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


Znconcentrate/t ore

0.2

0.2

0.25

0.2


Mbconcentrate/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 = X_{1},
Pit B = X_{2}, Pit C = X_{3}, Pit D = X_{4}
The linear
Model:
Cost
minimization; Z = 27X_{1} + 25x_{2}
+ 28x_{3} + 23x_{4}
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


CuConc/t Ore

0.2

0.2

0.15

0.2

480

≥

300

ZnConc/t Ore

0.2

0.2

0.25

0.2

530

≥

300

MbConc/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)

CuConc/t Ore

480

ZnConc/t Ore

530

MbConc/t Ore

400

The smelter’s payment
to Marapana Mining Ltd is; $300/t Cuconc, $250/t Znconc 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

ZnConc/(t) Ore Total

530

$F$6>=$H$6

Not Binding

230


$F$7

MbConc/(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 righthand side and
shown on the lefthand 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

ZnConc/(t) Ore Total

530

0

300

230

1E+30


$F$7

MbConc/(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.
Related Articles:
Mine Management Questions and Answers Series (3)