MSCI 224 Techniques for Management Decision Making 2018
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2018 EXAMINATIONS
PART
II (Second,
Third
and
Final
Year)
MANAGEMENT
SCIENCE
MSCI
224 Techniques
for
Management
Decision
Making
PART
A: Answer Question
A1 in
this
section
of
the
paper.
Question A1 (25
marks)
In
preparation
of
this
year’s
winter
season,
a
ski
resort
is
debating
to
expand
its
current
services
to
also
include
some
form
of
snowcat
skiing.
This
growing
trend
in
the
international ski
industry
started
about
30
years
ago
in
British
Columbia
and
uses
modern
fleets
of
ski
hill grooming
machines
to
provide
expert
skiers
with
access
to
the
deep
powder
backcountry, which
would
not
be
served
by
traditional
lifts
due
to a general
lack
of
demand
by
the
majority of
skiers.
Based
on
a
preliminary customer survey to
better
understand
the potential use
by its
current
visitors,
the
ski
resort
estimates
that
the
average
number
of
skiers
to
arrive
and queue
at a snowcat
collection
point
per
minute
will
follow
the
following
distribution:
|
No. |
0 |
1 |
2 |
3 |
4 |
5 |
|
Probability |
0.10 |
0.15 |
0.30 |
0.20 |
0.15 |
0.10 |
Based
on
its
current
snowcat
operations,
the
time
between
snowcat
departures
from
the collection
point is
predicted
to vary according
to
the
following
distribution:
|
No. |
2 |
3 |
4 |
|
Probability |
0.2 |
0.5 |
0.3 |
Once
skiers
have
arrived
at
the
snowcat
collection
point,
they
wait
in
a
queue
until
the
first snowcat
arrives
which
has
room
to
take
them.
Each
snowcat
has
a
capacity
for
10
people.
(a) Explain
how
you
would
use
random
numbers
to
model
the
variability
in
this
situation.
(4 marks)
(b) Carry
out
a
simulation
of
10
snowcat
departures
from
the
snowcat
collection
point.
Start
your
simulation
assuming
that
a
snowcat has
just
left
taking
all
the
skiers
who
were
waiting for
it.
For
the
simulation
of
the
time
between
all
following
snowcat
departures,
start
from
the first
line
of
the
random
number
tables
and
use
single
digits
(e.g.,
1,
8,
6,
9,
…)
Similarly,
for the
simulation
of
the
skiers
who
arrive
and
queue,
start
from
the
second
line
and
use
double digits
(e.g.,
90,
42,
07,
45,
…).
Use
your
simulation
to
estimate
the
proportion
of
skiers
who are able
or unable
to
get
on
the
first
snowcat
to
arrive
after
they
have
started
waiting.
(12 marks)
(c)
Explain
what
is
meant
by
a
“warm-up”
or
“running-in”
period
for
a
simulation.
How
would you
decide
whether
it
is
appropriate
to
use
such
a
period
in
this
simulation?
(2 marks)
(d)
Identify
two
ways
in
which
you
think
your simulation
model
may
oversimplify
what happens
in
an
actual ski
resort
in
which
snowcat
skiing
is
already
offered.
Describe
how
you could
modify
your
simulation
model
to
include
the
effects
you
have
identified.
(4 marks)
(e)
What
are three potential
advantages
or
benefits
of
using
a
simulation
model
of
a
situation compared
to
experimenting
with
the
real
system?
(3 marks)
2022-05-25