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Showing posts with label Mining Engineering. Show all posts
Showing posts with label Mining Engineering. Show all posts

Tuesday, 8 May 2018

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
X
X
X
X
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  X
0
400
Contin
$C$3
Production  X
0
600
Contin
$D$3
Production  X
0
500
Contin
$E$3
Production  X
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  X
400
0
27
1E+30
9.75
$C$3
Production  X
600
0
25
1E+30
13.5
$D$3
Production  X
500
0
28
1E+30
10.75
$E$3
Production  X
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:         9th 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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Mine Management Questions and Answers Series (3)

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