Mine Management Questions and Answers Series (3)

Table 1

Mining  and milling costs for each open pit mines
Satellite  Pit		A	B			C	D
Mining  cost		15	10			18	12
Milling  cost		12	15			10	11
Cu -concentrate/t ore		0.2	0.2			0.15	0.2
Zn-concentrate/t ore		0.2	0.2			0.25	0.2
Mb-concentrate/t ore		0.15	0.1			0.15	0.2
Table 2: Production for each satellite open pit Mines.
satellite  Pit	minimum ore production(t)			Max .Ore Production
A	400			800
B	600			1000
C	500			1500
D	200			2000

Let Pit A = X₁, Pit B = X₂, Pit C = X₃, Pit D = X₄

The linear Model: 

Cost minimization; Z = 27X₁ + 25x₂ + 28x₃ + 23x₄

Table3.

	Maximization of Production and Minimization of cost.
Column1	X₁	X₂	X₃	X₄	Total	Column2	Limits
Production	400	600	500	1025
Total Cost	27	25	28	23	63375
Cu-Conc/t Ore	0.2	0.2	0.15	0.2	480	≥	300
Zn-Conc/t Ore	0.2	0.2	0.25	0.2	530	≥	300
Mb-Conc/t Ore	0.15	0.1	0.15	0.2	400	≥	400
Total Conc.	0.55	0.5	0.55	0.6	1410	≤	2000
Pit A	1	0	0	0	400	≥	400
	1	0	0	0	400	≤	800
Pit B	0	1	0	0	600	≥	600
	0	1	0	0	600	≤	1000
Pit C	0	0	1	0	500	≥	500
	0	0	1	0	500	≤	1500
Pit D	0	0	0	1	1025	≥	200
	0	0	0	1	1025	≤	2000

Executive summary of the results for the model by answering the following questions.

    1.    What are the optimum productions from each satellite pit and total production per week

Optimum production for each pit and total production are given in the table below.

Table4

	Optimum Productions	Total production /week
Pit A	400	400
Pit B	600	600
Pit C	500	500
Pit D	1025	1025

      2.      What will be the profit from sales per week?

Table5 The  overall production for Marapana for each ore concentrate :
ore	total production of each conc.(tonnes/week)
Cu-Conc/t Ore	480
Zn-Conc/t Ore	530
Mb-Conc/t Ore	400

The smelter’s payment to Marapana Mining Ltd is; $300/t Cu-conc, $250/t Zn-conc and $550/t Mb.

Now, these amounts of money are paid to the Mining Company so it becomes the company’s revenue. So the revenue generated from sales per week is:

 Z = 480x300 + 530x250 + 400x550 = $496,500.00/week.

From the LP model, the total cost of mining and milling is $63,375/week.

Therefore, the profit from the sales is:

Profit = Revenue – Cost = $496,500 - $63,375 = $433,125/week.

     3.      What changes are required from analyzing the results?

From the results obtained from the analysis, it is required that the current production target needs to be maintained at the lowest possible cost given above. In order to achieve this objective, there are several things need to be changed as per required by the analysis. One of them is to change aging trucks and salvage them and replace with new ones. From experience, cost increases and high production loss could occur with aging trucks. Since the production targets are limited to some conditions which require almost exact values. There is a need to have skilled labors to maintain the steady flow of production at low cost. If there are unskilled labors then replace them with competitive and skilled labors or if they are many then remove some in order to reduce cost.

     4.      From the results of LP modeling using Solver(in excel), describe the results and write an executive summary to Marapana Mining limited telling about the optimum production levels being found by your LP modeling.

Table 6.

Answer report.

Objective Cell (Min)
			Cell		Name	Original Value	Final Value
			$F$4		Total Cost Total	0	63375
Variable Cells
	Cell				Name	Original Value	Final Value	Integer
	$B$3				Production  X₁	0	400	Contin
	$C$3				Production  X₂	0	600	Contin
	$D$3				Production  X₃	0	500	Contin
	$E$3				Production  X₄	0	1025	Contin
Constraints
	Cell	Name				Cell Value	Formula	Status	Slack
	$F$10	Pit A Total				400	$F$10<=$H$10	Not Binding	400
	$F$11	Pit B Total				600	$F$11>=$H$11	Binding	0
	$F$12	Pit B Total				600	$F$12<=$H$12	Not Binding	400
	$F$13	Pit C Total				500	$F$13>=$H$13	Binding	0
	$F$14	Pit C Total				500	$F$14<=$H$14	Not Binding	1000
	$F$15	Pit D Total				1025	$F$15>=$H$15	Not Binding	825
	$F$16	Pit D Total				1025	$F$16<=$H$16	Not Binding	975
	$F$5	Cu.Conc/(t) Ore Total				480	$F$5>=$H$5	Not Binding	180
	$F$6	Zn-Conc/(t) Ore Total				530	$F$6>=$H$6	Not Binding	230
	$F$7	Mb-Conc/(t) Ore Total				400	$F$7>=$H$7	Binding	0
	$F$8	Total Conc. Total				1410	$F$8<=$H$8	Not Binding	590
	$F$9	Pit A Total				400	$F$9>=$H$9	Binding	0

Answer report is in three parts: 1.Objective cell (Min), 2. Variable cells and 3. Constraints cell. Objective cell gives the optimal value in the final value column. In the Variable cells in the final value column, optimal values are also given. The constraints cells shows limits generated by solver on the right-hand side and shown on the left-hand side is the difference between the entered solver generated limit values. The slack column shows the amount of slack for each constraint which indicates there is flexibility exists. For example, removal or addition of one haulage truck from the total fleet size will affect the production or cost per week.

Table7

Sensitivity Report.

Variable Cells
			Final	Reduced		Objective		Allowable		Allowable
	Cell	Name	Value	Cost		Coefficient		Increase		Decrease
	$B$3	Production  X₁	400	0		27		1E+30		9.75
	$C$3	Production  X₂	600	0		25		1E+30		13.5
	$D$3	Production  X₃	500	0		28		1E+30		10.75
	$E$3	Production  X₄	1025	0		23		13		23
Constraints
			Final		Shadow		Constraint		Allowable	Allowable
	Cell	Name	Value		Price		R.H. Side		Increase	Decrease
	$F$10	Pit A Total	400		0		800		1E+30	400
	$F$11	Pit B Total	600		13.5		600		400	600
	$F$12	Pit B Total	600		0		1000		1E+30	400
	$F$13	Pit C Total	500		10.75		500		1000	500
	$F$14	Pit C Total	500		0		1500		1E+30	1000
	$F$15	Pit D Total	1025		0		200		825	1E+30
	$F$16	Pit D Total	1025		0		2000		1E+30	975
	$F$5	Cu.Conc/(t) Ore Total	480		0		300		180	1E+30
	$F$6	Zn-Conc/(t) Ore Total	530		0		300		230	1E+30
	$F$7	Mb-Conc/(t) Ore Total	400		115		400		195	165
	$F$8	Total Conc. Total	1410		0		2000		1E+30	590
	$F$9	Pit A Total	400		9.75		400		400	400

Sensitivity report above contains some relevant information regarding the effect of changes to either an objective function coefficient or right hand side as discussed in the answer report. The variable cells section includes the reduced cost and ranges of optimality for the objective function coefficient (expressed in terms of allowable increases and allowable decreases). The constraints section contains the shadow prices and ranges of feasibility for right hand side values (again expressed in allowable increases and allowable decreases). This is linear programming equivalent of marginal analysis in economics, as the results deal with the effects of making one parameter change to the model.

The value “1E+30” (for allowable increase and decrease) is an excel’s way of saying infinity.

Management Report.

The above results are used to produce a management report for Marapana Mining Ltd. Practically; these results are presented as attachments to the actual report to the Mine Superintendent. LP modeling was done by Mining & Mineral Processing Student Consulting Association..

Date:         9^th May 2018.

To:             Kuiwatinga, Marapana Open Pit Mine Production Manager.

From:       Mining & Mineral Processing Student Consulting Group Associates.

Subject:  Optimization of Production per week for Marapana’s Mining Ltd Four Satellite Open Pits.

The Marapana Open Pit Mine Manager wants to maximize the production levels and minimize cost as much as possible in order to expect a maximum return per week. It is understood the management wants to optimize returns by optimizing number of haulage fleet, drivers and mechanics to reduce cost and maximize production. The cost is minimized to about $63 375/week which places constraints on the operating fleet of trucks, drivers and mechanics.  

There is no exact recommendation made in this analysis as there were limited raw information such as haulage fleet size, drivers, mechanics and other parameters necessary for maximum production at lowest possible cost. But with the limited information given, we only recommend few. It is recommended the available resources must be utilized so as to keep the current production is maintained at a constant rate. Whenever the equipment needs maintenance then do so as soon as possible or for worn out fleets, they need to be replaced with new fleet size so that continuous flow of production is maintained throughout the week and even throughout the mine life if it is required. Not only that but also, labors must given  special consideration because they are the ones that will make things happen so competitive, skilled and required number of labors are necessary to achieve required production targets.

If our recommendations and work quality solve your Management’s problems, then do not hesitate to engage us for such services we provide.

Yours truly

…………………………………

Mara Hawks

Managing Director

Mining & Mineral Processing Student Consulting Group Associates.

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