and t-1-th decision-making units are the optimal mining and stripping production capacity in the t-th year. It can be seen that in the decision-making unit sequence {P *} N By finding the optimal subsequence, we can simultaneously obtain the optimal solution for the three elements of production planning: mining life, mining sequence and production capacity.

[0115] Step 2.1: The process of finding the optimal subsequence is a typical dynamic programming process; therefore, this project uses dynamic programming to optimize the mining plan:

[0116] Let mining time be the stage variable and decision-making unit be the state;

[0117] Consider the decision unit (i.e., state) P at stage t i * , it can be compared with P from the previous stage t-1 i * The smaller decision-making units are transferred; when P at stage t i * is the decision unit P at stage t-1 j * (t-1≤j≤i-1), the amount of ore mined in the tth stage (i.e., the tth year) is q t,i (t-1,j), unit is tons, the metal content is m t,i (t-1,j), in tons, the amount of waste rock stripped is wt,i (t-1,j), unit is tons, then the state transfer equation in the dynamic programming process can be expressed as:

[0118] q t,i (t-1, j) = Q i * -Q j * (1)

[0119] m t,i (t-1, j) = M i * -M j * (2)

[0120] w t,i (t-1, j)= W i * -W j * (3)

[0121] In the formula, Q i * : After considering the ore recovery rate and waste rock mixing rate during mining, the decision unit sequence {P *} N The i-th decision unit P i * The amount of ore, that is, P i * The amount of ore mined, in tons;

[0122] W i * : After considering the ore recovery rate and waste rock mixing rate during mining, the decision unit sequence {P *} N The i-th decision unit P i * The amount of waste rock, that is, P i * The amount of waste rock mined, in tons;

[0123] M i * :Q i * The amount of metal contained in the waste rock (taking into account the grade of waste rock mixed in), in tons;

[0124] The profit p generated by this state transition t,i (t-1,j), the identity element, is:

[0125]

[0126] Where Pp (t): concentrate price in year t, which can be a constant or change with time, in RMB;

[0127] c m (t): unit mining cost of ore in year t, in yuan;

[0128] c w (t): unit stripping and disposal cost of waste rock in year t, in Yuan;

[0129] c p (t): unit beneficiation cost of the beneficiation plant in year t, i.e., the cost of processing 1 ton of ore, in RMB;

[0130] r p : Ore dressing recovery rate;

[0131] g p : Concentrate grade;

[0132] The cumulative net present value (NPV) achieved at the end of year t t,i (t-1,j), the unit element, is

[0133]

[0134] In the formula, NPV t-1,j is the decision unit P that reaches the previous stage t-1 along the best path j * The cumulative net present value has been calculated when evaluating the states of the previous stage and is known. Starting from the first year, the net present value is compared for each additional year, and the path with the largest net present value, that is, the best path, is retained.

[0135] This equation is a recursive equation, which is a recursive equation of the NPV in the formula t-1,j Explain, explain what it means;

[0136] Step 2.2: Decision making unit P at stage t i * It can be transferred from multiple decision-making units in the previous stage t-1. Different transfers lead to different amounts of ore, metal and waste rock mined in year t (Formulas 1 to 3), and different profits realized in the current year (Formula 4). The decision-making unit P in stage t calculated by formula (5) is i * The cumulative NPV at is also different. The state transition with the largest cumulative NPV is the best state transition (i.e. the optimal decision in dynamic programming), so there is the following recursive objective function:

[0137]

[0138] The starting conditions at time 0 (initial state) are:

[0139]

[0140] Step 2.3: Using the above formulas, starting from stage 1, evaluate all states (decision-making units) at each stage step by step until all states at all stages are evaluated. The optimal state transfer and cumulative NPV of all decision-making units at all stages are obtained.

[0141] Step 3: Cut-off grade-mining plan collaborative optimization

[0142] In the final state Figure 1 After a series of decision-making units are generated, the traditional mining plan design approach is to use the same cut-off grade (generally the design cut-off grade when demarcating the boundary). However, considering that the cut-off grade is a function of variables such as price and cost, these variables may fluctuate at any time, especially the price, and mining production is a long-term behavior. Therefore, it is necessary to dynamically consider the cut-off grade every year during the mining plan optimization process to maximize the total net present value.

[0143] Step 3.1: Let one decision unit be one stage, so the number of stages is the number of decision units. The situation or condition of each stage is called state. The state is defined as the cumulative ore volume, that is, a state of a stage is the total amount of ore mined from the beginning of mining to the end of the stage, such as Figure 2 shown.

[0144] Figure 2 The dynamic planning diagram shown in the figure means that: the horizontal axis represents the stage, and the decision-making unit sequence order {P *} N There are N decision-making units in total. According to the above, one decision-making unit corresponds to one stage, so the number of stages is N. The vertical axis represents the cumulative ore volume. Taking stage 3 as an example, the vertical direction S corresponding to stage 3 is 3,1 , S 3,2 , S 3,3 …, S 3,M3 , is a state expression, which expresses that the decision unit 3 takes g at the boundary grade 3,j (1≤j≤M3) corresponds to the cumulative amount of ore. Let the state expression be S i,j , i represents the stage, i=1, ..., N, j represents that a state in the i-th stage is j; the state expression S 3,M3The subscripts in the table indicate that the total number of states in the third stage is M3. The number of states in each stage depends on the grade distribution of the decision-making units corresponding to this stage and the previous stages, as well as the required calculation resolution. The resolution here is the ore increment of adjacent states in a certain stage. In order to reduce the amount of calculation, the upper and lower limits of the boundary grade are generally preset [g dn ,g up ], and determine the maximum mine Q of each decision-making unit based on this upper and lower limits up Stone volume and minimum Q dn The amount of ore, and then according to the designed resolution (Δq, that is, the increment of adjacent states), all states corresponding to each stage can be obtained, such as S 3,2 and S 3,3 The difference in the amount of ore between the two is Δq. 1,2 Transfer to state S 2,2 (As shown by the red arrow in the figure), the ore increment is state S 2,2 The corresponding cumulative ore volume Q 2,2 Subtract state S 1,2 The corresponding cumulative ore volume Q 1,2 , this increment is q 2,2 (1,2) indicates that the cut-off grade corresponding to this increment (actually the amount of ore after decision unit 1 is removed from decision unit 2) is g 2,2 (1,2), state S 1,2 The corresponding cut-off grade is g 1,2 (0,0);

[0145] Step 3.2: Figure 2 Take stage i as an example, take the state S in stage i i,j , when S i,j It is the state S from the previous stage (i-1) i-1,k When it arrives, the amount of ore mined in the decision unit i corresponding to stage i in this state transition is q i,j (i-1,k), in tons, is:

[0146] q i,j (i-1,k)=Q i,j -Q i-1,k (8)

[0147] In the formula, Q i,j For state S i,j The corresponding cumulative ore volume, in tons;

[0148] Q i-1,k For state S i-1,k The corresponding cumulative ore volume, in tons;

[0149] To be precise, the amount of ore q i,j(i-1, k) is actually the incremental part ΔQ between decision unit i and decision unit i-1 i,i-1 The amount of ore that can be mined in the process (because decision unit i completely contains decision unit i-1); this equation establishes the connection between the states in adjacent stages, which is called the state transfer equation;

[0150] Step 3.3: Corresponding to the ore quantity q i,j The cut-off grade g of (i-1,k) i,j (i-1, k) can be obtained from the incremental part ΔQ between decision unit i and decision unit i-1 i,i-1 The grade-volume relationship is obtained, that is, g i,j (i-1,k) is the cut-off grade that satisfies the following equation:

[0151]

[0152] Where ΔQ i,i-1 is the total amount when the cut-off grade between decision unit i and decision unit i-1 is 0, in tons;

[0153] g i,i-1 represents the ore grade between decision making unit i and decision making unit i-1;

[0154] f i (g) is the incremental part ΔQ i,i-1 The distribution density function of the internal mineral grade is obtained based on the samples falling into the decision unit; the mineral quantity q can also be obtained based on the grade-ore quantity table i,j (i-1,k) corresponds to the boundary grade; here g i,j (i-1, k) is collectively called the production cutoff grade;

[0155] Step 3.4: In this state transfer, according to the production cut-off grade g i,j (i-1,k) The amount of ore mined q i,j The amount of metal contained in (i-1,k) is denoted as M i,j (i-1, k), in tons, is calculated by the following formula (can also be found in the grade-metal content table):

[0156]

[0157] In this state transition, the rock mass w i,j (i-1,k), unit tons:

[0158] w i,j (i-1,k)=ΔQ i,i-1 -q i,j (i-1,k) (11)

[0159] Step 3.5: So, when state S i,j It is the state S from the previous stage (i-1) i-1,k When transferred, the profit P from the sale of concentrate i,j (i-1,k), the identity element, can be calculated as follows:

[0160]

[0161] In the formula, c m (t) is the unit mining cost of mining stage i in year t, in RMB;

[0162] c p (t) is the unit beneficiation cost of mining stage i in year t, in RMB;

[0163] r m is the recovery rate;

[0164] r p is the mineral processing recovery rate;

[0165] r w is the waste rock mixing rate;

[0166] g p is the concentrate grade;

[0167] P(t) is the selling price of concentrate in mining stage i in year t, which can be a constant, in units of yuan;

[0168] In the above formula, the first item is the sales of mining products, the second item is the mining and mineral processing costs (taking into account the mixing of waste rock and the recovery rate) in the process of mining the ore and sending it to the beneficiation plant to select the concentrate, and the third item is the rock stripping cost (taking into account the mixing of waste rock and the recovery rate).

[0169] Step 3.6: Increment ΔQ i,i-1 Mining volume q i,j The time required for (i-1,k) is t i,j (i-1,k), in years, is:

[0170]

[0171] In the formula, m i is the mining increment ΔQ in stage i i,i-1 The planned mining capacity (in tons / year) can be a constant;

[0172] Step 3.7: When state S i,j From state S i-1,k When arriving, from the beginning to state S i,j The cumulative time required is recorded as T i,j (i-1,k), in years, is calculated using the following formula:

[0173] T i,j (i-1,k)=T i-1,k +t i,j (i-1,k) (14)

[0174] Step 3.8: Pass state S i-1,k To S i,j Transfer, S i,j The cumulative net present value NPV achieved i,j (i-1,k), the identity element, is:

[0175]

[0176] Step 3.9: If Figure 2 As shown, state S i,j It can be transferred from different states in the previous stage. It is not difficult to understand that when state S i,j When different states from stage i-1 (i.e. different k) are taken, the amount of ore mined in stage i (Equation 8) is different, and the corresponding cut-off grade, mining time and metal content are also different; then, state S i,j The cumulative NPV achieved at each state is also different; therefore, for a state S i,j , each state transition ( Figure 2 Middle finger pointing to S i,j Each arrow line of has a cut-off grade and cumulative net present value; then, the transition corresponding to the maximum NPV is the best transition, and its corresponding cut-off grade is state S i,j The best cut-off grade, g i,j ; Thus, the recursive function of dynamic programming is:

[0177]

[0178] Where: K i,j It is the state S that can be transferred from stage i-1 to stage i i,j The number of states;

[0179] The above formulas (8) to (14) combine the cut-off grade with the profit P i,j (i-1,k) and time T i,j (i-1, k), so formula (16) implies the optimal production cutoff grade g i,j Choice;

[0180] The initial conditions are:

[0181]

[0182] Step 3.10: Apply the above formulas, starting from the first stage, and evaluate the status stage by stage until completion Figure 2 All states at all stages in the process are calculated, and the optimal state transfer and the corresponding optimal cut-off grade and NPV of each state at each stage are obtained;

[0183] Step 3.11: Starting from the state with the maximum NPV in the last stage, trace the optimal state transfer of each stage in reverse until the first stage, and then get the optimal path, that is, the optimal strategy of dynamic programming; this optimal strategy gives the optimal cut-off grade, corresponding ore volume and economic benefits that should be used when mining each decision unit; according to the time cumulative recording function T i,j (i-1,k), with one year as a time length, then the decision unit corresponding to the end of a certain year is the mining position of the mine in that year, and the ore production capacity of the corresponding year is also obtained; in one year's production, multiple decision units may be mined across, which means that different production boundary grades may be used in different mining areas within a year; in this way, the annual production capacity of the mine and the boundary grade, mining sequence and mining life adopted in that year are obtained at the same time.

[0184] In order to illustrate the problem in a vivid and intuitive way, and in particular to quantitatively evaluate the effectiveness of the method of the present invention, this example optimizes the mining plan by dynamically considering the boundary grade within the boundary obtained when the iron ore price of a certain iron mine is 750 yuan / t.

[0185] The open-pit mining plan optimization method based on the dynamic change of cut-off grade includes the following steps:

[0186] Step 1: Generate decision-making units. In the final state of a certain iron ore obtained at 750 yuan / t, a series of 204 geological optimal decision-making units are generated according to the parameter settings in Table 1.

[0187] Table 1. Parameter settings for generating geological optimal decision-making units

[0188]

[0189] Step 1.1: Construct a cone shell template. The template's azimuth slope angle is designed according to the actual working slope design during mine production, which is 15°.

[0190] Step 1.2: The final boundary of Qidashan Iron Mine obtained when the price is set to 750 yuan / t is the initial decision unit (according to the initial boundary grade of 20%, the amount of ore within the boundary is 310.606 million tons and the amount of rock is 355.127 million tons).

[0191] Step 1.3: Set the module column number i=1, that is, take module column 1 within the current decision unit range.

[0192] Step 1.4: Place the vertex of the cone shell template at the center of the lowest module with module column i in the current decision-making unit. This module is the first module from the bottom whose center elevation is greater than the side or bottom elevation of the current decision-making unit.

[0193] Step 1.5: Find all modules (whole and part) that fall into the cone in the current decision-making unit, and calculate the ore volume, rock volume and average grade of the cone (average grade equals the metal content of the ore divided by the total amount of ore and rock). If the ore volume of the cone is less than or equal to 1.5 million tons, place the cone in a cone array from low to high according to the average grade, and proceed to the next step; if the ore volume of the cone is greater than 1.5 million tons, the cone is discarded and go to step 1.7.

[0194] Step 1.6: Move the cone up one step along module column i. If the top height of the cone shell template is already a given distance higher than the ground elevation at the module column, proceed to the next step; otherwise, return to step 1.5.

[0195] Step 1.7: If module column i is not the last module column within the current decision unit, take the next module column, that is, set i=i+1, and return to step 1.4; otherwise, execute the next step.

[0196] Step 1.8: So far, all the module columns within the current decision-making unit have been "scanned" and a cone array consisting of 2,500 cones sorted from low to high by average grade has been obtained. Find the "combination" of the first m cones from the array (the union does not include any overlapping parts between cones) so that the ore volume of the union is closest to 1.5 million tons.

[0197] Step 1.9: Exclude the cone union from the current decision unit, that is, raise the bottom elevation of each module column affected by the cone in the union to the cone shell elevation at the center line of this module column, and a new decision unit is obtained, which is stored.

[0198] Step 1.10: Calculate the ore volume of the decision-making unit obtained in the previous step. If the ore volume is greater than 1.5 million tons, use this new decision-making unit as the current decision-making unit and return to step 1.3 to generate the next smaller decision-making unit (1.5 million tons less ore volume); otherwise, all decision-making units have been generated and the algorithm ends.

[0199] So far, it takes 5 minutes to generate 204 decision-making units. The ore volume between adjacent decision-making units is basically around 1.5 million tons, and the error of the fluctuation range is less than 1%, as shown in Figure 3.

[0200] Step 2: Mining plan optimization

[0201] Step 2.1: The basic parameters for mining plan optimization are set as shown in Table 2.

[0202] Table 2. Mining plan optimization parameter settings

[0203]

[0204]

[0205] Step 2.2: For all decision-making units, starting from the boundary grade of 1%, gradually increase in steps of 1%, and count the corresponding cumulative ore volume (including original volume and mined volume), rock volume (including original volume and mined volume), concentrate volume, original grade, mined grade; the interval ore volume and concentrate volume corresponding to the step of 1%, etc., totaling 4.131 million sets of data. The boundary grade-ore and rock volume statistics chart and grade interval ore volume statistics chart for the 100th decision-making unit are as follows: Figure 4 and Figure 5 shown.

[0206] Step 3: Cutoff grade-mining plan collaborative optimization. During the optimization process, the net present value corresponding to different cutoff grades in different state transitions in a certain year is automatically calculated based on the dynamic programming model. Here, the traditional mining plan optimization results based on a given cutoff grade are compared with the cutoff grade-plan collaborative optimization results proposed in this application, as shown in Tables 3 and 4, respectively.

[0207] Table 3. Optimization results of mining plan based on given cut-off grade

[0208]

[0209]

[0210] Table 4. Results of collaborative optimization of cut-off grade and mining plan

[0211]

[0212] From the optimization results of the two mining plans, it can be seen that the total amount of ore and rock in the boundary is 665.3983 million tons. However, due to the different boundary grade values ​​each year, for example, in the first year, the boundary grade of the traditional mining plan is 20%, while according to the optimization design method proposed in this application, the boundary grade is 26.49%; the average grade in the first year is 33.11% for the former and 34.95 for the latter; from the average boundary grade, the former is 20% and the latter is 25.9%; from the average grade, the former is 29.15% and the latter is 32.87%; from the perspective of ore and rock volume, the boundary grade of the boundary grade dynamic optimization method proposed by this application is 29.5% higher than that of the traditional optimization design, so the ore volume is reduced by 85.653 million tons, which is classified as rock. However, from the perspective of overall economic benefits, the net present value increased by 14.2%. Huge economic benefits have been generated. The optimization results also give the mining period, annual stripping volume, mining location, annual economic benefits, etc.

[0213] In summary, compared with the traditional mining plan optimization design, the open-pit mining plan optimization method based on the dynamic change of the boundary grade in this embodiment has higher economic benefits. And for the optimization of mining plans under different market conditions, this embodiment has good generalization performance. The model of this embodiment can quickly make plan adjustments according to different technical and economic conditions, and can conduct comprehensive analysis of the economy and feasibility of multiple plans.

Claims

1. A method for optimizing open-pit mining plans based on dynamic changes in cut-off grade, characterized in that: The following steps are involved: Step 1: Generate decision-making units, that is, generate alternative mining locations The ore rock within the planned final boundary of the open-pit mine is discretized into many blocks. One or some of these discretized blocks are the locations that may be mined in a certain year in the future. These discretized blocks are called decision-making units. The decision-making unit is generated as follows: Step 1.1: Cut the planned final boundary range on the XY horizontal plane into several rectangular or square modules in the horizontal and vertical directions, and mark the ore grade of each module; and construct a cone shell template with the top of the cone facing upward and the angle between the cone shell and the horizontal plane equal to the working slope angle, which is large enough to cover the current final boundary range on the XY horizontal plane; The ore-rock increment between adjacent decision-making units is set to ΔQ; Step 1.2: Take the current final state as the initial decision-making unit, and the first current final state is the planned final state; Step 1.3: Set a row of modules in the vertical direction as a module column; set the module column serial number i, i = 1, 2, ..., n; Step 1.4: Place the vertex of the cone shell template at the center of the lowest module of module column i in the current decision-making unit, where the lowest module is the first module from the bottom whose center elevation is greater than the side or bottom elevation of the current decision-making unit; Step 1.5: Find all modules in the current decision-making unit that fall into the cone shell template, and calculate the ore volume, rock volume and average grade of the cone shell template; if the ore volume of the cone shell template is less than or equal to ΔQ, place the cone in a cone array from low to high according to the average grade, and then proceed to step 1.6; if the ore volume of the cone is greater than ΔQ, the cone is discarded and go to step 1.7; Step 1.6: Move the cone shell template upward along the module column i by one step. If the top height of the cone shell template is higher than the given distance of the ground elevation at the module column, proceed to step 1.7; otherwise, return to step 1.5; Step 1.7: If module column i is not the last module column within the current decision-making unit, take the next module column, that is, set i=i+1, and return to step 1.4; otherwise, execute the next step; Step 1.8: At this point, all module columns within the current decision-making unit have been "scanned" to obtain a cone array consisting of n cone shell templates sorted from low to high according to average grade; find the "combination" of the first m cone shell templates from the array so that the ore volume of the combination is closest to ΔQ; Step 1.9: Exclude the cone shell template complex from the current decision unit, that is, raise the bottom elevation of each module column affected by the cone shell template in the complex to the cone shell elevation at the center line of the module column, and a new decision unit is obtained, which is stored; Step 1.10: Calculate the ore volume of the new decision-making unit; if its ore volume is greater than ΔQ, use this new decision-making unit as the current decision-making unit and return to step 1.3 to generate the next smaller decision-making unit; otherwise, all decision-making units have been generated and the step ends; Step 2: Construction of mathematical model for mining plan optimization According to the above decision-making unit generation method, a series of optimal decision-making units {P * } N , the optimization of mining plan is the sequence {P * } N Find the optimal subsequence {P * } m (m≤N); in the sequence {P * } N Find the optimal subsequence {P * } m , is the number of years t (t = 1, 2, ..., m) in the mining plan at {P * } N Find an optimal decision unit as the stope to be mined until the end of the year to maximize the total net present value; the number of decision units m in the optimal subsequence is the optimal mining life of the mine; the tth (t = 1, 2, ..., m) decision unit in the subsequence is the optimal position and shape to which the stope should be advanced at the end of the tth year; the ore and waste rock amount of the first decision unit in the subsequence is the optimal mining and stripping production capacity in the first year, and the ore and waste rock amount between the tth and t-1th decision units is the optimal mining and stripping production capacity in the tth year; Step 3: Cut-off grade-mining plan collaborative optimization After a series of decision units are generated in the final realm, the cut-off grade needs to be dynamically considered each year in the mining plan optimization process to maximize the total net present value.

2. The method for optimizing open-pit mining plan based on dynamic change of cut-off grade according to claim 1 is characterized in that: Step 2 The specific method of constructing the mining plan optimization mathematical model includes the following steps: Step 2.1: Find the optimal subsequence and use dynamic programming to optimize the mining plan: Let mining time be the stage variable and decision-making unit be the state; The decision unit P at stage t i * , it can be compared with P from the previous stage t-1 i * The smaller decision-making units are transferred; when P at stage t i * is the decision unit P at stage t-1 j * (t-1≤j≤i-1), in the tth stage, that is, in the tth year, the amount of ore mined is q t,i (t-1,j), unit is tons, the metal content is m t,i (t-1,j), in tons, the amount of waste rock stripped is w t,i (t-1,j), unit is tons, then the state transfer equation in the dynamic programming process can be expressed as: In the formula, After considering the ore recovery rate and waste rock mixing rate during mining, the decision-making unit sequence {P * } N The i-th decision unit P i * The amount of ore, that is, P i * The amount of ore mined, in tons; After considering the ore recovery rate and waste rock mixing rate during mining, the decision-making unit sequence {P * } N The i-th decision unit P i * The amount of waste rock, that is, P i * The amount of waste rock mined, in tons; The amount of metal contained in the waste rock (taking into account the grade of waste rock mixed in), in tons; The profit p generated by this state transition t,i (t-1,j), the identity element, is: Where P p (t): concentrate price in year t, which can be a constant or change with time, in RMB; c m (t): unit mining cost of ore in year t, in yuan; c w (t): unit stripping and disposal cost of waste rock in year t, in Yuan; c p (t): unit beneficiation cost of the beneficiation plant in year t, i.e., the cost of processing 1 ton of ore, in RMB; r p : Ore dressing recovery rate; g p : Concentrate grade; The cumulative net present value (NPV) achieved at the end of year t t,i (t-1,j), the unit element, is In the formula, NPV t-1,j is the decision unit P that reaches the previous stage t-1 along the best path j * The cumulative net present value of , in units of yuan, has been calculated when evaluating the states of the previous stage and is known; Starting from the first year, a net present value comparison is made for each additional year, and the path with the largest net present value is retained, which is the best path; Step 2.2: The state transition with the maximum cumulative NPV is the best state transition, that is, the optimal decision in dynamic programming. Therefore, there is the following recursive objective function: The starting conditions at time 0 (initial state) are: Step 2.3: Using the above formulas, starting from stage 1, evaluate all states and decision-making units at each stage step by step until all states at all stages are evaluated. The optimal state transfer and cumulative NPV of all decision-making units at all stages are obtained.

3. The method for optimizing open-pit mining plan based on dynamic change of cut-off grade according to claim 1, characterized in that: Step 3 The specific method of the cut-off grade-mining plan collaborative optimization includes the following steps: Step 3.1: Since the decision unit sequence order {P * } N There are N decision-making units in total. According to the above, one decision-making unit corresponds to one stage, so the number of stages is the number of decision-making units, that is, the number of stages is N; the situation or condition of each stage is called state, and the state is defined as the cumulative ore volume, that is, a state of a stage is the total amount of ore mined from the beginning of mining to the end of the stage; let the state expression be S i,j , i represents the stage, i=1, ..., N, j represents that a state in the i-th stage is j; The number of states in each stage depends on the grade distribution of the decision-making units corresponding to this stage and the previous stages, as well as the required calculation resolution; the resolution here is the ore increment of adjacent states at a certain stage, the preset upper and lower limits of the boundary grade [g dn ,g up ], and determine the maximum ore quantity Q of each decision unit based on this upper and lower limit up and minimum ore quantity Q dn , and then according to the designed resolution Δq, that is, the increment of adjacent states, all states corresponding to each stage can be obtained; Step 3.2: Take the state S at stage i i,j , when S i,j It is the state S from the previous stage (i-1) i-1,k When it arrives, the amount of ore mined in the decision unit i corresponding to stage i in this state transition is q i,j (i-1,k), in tons, is: qi,j(i-1,k)=Qi,j-Qi-1,k (8) In the formula, Q i,j For state S i,j The corresponding cumulative ore volume, in tons; Q i-1,k For state S i-1,k The corresponding cumulative ore volume, in tons; This equation establishes the connection between states at adjacent stages and is called the state transfer equation; Step 3.3: Corresponding to the amount of ore q i,j The cut-off grade g of (i-1,k) i,j (i-1, k) can be obtained from the incremental part ΔQ between decision unit i and decision unit i-1 i,i-1 The grade-volume relationship is obtained, that is, g i,j (i-1,k) is the cut-off grade that satisfies the following equation: Where ΔQ i,i-1 is the total amount when the cut-off grade between decision unit i and decision unit i-1 is 0, in tons; g i,i-1 represents the ore grade between decision making unit i and decision making unit i-1; f i (g) is the incremental part ΔQ i,i-1 The distribution density function of the internal mineral grade is obtained based on the samples falling into the decision unit; the mineral quantity q can also be obtained based on the grade-ore quantity table i,j (i-1,k) corresponds to the boundary grade; here g i,j (i-1,k) is called the production cut-off grade; Step 3.4: In this state transfer, according to the production cut-off grade g i,j (i-1,k) The amount of ore mined q i,j The amount of metal contained in (i-1,k) is denoted as M i,j (i-1, k), in tons, is calculated by the following formula, or can be found in the grade-metal content table: In this state transition, the rock mass w i,j (i-1,k), unit tons: Step 3.5: So, when state S i,j It is the state S from the previous stage (i-1) i-1,k When transferred, the profit P from the sale of concentrate i,j (i-1,k), the identity element, can be calculated as follows: In the formula, c m (t) is the unit mining cost of mining stage i in year t, in RMB; c p (t) is the unit beneficiation cost of mining stage i in year t, in RMB; r m is the recovery rate; r p is the mineral processing recovery rate; r w is the waste rock mixing rate; g p is the concentrate grade; P(t) is the selling price of concentrate in mining stage i in year t, which can be a constant, in units of yuan; In the above formula, the first item is the sales of mining products, the second item is the mining and mineral processing costs in the process of extracting ore and sending it to the mineral processing plant to select concentrate, and the third item is the rock stripping cost; Step 3.6: Increment ΔQ i,i-1 Mining volume q i,j The time required for (i-1,k) is t i,j (i-1,k), unit: year: In the formula, m i For stage i, the mining increment ΔQ i,i-1 The planned mining capacity at that time can be a constant in tons / year; Step 3.7: When state S i,j From state S i-1,k When arriving, from the beginning to state S i,j The cumulative time required is recorded as T i,j (i-1,k), in years, is calculated using the following formula: Ti,j(i-1,k)=Ti-1,k+ti,j(i-1,k) (14) Step 3.8: Pass state S i-1,k To S i,j Transfer, S i,j The cumulative net present value NPV achieved i,j (i-1,k), the identity element, is: Step 3.9: When state S i,j Different states from stage i-1, that is, when different k is taken, the amount of ore mined in stage i is different, and the corresponding boundary grade, mining time and metal content are also different; then, state S i,j The cumulative NPV achieved at each state is also different; therefore, for a state S i,j , each state transition has a cut-off grade and cumulative net present value; then, the transition corresponding to the maximum NPV is the best transition, and its corresponding cut-off grade is state S i,j The best cut-off grade, g i,j ; Thus, the recursive function of dynamic programming is: Where: K i,j It is the state S that can be transferred from stage i-1 to stage i i,j The number of states; The above formulas (8) to (14) combine the cut-off grade with the profit P i,j (i-1,k) and time T i,j (i-1, k), so formula (16) implies the optimal production cut-off grade g i,j Choice; The initial conditions are: Step 3.10: Apply the above formulas, starting from the first stage, evaluate the state stage by stage until all states in all stages are completed, and the optimal state transfer and the corresponding optimal cut-off grade and NPV of each state in each stage are obtained; Step 3.11: Starting from the state with the maximum NPV in the last stage, trace the optimal state transfer of each stage in reverse until the first stage, and then get the optimal path, that is, the optimal strategy of dynamic programming; this optimal strategy gives the optimal cut-off grade, corresponding ore volume and economic benefits that should be used when mining each decision unit; according to the time cumulative recording function T i,j (i-1,k), with one year as a time length, then the decision unit corresponding to the end of a certain year is the mining position of the mine in that year, and the ore production capacity of the corresponding year is also obtained; in one year's production, multiple decision units may be mined across, which means that different production boundary grades may be used in different mining areas within a year; in this way, the annual production capacity of the mine and the boundary grade, mining sequence and mining life adopted in that year are obtained at the same time.

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