| 3. |
(a) Discuss the effectiveness of
simulation as a business tool. |
[5] |
|
The
candidates might discuss the effectiveness of simulation in terms of advantages only,
disadvantages only, or a mixture of both. In any case, a well reasoned argument should be
awarded (5 marks) with individual marks awarded for any valid points from the following: |
|
|
Advantages: |
|
|
|
Can
provide solutions when analytical techniques not available. |
|
|
|
Lack of
restrictive assumptions makes it a flexible tool. |
|
|
|
Less
costly than experiments. |
|
|
|
Can be
applied to a wide variety of situations. |
|
|
Disadvantages: |
|
|
|
Only gives
approximate behaviour. |
|
|
|
Model
building can be complex and time-consuming. |
|
|
|
Can only
be used to model situations with random elements. |
|
|
|
Only
practical where computers are available. |
|
|
[5
marks] |
|
|
|
|
|
(b) A retailer has placed in order
for 25 units of a certain item to be delivered daily.The estimated sales for each day are
expected to follow the probability distribution given below: |
|
|
| Demand |
Probability |
| 10 |
0.07 |
| 20 |
0.13 |
| 30 |
0.39 |
| 40 |
0.16 |
| 50 |
0.08 |
| 60 |
0.17 |
|
|
|
You are also provided with the
following information: |
|
|
|
each unit cost $20 and is sold for
$26 |
|
|
|
There is a loss of goodwill of $6
per unit (this is the loss suffered if there is no stock to satisfy a particular customer) |
|
|
|
the retailer does not have any
storage facilities so that any units remaining unsold at the end of the day are thrown
away. |
|
|
|
|
(i) What do the probability values listed
above indicate? |
[2] |
|
|
|
The probabilities give
an indication of the likely level of demand, the higher the probability, the more likely
that particular level of demand is to occur. |
|
|
[2
marks] |
|
|
|
|
(ii) Explain how pseudo-random numbers can be
assigned to each level of demand, and complete the assignment of pseudo-random numbers to
the table given above. |
[5] |
|
|
|
Random numbers in the
range 01, 02, up to 99, 00 are assigned to the table according to the cumulative
probability values associated with each level of demand, so that demand of 10 numbers
01-07, demand of 20 has 08-20 and so on, as listed below. |
[1] |
|
[1
mark] |
|
|
| Demand |
Probability |
Cumulative
Probability |
Random
Values |
| 10 |
0.07 |
0.07 |
01 - 07 |
| 20 |
0.13 |
0.20 |
08 - 20 |
| 30 |
0.39 |
0.59 |
21 - 59 |
| 40 |
0.16 |
0.75 |
60 - 75 |
| 50 |
0.08 |
0.83 |
76 - 83 |
| 60 |
0.17 |
1.00 |
84 - 00 |
|
|
|
[4
marks] |
|
|
Note: It is
equally valid to start from 00, so that for example the range 00 - 06 would be assigned to
a demand of 10. |
|
|
|
|
(iii) Given the stream of random digits
65065834589678832548, simulate demand for this business over a ten-day period. |
[3] |
|
|
|
| Day |
Random
Number |
Demand |
| 1 |
65 |
40 |
| 2 |
06 |
10 |
| 3 |
58 |
30 |
| 4 |
34 |
30 |
| 5 |
58 |
30 |
| 6 |
96 |
60 |
| 7 |
78 |
50 |
| 8 |
83 |
50 |
| 9 |
25 |
30 |
| 10 |
48 |
30 |
|
|
|
[3
marks] |
|
|
|
|
|
(c) Use your simulation to deduce
whether the business is likely to be profitable. |
[5] |
|
| Day |
Random
Number |
Demand |
Sales |
Loss |
| 1 |
65 |
40 |
25 |
15 |
| 2 |
06 |
10 |
10 |
0 |
| 3 |
58 |
30 |
25 |
5 |
| 4 |
34 |
30 |
25 |
5 |
| 5 |
58 |
30 |
25 |
5 |
| 6 |
96 |
60 |
25 |
35 |
| 7 |
78 |
50 |
25 |
25 |
| 8 |
83 |
50 |
25 |
25 |
| 9 |
25 |
30 |
25 |
5 |
| 10 |
48 |
30 |
25 |
5 |
| Total |
|
360 |
235 |
125 |
|
|
|
[3
marks] |
|
|
Profit
calculation = 235 X 26 - 250 X 20 - 125 X 6 = $360 |
|
|
i.e.
calculate the total revenue and deduct the costs (=cost price + goodwill cost). |
|
|
So the
business will be profitable (but not very!). |
|
|
[2
marks] |
|