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1
MINE3123 - Mine Planning
Project Management & Network Techniques
Week 13
ContentContentContentContent
� Project Management & Network Techniques
� Critical Path Method (CPM)
� Mine Closure Planning
� Final Exam Review
2
MINE3123 - Mine Planning
Project Management & Network Techniques
BackgroundBackgroundBackgroundBackground
Once feasibility studies have been completed, an optimal mine
plan has been generated that meets corporate objectives and
finance has been established - project construction may
commence.
Project Management is all about the best way in which to
complete a task (such as the construction of a mine) within the
shortest time frame at the lowest possible cost.
3
Mathematical AnalysisMathematical AnalysisMathematical AnalysisMathematical Analysis
Mathematical Analysis – may be used to model and then evaluate the
schedule of a series of activities required to complete a task. This may be
useful in an answering questions as such, what cost and resources are
required to reduce the time required to complete a task.
The most well-regarded mathematical/network analysis techniques are:
� Critical Path Method (CPM) – Calculates a single early and late start and a
completion date for each activity based on a specified single duration
estimate. CPM calculates a “Float Time” to determine which activities
have the least scheduling flexibility.
� Program Evaluation and Review Technique (PERT) – Average activity
duration estimate to calculate a project duration.
Critical Path Method (CPM)Critical Path Method (CPM)Critical Path Method (CPM)Critical Path Method (CPM)
Two types of project networks:
�Activity-on-Arc (AOA)
� In this diagram, the activity is 
represented on an arc, or an arrow, 
while a node is used to separate an 
activity from its immediate 
predecessors.
�Activity-on-Node (AON)
� In this diagram, the activity is 
represented by the node, while the arc 
or arrow is used to show the precedence 
relationship between the activities.
4
CPMCPMCPMCPM TerminologyTerminologyTerminologyTerminology
Start Node – This is a node that represents the beginning of
the project.
Finish Node – This node represents the end of the project.
Immediate Predecessor - These are activities that must be
completed by no later than the start time of the given activity.
Immediate Successor - Given the immediate predecessor of an
activity, this activity becomes the immediate successor of each
of these immediate predecessors.
If an immediate successor has multiple immediate
predecessors, then all must be finished before an activity can
begin.
CPMCPMCPMCPM TerminologyTerminologyTerminologyTerminology
Earliest start time of an activity (ES) - The earliest possible time
at which an activity will begin if there are no delays in a project.
Earliest finish time of an activity (EF) - The earliest possible time
at which an activity will finish if there are no delays in a project.
Latest start time of an activity (LS) - The latest possible time that
an activity can start without delaying the project.
Latest finish time of an activity (LF) - The latest possible time that
an activity can be completed without delaying the project.
5
CPMCPMCPMCPM TerminologyTerminologyTerminologyTerminology
Forward pass - The process of moving through a project from start to finish
to determine the earliest start and finish times for the activities in the
project.
Backward pass - The process of moving through a project from finish to
start to determine the latest start and finish times for the activities in the
project.
Slack for an activity - The amount of time that a particular activity can be
delayed without delaying the whole project. It is calculated by taking the
difference between the latest finish time with the earliest finish time.
Dummy activity - to indicate interdependencies that cannot be
represented correctly solely with the conventional activity and event
structure and are useful when doing hand solutions of the network for
creating parallel activities or merging several parallel activities.
Finding the Critical PathFinding the Critical PathFinding the Critical PathFinding the Critical Path
� Once the earliest and latest times have been determined for each
node or event in the network, the critical path is then defined as
those tasks for which the earliest times are equal to the latest times.
� The critical path or paths (there may be more than one critical path
within a network) represents the series of tasks or activities in which
no delay in their start or finish can be tolerated without delaying the
project as a whole.
� Other nodes that are not considered critical have what is termed float
or slack time. This float time is the difference between latest and
earliest times and represents flexibility of task initiation by a project
manager.
� A project manager can use float or slack time to delay initiation of
various project tasks in order to better schedule manpower,
equipment, or other company resources without delaying project
completion.
6
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
The development of an energy project involves the following activities:
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
a) Draw the Network Diagram for this project, indicating the duration of each activity.
b) Using the CPM method, determine the critical path for this project and the completion
time.
c) Crash the project in the cheapest possible way so as to have a completion time which
is 4 months shorter than the current completion time.
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
2
A=5
1
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
7
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
2
A=5
B=4
3
1
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
2
C=3A=5
B=4
3
41
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200(j) (g,h) 4 $3,600 0 na
8
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
5
2
C=3A=5
B=4
3
41
D=4
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
5
6
2
C=3A=5
B=4
E=6
3
41
D=4
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
9
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
7
5
6
2
C=3A=5
F=4
B=4
E=6
3
41
D=4
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
7
5
6
2
C=3A=5
F=4
B=4
E=6
3
41
D=4
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
8G=5
10
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
7
5
6
2
C=3A=5
F=4
B=4
E=6
3
41
D=4
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
8G=5
9H=6
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
7
5
6
2
C=3A=5
F=4
B=4
E=6
3
41
D=4
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
8G=5
9H=6
10
I=6
11
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
a) Draw the Network Diagram for this project, indicating the duration of each activity.
7
5
6
2
C=3A=5
F=4
B=4
E=6
3
41
D=4
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
8G=5
9H=6
10
I=6
J=4
Dummy
arc
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
b) Using the CPM method, determine the critical path for this project and the completion time.
7
5
6
2 10
C=3A=5
F=4
I=6
B=4
E=6
Notation:
LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
11/7
4/0
21/15
18/125/0
5/0
21/17
21/17
3
8
4
9
1
17/12
14/9
15/11
12/8
17/11
17/11
11/5
11/5
12/8
9/5
H=6
G=5
J=4
11/8
8/5
D=4
Dummy
arc
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
12
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
b) Using the CPM method, determine the critical path for this project and the completion time.
7
5
6
2 10
C=3A=5
F=4
I=6
B=4
E=6
Notation: LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
11/7
4/0
21/15
18/125/0
5/0
21/17
21/17
3
8
4
9
1
17/12
14/9
15/11
12/8
17/11
17/11
11/5
11/5
12/8
9/5
H=6
G=5
J=4
11/8
8/5
D=4
Dummy
arc
Dummy
arc
Therefore the critical path is �	 → �	 → �	 → �.
This requires 21 months completion time.
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
c) Crash the project in the cheapest possible way so as to have a completion time which is 4
months shorter than the current completion time.
7
5
6
2 10
C=3A=5
F=4
I=6
B=4
E=6
Notation:
LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
11/7
4/0
21/15
18/125/0
5/0
21/17
21/17
3
8
4
9
1
17/12
14/9
15/11
12/8
17/11
17/11
11/5
11/5
12/8
9/5
H=6
G=5
J=4
11/8
8/5
D=4
Dummy
arc
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200(j) (g,h) 4 $3,600 0 na
13
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
The activities that can be crashed are A, H and I. Of this A and H belong to the critical path.
� The crashing cost of A is $300 per month for up to 2 months.
� The crashing cost of H is $200 per month for up to 4 months.
c) Crash the project in the cheapest possible way so as to have a completion time which is 4
months shorter than the current completion time.
7
5
6
2 10
C=3A=5
F=4
I=6
B=4
E=6
Notation: LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
11/7
4/0
21/15
18/125/0
5/0
21/17
21/17
3
8
4
9
1
17/12
14/9
15/11
12/8
17/11
17/11
11/5
11/5
12/8
9/5
H=6
G=5
J=4
11/8
8/5
D=4
Dummy
arc
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
c) Crash the project in the cheapest possible way so as to have a completion time which is 4
months shorter than the current completion time.
7
5
6
2 10
C=3A=5
F=4
I=6
B=4
E=6
Notation:
LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
11/7
4/0
21/15
18/125/0
5/0
21/17
21/17
3
8
4
9
1
17/12
14/9
15/11
12/8
17/11
17/11
11/5
11/5
12/8
9/5
H=6
G=5
J=4
11/8
8/5
D=4
Dummy
arc
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
Since activity H is the cheapest, we should try crashing this first. Unfortunately it can only be 
crashed by 3 months because otherwise the critical path changes from:
�	 → �	 → �	 → � to 	�	 → �	 → �	 → �.
14
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
c) Crash the project in the cheapest possible way so as to have a completion time which is 4
months shorter than the current completion time.
7
5
6
2 10
C=3A=5
F=4
I=6
B=4
E=6
Notation: LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
11/7
4/0
21/15
18/125/0
5/0
21/17
21/17
3
8
4
9
1
17/12
14/9
15/11
12/8
17/11
17/11
11/5
11/5
12/8
9/5
H=6
G=5
J=4
11/8
8/5
D=4
Dummy
arc
Dummy
arc
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
Since D or G can’t be crashed the remaining month must be crashed from activity A.
The cheapest way to reduce the project’s completion time by 4 months costs 3 
 $200 � 1 
 $300 � $900.
InInInIn----class Exerciseclass Exerciseclass Exerciseclass Exercise
c) Crash the project in the cheapest possible way so as to have a completion time which is 4
months shorter than the current completion time.
7
5
6
2 10
C=3A=4
F=4
I=6
B=4
E=6
Notation:
LFLS
EFES
/
/
ES = Earliest Start
EF = Earliest Finish
LS = Latest Start
LF = Latest Finish
3
8
4
9
1
H=3
G=5
J=4
D=4
Dummy
arc
Dummy
arc
Notice that there are now 3 critical paths:
�	 → �	 → �	 → �
�	 → �	 → �	 → �
�	 → �	 → �	 → �
17/13
17/13
13/10
13/10
13/8
13/8
17/11
17/11
11/7
11/7
7/4
7/4
8/4
8/4
10/4
10/4
4/0
4/0
7/3
4/0
Activity Predecessor
Normal
Duration 
(months)
Cost Normal 
Duration 
($/month)
Crash
Duration 
(months)
Cost Crash / 
Duration 
($/month)
(a) - 5 $2,900 2 $300
(b) - 4 $3,400 0 na
(c) (a) 3 $3,700 0 na
(d) (a) 4 $4,500 0 na
(e) (a) 6 $3,300 0 na
(f) (b,c) 4 $3,100 0 na
(g) (d) 5 $5,800 0 na
(h) (e) 6 $3,700 4 $200
(i) (f) 6 $2,200 3 $1,200
(j) (g,h) 4 $3,600 0 na
15
MINE3123 - Mine Planning
Mine Closure Planning
BackgroundBackgroundBackgroundBackground
Environmental legislation typically requires mining
companies to return mine sites to a state whereby
they fit in and complement their natural surrounds.
This may require (but is not limited to):
� Dismantling of infrastructure.
� Appropriate disposal/burial of waste/reactive
materials and products.
� Reclamation and revegetation of disturbed land.
� Re-introduction of native flora & fauna.
16
BackgroundBackgroundBackgroundBackground
Mine closure also presents other costs to mining
companies which may include (but is not limited to):
� Redundancy payments to workforce.
� Contract closure payments.
� Community & native title settlement payments.
Mine Closure ConsiderationsMine Closure ConsiderationsMine Closure ConsiderationsMine Closure Considerations
� For most new operations, environmental legislation
requires that mining companies make a bond payment
before project approval to cover the costs of unfinished
environmental rehabilitation in the event that the
company files for bankruptcy.
� A mining operation may also receive a salvage value for
old plant and infrastructure (typically 5% – 10% of CAPEX).
� Mine closure is an important part of the mine financial
evaluation process.
� It should be considered from the outset during the
feasibility and strategic planning phase.
17
Mine Closure ConsiderationsMine Closure ConsiderationsMine Closure ConsiderationsMine Closure Considerations
From an NPV perspective, in many cases it is actually better
for a company to extend mine life by continuing to mine and
process low grade ore (even at a slight loss) if it means that it
delays the cost associated with mine closure.
InInInIn----classclassclassclass Case StudyCase StudyCase StudyCase Study
A small mining operation nearing the end of its life has 7 potential remaining
copper satellite deposits as displayed in the Table below.
The company is utilising its lowest possible mill throughput rate of 5Mtpa in order
to achieve a maximum recovery of 95% Cu. The cost associated with mining and
processing each tonne of ore is $17.80. A discount rate of 18% applies. The copper
price is $5,000/t.
Investigate the impact that present value mine closure costs of $30M, $50M and
$70M (in the year immediately after ceasing operations) have on the NPV of the
project and if altering the closure costs in any way changes the optimal production
schedule for this operation.
Tonnes (Mt) Grade (% Cu)
Deposit L 5.0 0.50
Deposit M 5.0 0.44
Deposit N 5.0 0.41
Deposit O 5.0 0.37
Deposit P 5.0 0.35
Deposit Q 5.0 0.33
Deposit R 5.0 0.22
18
InInInIn----classclassclassclass Case StudyCase StudyCase StudyCase Study
The present values for each deposit is firstly calculated to form the basis for
production scheduling:Tonnes (Mt) Grade (% Cu) Present Value ($M)
Deposit L 5.0 0.50 29.75
Deposit M 5.0 0.44 15.50
Deposit N 5.0 0.41 8.38
Deposit O 5.0 0.37 -1.13
Deposit P 5.0 0.35 -5.88
Deposit Q 5.0 0.33 -10.63
Deposit R 5.0 0.22 -36.75
Cu%3747.0
000,5$95.0
80.17$
=
×
As expected, the cut-off grade is somewhere between the grades for deposit N and O:
Under normal circumstances any grade below 0.3747% Cu would thus not be 
considered as part of the mine planning and scheduling process.
Breakeven Cut-off Grade =
InInInIn----classclassclassclass Case StudyCase StudyCase StudyCase Study
As shown below, the greater the closure cost the better it is to alter the mine plan to 
increase mine life, even if this is at a loss:
Closure costs ($M)
30 50 70
Deposit L
Deposit M
Deposit N 25.97 15.65 5.34
Deposit O 27.75 19.00 10.26
Deposit P 27.18 19.77 12.36
Deposit Q 24.94 18.66 12.38
Deposit R 14.84 9.52 4.20
NPV’s associated with mining to each deposit at each closure cost 
Tonnes (Mt) Grade (% Cu) Present Value ($M)
Deposit L 5.0 0.50 29.75
Deposit M 5.0 0.44 15.50
Deposit N 5.0 0.41 8.38
Deposit O 5.0 0.37 -1.13
Deposit P 5.0 0.35 -5.88
Deposit Q 5.0 0.33 -10.63
Deposit R 5.0 0.22 -36.75
19
MINE3123 - Mine Planning
Final Exam Review
Are YouAre YouAre YouAre You Prepared?Prepared?Prepared?Prepared?
Do you: 
(i) have your current student ID card? 
(ii) know where your exam is? 
(iii) know what materials you are permitted to bring to the exam? – check with your 
course coordinator.
(iv) have your calculator tagged by EAIT Faculty.
For each exam, ensure you:
(i) have rechecked the timetable for exam date, time and venue and checked your 
emails.
(ii) have your student ID card on hand, and ready to present on entry to the exam 
room – should you forget it, you should report to the Student Centre before your 
exam.
(iii) have spare pencils and pens.
(iv) have any permitted materials.
(v) arrive at your exam venue at least 15 minutes before the scheduled start of the 
exam.
20
MINE3123 Exam InformationMINE3123 Exam InformationMINE3123 Exam InformationMINE3123 Exam Information
� Date & Time: Monday 17th November at 2:30pm.
� Location: Michie Building (9):
� Banister, Sam - Maher, Kim: Room 217.
� Mastrogiannis, Yia - Zhou, Nin: Room 211.
� Worth 40% of the MINE3123 course.
� 2 Hours plus 10 minutes perusal time (no writing during perusal).
� Provided with on 14 page answer booklet.
� Calculators - Casio FX82 series or UQ approved (labelled), no other electronic aids 
permitted (eg. laptops, phones, etc.).
� Closed book exam. No notes are permitted.
� Formulas provided.
� 5 Questions:
� Each worth 25%.
� Answer any 4 of the 5 questions.
� Answer each question in the writing booklet unless stated otherwise.
Question 1Question 1Question 1Question 1 (25%)(25%)(25%)(25%)
�Open pit mine optimisation
�Floating Cone / Lerchs Grossmann
�Determine ultimate pit limit
�Sequencing
�Capacity constrained scheduling
�Present value calculation of mine plan
21
Question 2Question 2Question 2Question 2 (25%)(25%)(25%)(25%)
�Open pit phase/pushback analysis
�Scheduling
�Mine life / phase life / stripping ratios
�Overall optimum mining strategy.
�Phase-wise stripping schedules
�Inventory/Saw-Graphs
Question 3Question 3Question 3Question 3 (25%)(25%)(25%)(25%)
�Linear/Mixed Integer Programming & Critical Path Method
�LP/MIP modelling for a given problem
�Define variables
�Formulate objective function
�Formulate constraint equations
�Graphical representation
�Sensitivity
�Draw a network flow diagram for a given set of activities
�Consider all precedence information carefully
�Be familiar with what the critical path represents
�Be familiar with float times
�Be familiar with earliest & latest, start & finish times and all other 
definitions
�Reducing completion time – crashing
22
Question 4Question 4Question 4Question 4 (25%)(25%)(25%)(25%)
�Cut-off grade
�Breakeven/Basic cut-off
�Strategic life of mine cut-off grade policy
�Lane’s 6 cut-off grades
�Know the grade-tonnage curve and be prepared to be able to 
calculate/determine cut-off/average grades within each 
interval
Question 5Question 5Question 5Question 5 (25%)(25%)(25%)(25%)
�Financial Technical Modelling (FTM)
�WACC
�Debt to equity
�Interest
�Taxation
�Carry forward tax loses
�Debt repayments
�Present value factors
�Present values
�Net Smelter Return
�ROM Tonnes versus Washed Tonnes