Mining & Mineral Economics

Network Analysis (PERT/CPM)

Critical path, the three-point PERT estimate and float — the project-scheduling tools for mine development and shutdowns.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Network analysis schedules interdependent activities (sinking, drivages, plant installation, shutdowns). Activities and their dependencies form a network; the critical path is the longest chain of activities, and its length is the shortest possible project duration. CPM (Critical Path Method) uses single deterministic durations; PERT treats durations as uncertain, combining an **optimistic (

o

), most-likely (

m

) and pessimistic (

p

) estimate into an expected time. Float (slack) is the spare time a non-critical activity has before it delays the project; critical activities have zero float**.

The Core Formula Matrix

PERT expected time:

t_{e} = \frac{o + 4 m + p}{6}

Activity variance:

σ^{2} = (\frac{p - o}{6})^{2}

Total float:

T F = L S - E S = L F - E F

(late minus early start/finish)

Project duration = sum of

t_{e}

along the critical path (the path with zero total float).

The ‘IIT Traps’

⚠
**The most-likely estimate $m$ carries a weight of 4** in $t_{e} = (o + 4 m + p) /6$ ; treating all three equally is wrong.
⚠
The critical path is the *longest* path, because every activity on it must finish for the project to end.
⚠
Critical activities have zero float. Any float means the activity is not critical.
⚠
**Variance uses $(p - o) /6$ squared** — only the spread of the extremes, not $m$ .

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

In project network analysis, an activity that lies on the critical path has a total float of:

Q2MEDIUM2 Marks · NAT

An activity has an optimistic time of

4 days

, most-likely

6 days

and pessimistic

14 days

. Its PERT expected time is ______ days. (Round off to one decimal place.)

days

Q3HARD2 Marks · NAT

For the activity above (

o = 4

p = 14

), the standard deviation of its duration is ______ days. (Round off to two decimal places.)

days