Mining & Mineral Economics

Mine Planning & Facility Location

The centre-of-gravity method that places a facility to minimise weighted transport, working coordinate by coordinate.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Locating a central facility (crusher, plant, workshop) to minimise haulage uses the centre-of-gravity (centroid) method. Each demand/supply point has a weight (tonnage or trips) and coordinates. The optimal location's coordinates are the weight-weighted averages of the point coordinates — computed independently for

x

and

y

The Core Formula Matrix

Centre of gravity:

x^{*} = \frac{\sum w _{i} x _{i}}{\sum w _{i}}, y^{*} = \frac{\sum w _{i} y _{i}}{\sum w _{i}}

w_{i}

= weight (tonnage/trips) at point

i

The ‘IIT Traps’

⚠
Weight by tonnage/trips, not by the number of points.
⚠
**Compute $x^{*}$ and $y^{*}$ separately**, each with the same total weight in the denominator.
⚠
**Use total weight $\sum w_{i}$ ** in the denominator, not the count.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Two sources: weight

10

x = 0

and weight

30

x = 8

. The centre-of-gravity

x

-coordinate is:

Q2MEDIUM2 Marks · NAT

Weights

20, 30, 50

sit at

y = 2, 4, 6

. The centre-of-gravity

y

-coordinate is ______. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

Three loading points with trip-weights

100, 200, 300

lie at

x = 10, 20, 40 km

. The centre-of-gravity

x

-coordinate is ______ km. (Round off to two decimal places.)