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Blast schedule planning and shiftwise production scheduling of an opencast iron ore mine
~ Pergamon
Computers ind. Engng Vol. 28, No. 4, pp. 927-935, 1995 Copyright © 1995 Elsevier Science Ltd 0360-8352(94)00221-5 Printed in Great Britain. All rights reserved 0360-S352/95 $9.50+0.00
BLAST SCHEDULE PLANNING AND SHIFTWISE PRODUCTION SCHEDULING OF AN OPENCAST IRON ORE MINE DIATHA KRISHNA SUNDAR t and DAMODAR ACHARYA 2 IVinod Gupta School of Management, Indian Institute of Technology, Kharagpur 721 302, India 2Department of Industrial Engineering and Management, Indian Institute of Technology, Kharagpur 721, India
(Received 2 December 1994) Abstract--In this paper we present a computer integrated system for short-range mine production planning that uses: (i) a linear programming model for the choice of blocks to be blasted; (ii) a stochastic programming model for the selection of the blasted areas to be excavated and in deciding the quantity of ores and wastes to be mined from each of the selected blocks. The model also gives the shiftwise allocation of dumpers to support the excavation plan. The above two models use improved estimates for the ore body characteristics utilizing: the blast hole data in addition to the usual bore hole statistics to improve the prediction accuracy of the block level ore body characteristics. The software is developed in C-language and has four modules for ore body characteristics prediction, blast scheduling, shiftwise production planning and report generation. The results include shiftwise block level blasting and excavation plans for each bench, benchwise shovel-dumper allocation plan. The developed software has been applied to planning the production of a captive iron ore mine of Steel Authority of India Ltd.
1. INTRODUCTION
Production planning in an opencast mine deals with the problems of." (i) selecting the blocks to be blasted in the benches exposed for mining; (ii) deciding the quantities of ores and wastes to be excavated in each time period from each of the blasted blocks; and (iii) blending of the mined ores so that the periodwise demands, in terms of quality and quantity, for ores can be met utilizing the limited resources available to the mine. These short-range decisions are made within the limitations of the long-range mine plan that maximizes the utilization of ore reserves while giving a mine face development programme. Thus a good mine production plan must not only meet both the longand short-range mining requirements but also satisfy many practical details that are unique to day-to-day operations. For example average quality and quantity estimates are good enough for both long- and short-range mine planning but inadequate for day-to-day production scheduling. For such purposes, the variations in these estimates are equally important. Intra block and inter block variations in the quality and quantity of available reserve, uncertainty in quantum of available resources due to breakdown and absenteeism call for frequent updating of a production plan. This necessitates the use of a user-friendly, flexible computer integrated system for mine production planning. The complexity of the system increases further due to large number of variables and constraints whose parameter values cannot be estimated with certainty. Practical mining constraints like minimum desirable safety width, bench height and accessibility constraints add to this complexity. Several authors have considered the problem of production planning in mines. Mutmansky [6] gives a comprehensive review of the application of various operations research techniques including linear programming, integer linear programming, quadratic programming, dynamic programming, simulation and heuristics to production scheduling in mines. Gershon [5] and Barbaro and Ramani [1] considered the problem of finding a production schedule for opencast mines. While Barbaro and Ramani [1] aim at maximizing the financial benefit for a situation where a group of mines supply ore to a set of plants each with its known demand in terms of quantity and quality, the emphasis of Gershon [5] is to optimize the life of a mine in long-, intermediate- and short-range planning. Kostas et aL [8] considered the problem of long- and short-range open pit production 927
928
Diatha Krishna Sundar and DamodarAcharya
scheduling using a simulation approach for the former and a linear programming model for the latter. Very few authors have considered the problem of developing shiftwise operational plans. Exceptions are the works of Chanda [2] and Wooller [I1]. Chanda [2] uses a mixed-integer programming formulation to minimize the deviation from the quality targets for developing a shiftwise production schedule for an underground mine. The software package of Wooller [11] does not give the details of the models/techniques used in finding intermediate or short-range production schedules for opencast/underground mines. This paper deals with the problem of shiftwise production planning for a captive opencast iron ore mine so that the demands for iron ore can be effectively met using available resources like shovels, dumpers and crushing mill of known capacities. While doing so, the plan ensures a supply of ores to the plants such that the quality (in terms of Fe, A1203, SiO2 contents) are within the acceptable range. The system proposed consists of the following four distinct modules: a module for getting improved Kriging estimators for the ore quality and quantity of the blocks to be blasted and excavated, a linear programming module for blast planning, and a stochastic linear programming module for shiftwise excavation planning and a report generation module. A central database and user interfaces facilitate the communication between modules and the system with the users. The model developed has been applied to planning the production of a captive mine of Steel Authority of India Ltd (SAIL).
2. IMPROVEDKRIGING ESTIMATION MODULE At a given point of time, the choice of blocks for excavation is limited to already blasted ones as the blasting is done only at fixed intervals (usually weekly off days). This makes blast planning and the production planning problems inseparable. Further, blast planning as to necessarily depend on relatively inaccurate Kriging estimates obtained from the analysis of basic bore hole statistics. As for a block more reliable estimates can be obtained by analyzing the blast hole data, and the deficiencies in earlier estimates can be at least partially made up by excavating from several blasted blocks and by blending them in suitable proportions. However, it is important to note that blending alone cannot help to meet the quality and quantity characteristics of customer demand if the initial choice of blasting blocks is wrong. The solution lies in getting a more accurate estimate of the block level reserve characteristics before blasting. As the drift in the ore quality in the vertical direction of the ore body under consideration is negligible, the improvement in block level 2-D Kriging estimators has primarily come from the use of blast hole data from the adjacent blocks, in addition to the bore hole statistics. The model uses the conventional method of normal Kriging (David [3], Journal [7]). The details of the methodology used for getting updated and improved estimators are discussed in a separate paper (Sundar and Acharya [4]).
3. BLASTPLANNING MODEL The objective of the blast planning module is to determine the blocks, from the available benches of an opencast mine, to blast for the following production period so that the demand in terms of both quality and quantity of the period can be met. This situation is modelled as a linear programming problem. The module maximizes the number of blocks to blast, subject to the transport capacity, demand (quality and quantity), and block size, bench safety width, and block, bench precedence constraints. For the purpose of modelling, the ore body has been divided into several benches of 10/12 m height each and each bench into rectangular blocks of 30 x 30 m size. A smaller block size could not be used as the accuracy of the Kriging estimators becomes questionable if the block size is less than 30 x 30 m for a bore hole grid size of 60 x 60 m [3, 7]. A block in the ore body is uniquely defined by specifying the column numbers (grid numbers) in the x, y and z directions from the orion.
Blast schedule p l a n n i n g a n d shiftwise p r o d u c t i o n scheduling
929
Table 1 x, y
z (bench) 1
1.5 1.7 1.9 2.3 2.5 2.7 3.9 4.7 4.9
2
3 0.290
4
5
1.000 1.000 0.425 1.000 1.000 1.000 1.000 1.000
3.1. Notation B~.y,z= a block B located in the intersection of xth, yth and zth columns;
Ox.y,z = ore available in block Bx,y,:; W~.~.~= waste available in Bx.~.:; QoldO:x,y,:= uncleared ore of the previous blasts in block Bx,y,~; uncleared waste of the previous blasts in block Bx,y,~; average transport cycle time for ore from block B~,y,~ to crushing mill; average transport cycle time for waste from block Bx,y,~ to waste yard; total transport time available; average quality of ith mineral in block B~,y,~; Ki:~ow,r= lower limit on acceptable quality of ith mineral for the planning period; K~:upp,r= upper limit on acceptable quality of ith mineral for the planning period; Sw = safety width (minimum width to be maintained for any bench in terms of block width); Cap = capacity of the dumper; De = ore demand; 6x,y.~= a variable that takes value one if block B~,~,~is fully to be blasted and zero if it is not to be blasted. Fractional values of 6(x, y, z) represent the portion of block Bx,y,~ to be blasted;
Qo~dW:,,~.= TrOx, y,~ = TrWx,y,~ = ToTr = Ki:~,y,~=
3.2. Model Maximize the number blocks to be blasted for the given production period from all the available benches, rows and columns:
Maximize Z = Z Z Z z
x
6x.,.~
)'
Table 2 Production plan details of the week considered No. of shovels deployed = No. of dumpers deployed = Tons of ore raised = Tons of waste raised = Average quality = No. of planned dumper trips = No. of planned dumper trips/shift from Bench 1 = 40 Bench 2 = 30 Bench 3 = 25 Bench 4 = 30 Bench 5 = 30 No. of actual dumper trips made
6 8-10 52,550 T 5400 T 62.51% Fe 1860
= I 159
(1)
930
Diatha Krishna Sundarand DamodarAcharya Table 3 Resource available during the planning ~ r i o d No. of shovels No. of dumpers No. of available benches
= 6 = 10 = 5
Acceptable ore quality in any shift Minimum Fe (%) Maximum AI203 (%) Maximum SiO2 (%) Confidence interval (%)
= = = =
61.5 4 2.5 95
subject to available transport capacity constraint:
E E E [(Oo,dO:x,y,z"TrOx,y,z + QoldW:x,y,z"TrWx,y,z) + (Ox, y,z "TrOx,y,z + Wx,y,z)" TrWx, y,z)bx,y,z] z x y
Cap ~ToTr.
(2)
Demand constraint:
L 2 E (QoldO:x,y.z+ Ox, y.z "(~x.y.z) ~/De. z x y
(3)
Quality requirement constraint: E ~ ~(Qo,do:x,y,z + Ox,y/6x, y,z)
Ki:tower~<
~< Kt:upp~,•
(4)
EZ Ex Ey (QoldO:x.y,z"Ki:x,y,z+ Ox,y;" Ki:x,y;" 6x,r,z Safety width constraint:
(5)
(Ym.... - y)'6~,y.~ >1 Sw.6~,y;,
for all x, y and z. Block size constraint: 0 ~< 6x,y,~ ~< 1,
(6)
for all x, y and z. It may be noted that the scope for blending of relatively poor quality ore with rich quality ore increases if one has options to excavate from a larger number of blocks. Theoretically, utilization of the deposit can be maximized, if the entire deposit can be excavated first and stacked (possibly at a different place) according to similarity of ore quality before crushing and blending. Since, this is not practically feasible, in the blast planning model, we aim at maximizing the number of blocks to be blasted [equation (1)]. Within the practical constraints, this will maximize the scope for selective excavation, crushing and blending. Table 4. Summary sheet of shiftwise and benchwise ore excavation Shift 1 2 3 4 5 6 7 8 9 10 11 12
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5 0 2287 141 0 822 0 2287 0 0 0 0 0
2430 0 2226 2578 0 2259 0 340 2376 1335 3054 2748
0 0 1336 0 4826 368 0 0 0 3236 0 0
3403 4013 0 3504 652 605 4013 3924 1729 0 3552
459 0 2596 38 0 3068 0 360 0 0 3246 0
Blast schedule p l a n n i n g and shiftwise p r o d u c t i o n scheduling
931
Table 5. Summary sheet of shiftwise and benchwise waste excavation Shift 1 2 3 4 5 6 7 8 9 10 I1 12
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5 0 0 0 0 0 0 0 0 0 0 0 0
2930 0 0 0 0 0 0 0 0 0 0 0
4. P R O D U C T I O N
0 0 0 0 0 0 0 0 0 977 0 976
PLANNING
488 0 0 0 0 0 0 1465 0 0 0 0
0 0 0 0 0 0 0 2930 0 0 0 0
MODEL
To meet the market demand, for a defined production period, in terms o f quality and quantity o f ore, the mine production plan aims at finding the benches and blocks that are to be excavated shiftwise from the available ones. This is modelled as a chance constrained program to take care o f the random nature of ore quality and quantity characteristics and variations in operation time requirements. The important constraints on quality, mill capacity, transport capacity, ore availability and waste are explicitly considered in this model.
4.1. Notation XO,s J = XW, sJ = TrO~j = Tr I~,j = ToT, = /~.,:~,j =
Kt,,,,:l.... = K,,,.:upp~r= O~j =
Wi,j = De = CMC = SCi,, = CI =
ore to be mined from ith bench, j t h blast area in the shift t (in tons); waste to be mined from ith bench, jth blast area in the shift t (in tons); mean transport time o f ore from blast area j in bench i to ore crushing mill; mean transport time o f waste from blast area j in bench i to waste dump yard; total transport time available in shift t; mean quality of mth mineral in jth blast area of ith bench; lower limit on acceptable quality of mineral m in shift t (in percentage); upper on the quality of mineral m in shift t (in percentage); ore availability in blast area j in bench i (in tons); waste availability in blast area j in bench i (in tons); ore demand (in tons); crushing mill capacity (in tons); shoveling capacity from bench i in shift t (in tons); confidence interval.
4.2. Model
Objective. mining o f maximum ore and waste tonnage from the available blast areas during a period is considered a superior objective compared to the conventional objective of maximizing ore tonnage due to the following reasons: Table 6. Summary sheet of shifiwise and benchwise total excavation Shift 1 2 3 4 5 6 7 8 9 lO
II 12
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5 0 2287 141 0 822 0 2287 0 0 0 0 0
5369 0 2226 2758 0 2259 0 340 2376 1335 3054 2748
0 0 1336 0 4826 368 0 0 0 4213 0 976
3891 4013 0 3504 652 605 4013 1465 3924 1729 0 3552
459 0 2596 38 0 3068 0 3290 0 0 3246 0
932
Diatha Krishna Sundar and Damodar Acharya Table 7. Summary sheet of shiftwise nad bcnchwis¢ dumper trips Shift
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5
1 2 3 4 5 6 7 8 9 10 11 12
0 45 2 0 16 0 45 0 0 0 0 0
107 0 44 55 0 45 0 6 47 26 61 54
0 0 26 0 96 7 0 0 0 84 0 19
77 80 0 70 13 12 80 29 78 34 0 71
9 0 51 0 0 61 0 65 0 0 64 0
1. Often a good quality ore patch cannot be accessed unless one completely removes the waste patch in a block. In such situations removal of both waste and ore becomes essential. Further, a block in a bench cannot be accessed unless the ores and the wastes from the blocks above it are not removed. 2. The same fleet of material handling equipments are used for excavation and transportation of both ore and waste. 3. Maximization of ore tonnage excavation requires selective mining. This unhealthy practice shortens the mine's life. In view of the above, we maximize the total ore and waste to be mined from the available blast areas during the planning horizon of t shifts. This objective can be written as: maximize Z = ~ ~ ~ subject to
t
i
j
[XOt,i,j -I- XWt,i,j].
(7)
Quality restriction: ~" E XOt,i,J
PROB{Ktm.lower~. i j ~CI, for all m and t. ,. ~ Kin:ij" XOt.i,j i j
(8)
Transport capacity constraint: for all t.
(9)
Ore availability constraint: PROB { ~
XO,,i,/
Oi.j} ~ CI, for all i, j.
(lO)
Waste availability constraint:
PROB{~ XWtj,j <~IY~i,j}>~CI,
for all i, j.
(11)
Demand constraint:
~ ~ XO,,,,j >I De.
(12)
t i j
Crushing mill capacity constraint: ~/CI,
for all t.
(13)
Shoveling capacity constraint:
PROB{~[XOtij+XW, i / ],, . ., <~SC,,}>~, CI, for all i and t.
(14)
Blast scheduleplanning and shiftwiseproduction scheduling
933
XO,,ij >1O,
(15)
XW, jj i> 0.
(16)
Nonnegativity
5. COMPUTER INTEGRATED SYSTEM The weekly blast schedule module interacts with the central data base to generate the input data for the model. It generates the blast planning LP model and solves to obtain the optimal blast plan. Once the optimal solution is found it prepares the reports for the blasting department. The blast hole data from the blasted blocks are used to obtain fresh Kriging estimators for the same blocks for the purpose of excavation planning. The system then generates the stochastic production planning model and solves it to obtain the excavation plan. The report generator module utilizes the results obtained from the blast planning module to provide working plan for the production planning and control department of the mines. The actual performance data at the end of each shift is fed to the data base to generate the rolling shiftwise plan for the next week (12 shifts). This also helps in developing an alternate plan to take care of the situations arising out of equipment (shovels, dumpers, mill) failure and absenteeism. The Flow chart for the computer integrated system is given in Fig. 1. The designed computer integrated production planning system has a user interface, central data base, model generator and a report generator. The blast planning model generates blast plans and reports to blasting and production planning and control departments, and the production planning model generates the shiftwise production plans and reports to production planning and control department, truck maintenance department and production shift in-charge.
6. RESULTS The blast and production planning modules were tested on live data from one of the iron ore mines of SAIL. Blast schedule planning module results are given in Table I. Details of the production plan (old method) are given in Table 2. The resource availability for the period is shown
Prodoctionl g:dn~lri~iPonUt~ - ~
I data
Blast model input generation
I
Model generation
Model generation
I
Model solution
Model solution
Report generation
Report generation
I Production I planning and control dept.
Truck [ [ Production Blasting maintenancel shift department department I in-charge Fig. 1. Computer integrated production planning.
Production planning and control dept.
934
Diatha Krishna Sundar and D a m o d a r Acharya Table 8. Comparison of old and computer integrated system output
Sl. No. 1 2 3 4 5 6 7
Resources used
Actual practice (old method)
Shovels Dumpers Benches accessed Shiftwise requirements of: dumpers shovels Quantity of ore produced Quality of ore produced Quantity of waste produced
Computer
integrated system output
6 10 all five
5 10 all five
8-10 6 52,550 T 61.18% Fe 5400 T
6-10 4-6 69,000 T 62.4% Fe 9650 T
in Table 3. Computer integrated blast and production planning system's summarized results are given in Tables 4-7. A comparison of the old method and the new computer integrated production planning method are given in Table 8. 6.1. Blast schedule planning module results
Results obtained from the blast schedule planning module are given in Table 1. The results shown in Table 1 give the blocks selected for blasting in the considered planning period. Fractional values indicate the partial blasting of the selected blocks. For example 0.290 in the above table indicates that only 29% of the block Bt,5,3 is to be blasted during the period. 6.2. Production module results
Details of the production plan (old method) shown in Table 2. It may be noted that the old manual method assigns fixed number of dumper trips to each of the benches, where the number of trips from the bench is dependent on the average bench ore quality, available quantity of ore, available quality of waste, and the desired mine output quality and quantity. The old method restricts the excavation mostly to one block per bench. For the purpose of planning, the old method used the following resource constraints. The same set of resource constraints have also been used for planning by the proposed method. Shiftwise Shiftwise Shiftwise Shiftwise
and and and and
benchwise benchwise benchwise benchwise
ore excavation (in tons) is given in Table 4. waste excavation (in tons) is given in Table 5. total excavation (in tons) is given in Table 6. required dumper trips are given in Table 7.
A comparison of results obtained from the computer integrated system with the old method for the considered planning period is given in Table 8. Results given in Table 8 shows that the proposed computer integrated planning system requires minimum of 4 shovels as against 6 shovels in the old method. This also gives higher planned production of 69,000 tons of ore and 9650 tons of waste compared to 52,500 tons of ore and 5400 tons of waste in the old method. The proposed computer integrated planning system requires minimum of only 6 dumpers (against 8 in the old method). The greater number of spare dumpers may now be available as a standby to take care of breakdowns. The new method also gives marginally higher Fe quality (62.4% compared to 62.18% in the old method). REFERENCES 1. R. W. Barbaro and R. V. Ramani. Generalized multi-period M I P model for production scheduling and processing facilities selection and location. Min. Engng 107-114 (1986). 2. E. C. K. Chanda. An application o f integer programming and simulation to production planning for a stratiform body. Min. Sci. Technol. 11, 165-172 (1990). 3. M. David. Geostatistical Ore Reserve Estimation. Elsevier Scientific, A m s t e r d a m (1977). 4. D. K. Sundar and D. Acharya. 2D-Kriging: removing the shadow effect. Trans. Insm. Min. Met. (Section A: Min. Ind.). Communicated. 5. M. E. Gershon. Mine scheduling optimization using MIP. Min. Engng, Apr. 351-353 (1983). 6. Jan M. Mutmansky. Computing and operations research techniques for production scheduling. Computer Methods for 80's. (Edited by A. Weiss), pp. 610-614 (1980).
Blast schedule planning and shiftwise production scheduling
935
7. A. G. Journal and Ch. J. Huijbregts. Mining Geostatistics. Academic Press, New York (1978). 8. K. Fytas et al. Optimization of open pit short and long range production scheduling. CIM Bull. Aug. 55-61 (1987). 9. E. R. Muller and C. K. Young. Introductory Review. Computer Methods for 80's. (Edited by A. Weiss), pp. 610-614 (1980). I0. Q. X. Yun and T. M. Yegulalp. Optimum scheduling of overburden removal in open-pit mines. CIM Bull. Dec. (1982). 11. R. Wooller. Production scheduling system. Trans. Instn. Min. Metall. (Sec. A, Min. Industry), Vol. 101 (1992). 12. C. K. Young. Production scheduling--technical overview. Computer Methods for 80's. (Edited by A. Weiss), pp. 610-614 (1980). 13. F. L. Wilke and W. Woehrle. A model for short-range planning and monitoring of mining in potassium deposits of level formation. 16th APCOM (Edited by T. J. O'Neil), pp. 304-312 (1980).
CAIE 28/4~-Q
Computers ind. Engng Vol. 28, No. 4, pp. 927-935, 1995 Copyright © 1995 Elsevier Science Ltd 0360-8352(94)00221-5 Printed in Great Britain. All rights reserved 0360-S352/95 $9.50+0.00
BLAST SCHEDULE PLANNING AND SHIFTWISE PRODUCTION SCHEDULING OF AN OPENCAST IRON ORE MINE DIATHA KRISHNA SUNDAR t and DAMODAR ACHARYA 2 IVinod Gupta School of Management, Indian Institute of Technology, Kharagpur 721 302, India 2Department of Industrial Engineering and Management, Indian Institute of Technology, Kharagpur 721, India
(Received 2 December 1994) Abstract--In this paper we present a computer integrated system for short-range mine production planning that uses: (i) a linear programming model for the choice of blocks to be blasted; (ii) a stochastic programming model for the selection of the blasted areas to be excavated and in deciding the quantity of ores and wastes to be mined from each of the selected blocks. The model also gives the shiftwise allocation of dumpers to support the excavation plan. The above two models use improved estimates for the ore body characteristics utilizing: the blast hole data in addition to the usual bore hole statistics to improve the prediction accuracy of the block level ore body characteristics. The software is developed in C-language and has four modules for ore body characteristics prediction, blast scheduling, shiftwise production planning and report generation. The results include shiftwise block level blasting and excavation plans for each bench, benchwise shovel-dumper allocation plan. The developed software has been applied to planning the production of a captive iron ore mine of Steel Authority of India Ltd.
1. INTRODUCTION
Production planning in an opencast mine deals with the problems of." (i) selecting the blocks to be blasted in the benches exposed for mining; (ii) deciding the quantities of ores and wastes to be excavated in each time period from each of the blasted blocks; and (iii) blending of the mined ores so that the periodwise demands, in terms of quality and quantity, for ores can be met utilizing the limited resources available to the mine. These short-range decisions are made within the limitations of the long-range mine plan that maximizes the utilization of ore reserves while giving a mine face development programme. Thus a good mine production plan must not only meet both the longand short-range mining requirements but also satisfy many practical details that are unique to day-to-day operations. For example average quality and quantity estimates are good enough for both long- and short-range mine planning but inadequate for day-to-day production scheduling. For such purposes, the variations in these estimates are equally important. Intra block and inter block variations in the quality and quantity of available reserve, uncertainty in quantum of available resources due to breakdown and absenteeism call for frequent updating of a production plan. This necessitates the use of a user-friendly, flexible computer integrated system for mine production planning. The complexity of the system increases further due to large number of variables and constraints whose parameter values cannot be estimated with certainty. Practical mining constraints like minimum desirable safety width, bench height and accessibility constraints add to this complexity. Several authors have considered the problem of production planning in mines. Mutmansky [6] gives a comprehensive review of the application of various operations research techniques including linear programming, integer linear programming, quadratic programming, dynamic programming, simulation and heuristics to production scheduling in mines. Gershon [5] and Barbaro and Ramani [1] considered the problem of finding a production schedule for opencast mines. While Barbaro and Ramani [1] aim at maximizing the financial benefit for a situation where a group of mines supply ore to a set of plants each with its known demand in terms of quantity and quality, the emphasis of Gershon [5] is to optimize the life of a mine in long-, intermediate- and short-range planning. Kostas et aL [8] considered the problem of long- and short-range open pit production 927
928
Diatha Krishna Sundar and DamodarAcharya
scheduling using a simulation approach for the former and a linear programming model for the latter. Very few authors have considered the problem of developing shiftwise operational plans. Exceptions are the works of Chanda [2] and Wooller [I1]. Chanda [2] uses a mixed-integer programming formulation to minimize the deviation from the quality targets for developing a shiftwise production schedule for an underground mine. The software package of Wooller [11] does not give the details of the models/techniques used in finding intermediate or short-range production schedules for opencast/underground mines. This paper deals with the problem of shiftwise production planning for a captive opencast iron ore mine so that the demands for iron ore can be effectively met using available resources like shovels, dumpers and crushing mill of known capacities. While doing so, the plan ensures a supply of ores to the plants such that the quality (in terms of Fe, A1203, SiO2 contents) are within the acceptable range. The system proposed consists of the following four distinct modules: a module for getting improved Kriging estimators for the ore quality and quantity of the blocks to be blasted and excavated, a linear programming module for blast planning, and a stochastic linear programming module for shiftwise excavation planning and a report generation module. A central database and user interfaces facilitate the communication between modules and the system with the users. The model developed has been applied to planning the production of a captive mine of Steel Authority of India Ltd (SAIL).
2. IMPROVEDKRIGING ESTIMATION MODULE At a given point of time, the choice of blocks for excavation is limited to already blasted ones as the blasting is done only at fixed intervals (usually weekly off days). This makes blast planning and the production planning problems inseparable. Further, blast planning as to necessarily depend on relatively inaccurate Kriging estimates obtained from the analysis of basic bore hole statistics. As for a block more reliable estimates can be obtained by analyzing the blast hole data, and the deficiencies in earlier estimates can be at least partially made up by excavating from several blasted blocks and by blending them in suitable proportions. However, it is important to note that blending alone cannot help to meet the quality and quantity characteristics of customer demand if the initial choice of blasting blocks is wrong. The solution lies in getting a more accurate estimate of the block level reserve characteristics before blasting. As the drift in the ore quality in the vertical direction of the ore body under consideration is negligible, the improvement in block level 2-D Kriging estimators has primarily come from the use of blast hole data from the adjacent blocks, in addition to the bore hole statistics. The model uses the conventional method of normal Kriging (David [3], Journal [7]). The details of the methodology used for getting updated and improved estimators are discussed in a separate paper (Sundar and Acharya [4]).
3. BLASTPLANNING MODEL The objective of the blast planning module is to determine the blocks, from the available benches of an opencast mine, to blast for the following production period so that the demand in terms of both quality and quantity of the period can be met. This situation is modelled as a linear programming problem. The module maximizes the number of blocks to blast, subject to the transport capacity, demand (quality and quantity), and block size, bench safety width, and block, bench precedence constraints. For the purpose of modelling, the ore body has been divided into several benches of 10/12 m height each and each bench into rectangular blocks of 30 x 30 m size. A smaller block size could not be used as the accuracy of the Kriging estimators becomes questionable if the block size is less than 30 x 30 m for a bore hole grid size of 60 x 60 m [3, 7]. A block in the ore body is uniquely defined by specifying the column numbers (grid numbers) in the x, y and z directions from the orion.
Blast schedule p l a n n i n g a n d shiftwise p r o d u c t i o n scheduling
929
Table 1 x, y
z (bench) 1
1.5 1.7 1.9 2.3 2.5 2.7 3.9 4.7 4.9
2
3 0.290
4
5
1.000 1.000 0.425 1.000 1.000 1.000 1.000 1.000
3.1. Notation B~.y,z= a block B located in the intersection of xth, yth and zth columns;
Ox.y,z = ore available in block Bx,y,:; W~.~.~= waste available in Bx.~.:; QoldO:x,y,:= uncleared ore of the previous blasts in block Bx,y,~; uncleared waste of the previous blasts in block Bx,y,~; average transport cycle time for ore from block B~,y,~ to crushing mill; average transport cycle time for waste from block Bx,y,~ to waste yard; total transport time available; average quality of ith mineral in block B~,y,~; Ki:~ow,r= lower limit on acceptable quality of ith mineral for the planning period; K~:upp,r= upper limit on acceptable quality of ith mineral for the planning period; Sw = safety width (minimum width to be maintained for any bench in terms of block width); Cap = capacity of the dumper; De = ore demand; 6x,y.~= a variable that takes value one if block B~,~,~is fully to be blasted and zero if it is not to be blasted. Fractional values of 6(x, y, z) represent the portion of block Bx,y,~ to be blasted;
Qo~dW:,,~.= TrOx, y,~ = TrWx,y,~ = ToTr = Ki:~,y,~=
3.2. Model Maximize the number blocks to be blasted for the given production period from all the available benches, rows and columns:
Maximize Z = Z Z Z z
x
6x.,.~
)'
Table 2 Production plan details of the week considered No. of shovels deployed = No. of dumpers deployed = Tons of ore raised = Tons of waste raised = Average quality = No. of planned dumper trips = No. of planned dumper trips/shift from Bench 1 = 40 Bench 2 = 30 Bench 3 = 25 Bench 4 = 30 Bench 5 = 30 No. of actual dumper trips made
6 8-10 52,550 T 5400 T 62.51% Fe 1860
= I 159
(1)
930
Diatha Krishna Sundarand DamodarAcharya Table 3 Resource available during the planning ~ r i o d No. of shovels No. of dumpers No. of available benches
= 6 = 10 = 5
Acceptable ore quality in any shift Minimum Fe (%) Maximum AI203 (%) Maximum SiO2 (%) Confidence interval (%)
= = = =
61.5 4 2.5 95
subject to available transport capacity constraint:
E E E [(Oo,dO:x,y,z"TrOx,y,z + QoldW:x,y,z"TrWx,y,z) + (Ox, y,z "TrOx,y,z + Wx,y,z)" TrWx, y,z)bx,y,z] z x y
Cap ~ToTr.
(2)
Demand constraint:
L 2 E (QoldO:x,y.z+ Ox, y.z "(~x.y.z) ~/De. z x y
(3)
Quality requirement constraint: E ~ ~(Qo,do:x,y,z + Ox,y/6x, y,z)
Ki:tower~<
~< Kt:upp~,•
(4)
EZ Ex Ey (QoldO:x.y,z"Ki:x,y,z+ Ox,y;" Ki:x,y;" 6x,r,z Safety width constraint:
(5)
(Ym.... - y)'6~,y.~ >1 Sw.6~,y;,
for all x, y and z. Block size constraint: 0 ~< 6x,y,~ ~< 1,
(6)
for all x, y and z. It may be noted that the scope for blending of relatively poor quality ore with rich quality ore increases if one has options to excavate from a larger number of blocks. Theoretically, utilization of the deposit can be maximized, if the entire deposit can be excavated first and stacked (possibly at a different place) according to similarity of ore quality before crushing and blending. Since, this is not practically feasible, in the blast planning model, we aim at maximizing the number of blocks to be blasted [equation (1)]. Within the practical constraints, this will maximize the scope for selective excavation, crushing and blending. Table 4. Summary sheet of shiftwise and benchwise ore excavation Shift 1 2 3 4 5 6 7 8 9 10 11 12
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5 0 2287 141 0 822 0 2287 0 0 0 0 0
2430 0 2226 2578 0 2259 0 340 2376 1335 3054 2748
0 0 1336 0 4826 368 0 0 0 3236 0 0
3403 4013 0 3504 652 605 4013 3924 1729 0 3552
459 0 2596 38 0 3068 0 360 0 0 3246 0
Blast schedule p l a n n i n g and shiftwise p r o d u c t i o n scheduling
931
Table 5. Summary sheet of shiftwise and benchwise waste excavation Shift 1 2 3 4 5 6 7 8 9 10 I1 12
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5 0 0 0 0 0 0 0 0 0 0 0 0
2930 0 0 0 0 0 0 0 0 0 0 0
4. P R O D U C T I O N
0 0 0 0 0 0 0 0 0 977 0 976
PLANNING
488 0 0 0 0 0 0 1465 0 0 0 0
0 0 0 0 0 0 0 2930 0 0 0 0
MODEL
To meet the market demand, for a defined production period, in terms o f quality and quantity o f ore, the mine production plan aims at finding the benches and blocks that are to be excavated shiftwise from the available ones. This is modelled as a chance constrained program to take care o f the random nature of ore quality and quantity characteristics and variations in operation time requirements. The important constraints on quality, mill capacity, transport capacity, ore availability and waste are explicitly considered in this model.
4.1. Notation XO,s J = XW, sJ = TrO~j = Tr I~,j = ToT, = /~.,:~,j =
Kt,,,,:l.... = K,,,.:upp~r= O~j =
Wi,j = De = CMC = SCi,, = CI =
ore to be mined from ith bench, j t h blast area in the shift t (in tons); waste to be mined from ith bench, jth blast area in the shift t (in tons); mean transport time o f ore from blast area j in bench i to ore crushing mill; mean transport time o f waste from blast area j in bench i to waste dump yard; total transport time available in shift t; mean quality of mth mineral in jth blast area of ith bench; lower limit on acceptable quality of mineral m in shift t (in percentage); upper on the quality of mineral m in shift t (in percentage); ore availability in blast area j in bench i (in tons); waste availability in blast area j in bench i (in tons); ore demand (in tons); crushing mill capacity (in tons); shoveling capacity from bench i in shift t (in tons); confidence interval.
4.2. Model
Objective. mining o f maximum ore and waste tonnage from the available blast areas during a period is considered a superior objective compared to the conventional objective of maximizing ore tonnage due to the following reasons: Table 6. Summary sheet of shifiwise and benchwise total excavation Shift 1 2 3 4 5 6 7 8 9 lO
II 12
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5 0 2287 141 0 822 0 2287 0 0 0 0 0
5369 0 2226 2758 0 2259 0 340 2376 1335 3054 2748
0 0 1336 0 4826 368 0 0 0 4213 0 976
3891 4013 0 3504 652 605 4013 1465 3924 1729 0 3552
459 0 2596 38 0 3068 0 3290 0 0 3246 0
932
Diatha Krishna Sundar and Damodar Acharya Table 7. Summary sheet of shiftwise nad bcnchwis¢ dumper trips Shift
Bench 1 Bench 2 Bench 3 Bench 4 Bench 5
1 2 3 4 5 6 7 8 9 10 11 12
0 45 2 0 16 0 45 0 0 0 0 0
107 0 44 55 0 45 0 6 47 26 61 54
0 0 26 0 96 7 0 0 0 84 0 19
77 80 0 70 13 12 80 29 78 34 0 71
9 0 51 0 0 61 0 65 0 0 64 0
1. Often a good quality ore patch cannot be accessed unless one completely removes the waste patch in a block. In such situations removal of both waste and ore becomes essential. Further, a block in a bench cannot be accessed unless the ores and the wastes from the blocks above it are not removed. 2. The same fleet of material handling equipments are used for excavation and transportation of both ore and waste. 3. Maximization of ore tonnage excavation requires selective mining. This unhealthy practice shortens the mine's life. In view of the above, we maximize the total ore and waste to be mined from the available blast areas during the planning horizon of t shifts. This objective can be written as: maximize Z = ~ ~ ~ subject to
t
i
j
[XOt,i,j -I- XWt,i,j].
(7)
Quality restriction: ~" E XOt,i,J
PROB{Ktm.lower~. i j ~
(8)
Transport capacity constraint: for all t.
(9)
Ore availability constraint: PROB { ~
XO,,i,/
Oi.j} ~ CI, for all i, j.
(lO)
Waste availability constraint:
PROB{~ XWtj,j <~IY~i,j}>~CI,
for all i, j.
(11)
Demand constraint:
~ ~ XO,,,,j >I De.
(12)
t i j
Crushing mill capacity constraint: ~
for all t.
(13)
Shoveling capacity constraint:
PROB{~[XOtij+XW, i / ],, . ., <~SC,,}>~, CI, for all i and t.
(14)
Blast scheduleplanning and shiftwiseproduction scheduling
933
XO,,ij >1O,
(15)
XW, jj i> 0.
(16)
Nonnegativity
5. COMPUTER INTEGRATED SYSTEM The weekly blast schedule module interacts with the central data base to generate the input data for the model. It generates the blast planning LP model and solves to obtain the optimal blast plan. Once the optimal solution is found it prepares the reports for the blasting department. The blast hole data from the blasted blocks are used to obtain fresh Kriging estimators for the same blocks for the purpose of excavation planning. The system then generates the stochastic production planning model and solves it to obtain the excavation plan. The report generator module utilizes the results obtained from the blast planning module to provide working plan for the production planning and control department of the mines. The actual performance data at the end of each shift is fed to the data base to generate the rolling shiftwise plan for the next week (12 shifts). This also helps in developing an alternate plan to take care of the situations arising out of equipment (shovels, dumpers, mill) failure and absenteeism. The Flow chart for the computer integrated system is given in Fig. 1. The designed computer integrated production planning system has a user interface, central data base, model generator and a report generator. The blast planning model generates blast plans and reports to blasting and production planning and control departments, and the production planning model generates the shiftwise production plans and reports to production planning and control department, truck maintenance department and production shift in-charge.
6. RESULTS The blast and production planning modules were tested on live data from one of the iron ore mines of SAIL. Blast schedule planning module results are given in Table I. Details of the production plan (old method) are given in Table 2. The resource availability for the period is shown
Prodoctionl g:dn~lri~iPonUt~ - ~
I data
Blast model input generation
I
Model generation
Model generation
I
Model solution
Model solution
Report generation
Report generation
I Production I planning and control dept.
Truck [ [ Production Blasting maintenancel shift department department I in-charge Fig. 1. Computer integrated production planning.
Production planning and control dept.
934
Diatha Krishna Sundar and D a m o d a r Acharya Table 8. Comparison of old and computer integrated system output
Sl. No. 1 2 3 4 5 6 7
Resources used
Actual practice (old method)
Shovels Dumpers Benches accessed Shiftwise requirements of: dumpers shovels Quantity of ore produced Quality of ore produced Quantity of waste produced
Computer
integrated system output
6 10 all five
5 10 all five
8-10 6 52,550 T 61.18% Fe 5400 T
6-10 4-6 69,000 T 62.4% Fe 9650 T
in Table 3. Computer integrated blast and production planning system's summarized results are given in Tables 4-7. A comparison of the old method and the new computer integrated production planning method are given in Table 8. 6.1. Blast schedule planning module results
Results obtained from the blast schedule planning module are given in Table 1. The results shown in Table 1 give the blocks selected for blasting in the considered planning period. Fractional values indicate the partial blasting of the selected blocks. For example 0.290 in the above table indicates that only 29% of the block Bt,5,3 is to be blasted during the period. 6.2. Production module results
Details of the production plan (old method) shown in Table 2. It may be noted that the old manual method assigns fixed number of dumper trips to each of the benches, where the number of trips from the bench is dependent on the average bench ore quality, available quantity of ore, available quality of waste, and the desired mine output quality and quantity. The old method restricts the excavation mostly to one block per bench. For the purpose of planning, the old method used the following resource constraints. The same set of resource constraints have also been used for planning by the proposed method. Shiftwise Shiftwise Shiftwise Shiftwise
and and and and
benchwise benchwise benchwise benchwise
ore excavation (in tons) is given in Table 4. waste excavation (in tons) is given in Table 5. total excavation (in tons) is given in Table 6. required dumper trips are given in Table 7.
A comparison of results obtained from the computer integrated system with the old method for the considered planning period is given in Table 8. Results given in Table 8 shows that the proposed computer integrated planning system requires minimum of 4 shovels as against 6 shovels in the old method. This also gives higher planned production of 69,000 tons of ore and 9650 tons of waste compared to 52,500 tons of ore and 5400 tons of waste in the old method. The proposed computer integrated planning system requires minimum of only 6 dumpers (against 8 in the old method). The greater number of spare dumpers may now be available as a standby to take care of breakdowns. The new method also gives marginally higher Fe quality (62.4% compared to 62.18% in the old method). REFERENCES 1. R. W. Barbaro and R. V. Ramani. Generalized multi-period M I P model for production scheduling and processing facilities selection and location. Min. Engng 107-114 (1986). 2. E. C. K. Chanda. An application o f integer programming and simulation to production planning for a stratiform body. Min. Sci. Technol. 11, 165-172 (1990). 3. M. David. Geostatistical Ore Reserve Estimation. Elsevier Scientific, A m s t e r d a m (1977). 4. D. K. Sundar and D. Acharya. 2D-Kriging: removing the shadow effect. Trans. Insm. Min. Met. (Section A: Min. Ind.). Communicated. 5. M. E. Gershon. Mine scheduling optimization using MIP. Min. Engng, Apr. 351-353 (1983). 6. Jan M. Mutmansky. Computing and operations research techniques for production scheduling. Computer Methods for 80's. (Edited by A. Weiss), pp. 610-614 (1980).
Blast schedule planning and shiftwise production scheduling
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7. A. G. Journal and Ch. J. Huijbregts. Mining Geostatistics. Academic Press, New York (1978). 8. K. Fytas et al. Optimization of open pit short and long range production scheduling. CIM Bull. Aug. 55-61 (1987). 9. E. R. Muller and C. K. Young. Introductory Review. Computer Methods for 80's. (Edited by A. Weiss), pp. 610-614 (1980). I0. Q. X. Yun and T. M. Yegulalp. Optimum scheduling of overburden removal in open-pit mines. CIM Bull. Dec. (1982). 11. R. Wooller. Production scheduling system. Trans. Instn. Min. Metall. (Sec. A, Min. Industry), Vol. 101 (1992). 12. C. K. Young. Production scheduling--technical overview. Computer Methods for 80's. (Edited by A. Weiss), pp. 610-614 (1980). 13. F. L. Wilke and W. Woehrle. A model for short-range planning and monitoring of mining in potassium deposits of level formation. 16th APCOM (Edited by T. J. O'Neil), pp. 304-312 (1980).
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