Transcript Document

Simulation
An Example
A garage hires out cars. It currently owns four
cars which are hired out on a daily basis for a
number of days. The demand pattern in the past
has been as follows
Number
of cars
0
1
2
3
4
Demand
per day
probability
0.15
0.25
0.30
0.20
0.10
The length of rental is shown below
Length 1
of rental
(days)
Probability 0.60
2
3
0.30
0.10
The company charges £40 a day for hire. It
estimates that the total fixed overheads
attributed to this operation are £10 a day. If
the car is hired out the extra repair and
maintenance costs generated are estimated
at £6 a car a day.
If the demand for hired cars exceeds the current
number of four cars they then hire from another
garage at additional cost of £24 a day.
Carry out a simulation to forecast the overall
demand pattern for car hire and estimate the
annual contribution to overheads and profits
from the car hire business.
The first thing to do is to construct cumulative
frequency tables to decide which random
numbers refer to a particular scenario.
Number
of cars
0
1
2
3
4
Demand
0.15
per day
probability
Cumulative 0.15
probability
0.25
0.30
0.20
0.10
0.40
0.70
0.90
1.00
Random
numbers
16-40
41-70
71-90
91-00
1-15
This means, for example, that a random
number of 17 would interpret as a demand of
1 on that particular day, whilst a value of 95
would imply a demand of 4.
The same process is carried out for length of
hire.
The length of rental is shown below
Length of
1
rental (days)
Probability
0.60
2
3
0.30
0.10
Cumulative
probability
0.60
0.90
1.00
Random
Numbers
1-60
61-90
91-00
We will use the following random numbers
(from a book of tables)
84 42 56 73 87 75 18 91 76 66 64 83 97 11
69 41 80 92 38 75 28 87 77 03 57 09 85 86
46 86 40 15 31 81 78 91 30 22 88 58
Generate 10 days of business
Day
1
2
3
4
5
Hire Car Number Other Garage
Demand Total
Demand 1 2
3
4 5 6 7 8
Day 1
Random Number is 84
This means a demand of 3
Day
Hire Car Number Other Garage
Demand Total
Demand 1 2
3
4 5 6 7 8
1
3
2
3
4
5
3
X
X
X
Day 1
We now need to work out how long each
car is out for
Length of Rental
Car 1
Next Random Number is 42
This corresponds to a duration of 1 day
Day
Hire Car Number Other Garage
Demand Total
Demand 1 2
3
4 5 6 7 8
1
3
2
3
4
5
3
X
X
X
Length of Rental
Car 2
Next Random Number is 56
This corresponds to a duration of 1 day
Car 3
Next Random Number is 73
This corresponds to a duration of 2 days
Day
Hire Car Number Other Garage
Demand Total
Demand 1 2
3
4 5 6 7 8
1
3
2
3
4
5
3
X
X
X
X
Day 2
Random Number is 87
This means a demand of 3
Day
Hire Car Number Other Garage
Demand Total
Demand 1 2
3
4 5 6 7 8
1
3
3
X
X
X
2
3
4
X
X
X
3
4
5
X
Length of Rental
The next three random numbers are
75, 18 and 91 meaning rental durations of
2, 1 and 3 respectively
Day
Hire Car Number Other Garage
Demand Total
Demand 1 2
3
4 5 6 7 8
1
3
3
X
X
X
2
3
4
X
X
X
3
4
5
X
X
X
X
This can be carried on for a ten day period
and the costs calculated.