The managers of a food company are about to install a number of automatic vendin
ID: 459506 • Letter: T
Question
The managers of a food company are about to install a number of automatic vending machines at various locationa in a major city. A number of types of machines are avaliable and the managers would like to choose the design which will minimize the profit that will be lost because the machine is out of order. The following models is to be used to represent the lost profit: Cost of lost profit per month=(number of breakdowns per month)X (Time to repair machine after each breakdow, in hours) X (Profits lost per hour)
One machine that is being considered is the Supervend, and the following probability distribution have been estimated for this machine:
(a) use the table of random numbers, to simulate the operation of a machine for 12 months and hence estimate a probability distribution for the profit that would be lost per monthif the machine was purchased.
(B) Explain why the model is likely to be a simplification of the real problem.
Number of Break downs p. mth. Prob. Repair Time in HRS Prob. Aver. Profit lost per Hr. Prob. 0 0.5 1 0.45 $10 0.7 1 0.3 2 0.55 $20 0.3 2 0.2Explanation / Answer
Steps in the Monte Carlo Simulation Process
The Monte Carlo simulation technique consists of following steps:
Step 1: in the simulation model, set-up probability distribution for the variables to be analyzed.
Step 2: build cumulative probability distribution for each random variable.
Step 3: generate random numbers and then, assign an appropriate set of random numbers (RN) to represent a value or range (RN interval) of values for each random variable. Normally, random numbers 00—99 (100 in count) are assigned to variables.
Step 4: conduct the simulation experiment using random sampling or according to the given sets of random numbers.
Step 5: repeat step 4 until the required number of simulation runs have been generated.
Step 6: design and implement a course of action and maintain control.
Allocation of Random Number Intervals (RNI) for each factor:
No. of Breakdown/mth
Prob.
Cum. Prob.
Random Number Interval
0
0.5
0.5
00 – 49
1
0.3
0.8
50 – 79
2
0.2
1
80 – 99
Repair time in HRS
Prob.
Cum. Prob.
Random Number Interval
1
0.45
0.45
00 – 44
2
0.55
1
45 -99
Avrg. Profit lost per Hr.
Prob.
Cum. Prob.
Random Number Interval
$10
0.7
0.7
00 – 69
$20
0.3
1
70 – 99
Simulating model for 12 months:
For No. of Breakdown per month
For Repair time in Hours
For Avrg. Profit lost per Hour
Simulated Cost of Lost profit per month
Simulated Months
RN
RNI
Simulated Value
RN
RNI
Simulated Value
RN
RNI
Simulated Value
1
37
00 - 49
0
79
45 -99
2
88
70 - 99
$20
$0
2
99
80 - 99
2
10
00 - 44
1
69
00 - 69
$10
$20
3
90
80 - 99
2
73
45 -99
2
11
00 - 69
$10
$40
4
58
50 - 79
1
78
45 -99
2
9
00 - 69
$10
$20
5
21
00 - 49
0
19
00 - 44
1
47
00 - 69
$10
$0
6
53
50 - 79
1
62
45 -99
2
64
00 - 69
$10
$20
7
71
50 - 79
1
62
45 -99
2
83
70 - 99
$20
$40
8
4
00 - 49
0
36
00 - 44
1
23
00 - 69
$10
$0
9
24
00 - 49
0
64
45 -99
2
40
00 - 69
$10
$0
10
47
00 - 49
0
42
00 - 44
1
72
70 - 99
$20
$0
11
56
50 - 79
1
28
00 - 44
1
83
70 - 99
$20
$20
12
82
80 - 99
2
22
00 - 44
1
2
00 - 69
$10
$20
Estimating Probabilities from Simulation Results:
Cost of Lost profit per month
Number of simulations resulting in this cost
Probability
$0
5
0.42
$10
0
0.00
$20
5
0.42
$40
2
0.17
Total
12
1
b>
The cost of lost profit per month is depended on three factors:
Each of these factors have their own probability distribution, thus it very difficult task to obtain probability distribution of cost of lost profit. Monte Carlo Simulation is best method which generates large number of possible combinations for each factor depending on their probability distribution. When the simulation is performed the circumstances which are more likely are frequently generated and those which are unlikely and rarely generated. Effect of each factor is combined for each simulation run and payoff of output is calculated. Then by counting the occurrence for output payoff, the probability distribution for the output factor is estimated.
No. of Breakdown/mth
Prob.
Cum. Prob.
Random Number Interval
0
0.5
0.5
00 – 49
1
0.3
0.8
50 – 79
2
0.2
1
80 – 99
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