SME
Construction Engineering · Problem type
Trucks to match a loader
Use this for “Trucks of 14 m³ take 18.98 min for each cycle, and the loader fills one in 4.2 min. With 4 trucks at 50 min/h, how many trucks balance the loader, and which one limits production?”
Chart
Ringed: Spread production, P = 147.5 m³/h
Trucks used N = 4
Balanced fleet size Nb = 4.519
This is an example. Type your own values to start a new problem.
Nb
=
tc (min)
tₗ (min)
Pₜ (m³/h)
=
×
q (m³)
×
E (min/h)
tc (min)
Pₗ (m³/h)
=
q (m³)
×
E (min/h)
tₗ (min)
q is a truck’s load, tc its round trip and tₗ its loading time; N trucks work E minutes an hour, and Nb trucks would keep the loader busy.
P
Spread production
worked out (not typed) · m³/h
Formulas
Nb
=
tc
tₗ
4.519
=
18.98
4.2
Pₜ
=
N
×
q
×
E
tc
147.5
=
4
×
14
×
50
18.98
Pₗ
=
q
×
E
tₗ
166.7
=
14
×
50
4.2
P
=
min(Pₜ,
Pₗ)
147.5 = min(147.5, 166.7)
Assumptions
•
The loader fills one truck at a time and never waits for a truck when N ≥ Nb.
•
The spread produces the smaller of Pₜ and Pₗ: trucks queue or the loader waits.
•
Loader and trucks work the same E minutes in each hour; tc includes the loading time.
Step-by-step
WE KNOW
q = 14 m³, tc = 18.98 min, tₗ = 4.2 min, E = 50 min/h, N = 4
FIND
balanced fleet size (Nb), fleet production (Pₜ), loader production (Pₗ), spread production (P)
Step 1 · Find balanced fleet size (Nb)
Use Nb = tc ÷ tₗ
While
one
truck
goes
round
its
cycle,
the
loader
can
fill
tc
tₗ
trucks:
that
many
keep
it
busy.
Nb
=
18.98
4.2
Nb = 4.519
Step 2 · Find fleet production (Pₜ)
Use Pₜ = N × q × E ÷ tc
Each
truck
makes
E
tc
trips
in
each
hour
with
q
on
board;
N
trucks
move
N
times
that.
Pₜ
=
4
×
14
×
50
18.98
Pₜ
=
56
×
50
18.98
Pₜ
=
2,800
18.98
Pₜ = 147.5 m³/h
Step 3 · Find loader production (Pₗ)
Use Pₗ = q × E ÷ tₗ
E
tₗ
is
how
many
times
the
truck
loading
fits
in
the
working
minutes
of
each
hour;
each
time
moves
one
load
q
.
Pₗ
=
14
×
50
4.2
Pₗ
=
700
4.2
Pₗ = 166.7 m³/h
Step 4 · Find spread production (P)
Use P = min(Pₜ, Pₗ)
The trucks limit production: the loader waits for trucks. 5 trucks would keep the loader busy.
P
=
min(147.5,
166.7)
P
=
147.5
m³/h
Check
Put the numbers back in. Both sides should match.
4.519
=
18.98
4.2
✓
147.5
=
4
×
14
×
50
18.98
✓
166.7
=
14
×
50
4.2
✓
147.5 = min(147.5, 166.7) ✓
Topic check
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