2. The night manager of a resort hotel has asked the telephone operator to keep
ID: 371124 • Letter: 2
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2. The night manager of a resort hotel has asked the telephone operator to keep track of the nature of all calls received from outside of the hotel. The results for 100 calls are shown below Number of Calls Nature of Call R: Make a reservation C: Confirm/cancel A Check availability P: Price Inquiry O: Other 42 27 14 10 The manger knows that the amount of time spent by the operator in responding to the calls differs depending on the nature of the call. The manager is, therefore, particularly interested in getting an idea of the sequence of calls, in order to gain insight into how the operator's time might be spent with the calls. To do this, the manager wants to simulate 10 calls. a) Keeping the list of call types in the order shown, indicate how random numbers would be assigned to each cali type b) g two-digit numbers from Row 8 of Table 1, simulate 10 calls.Explanation / Answer
Monte Carlo Simulation:
1. In the simulation model, set-up probability distribution for the variables to be analyzed.
2. Build cumulative probability distribution for each random variable.
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 0.0—.99 (100 in count) are assigned to variables.
4. Conduct the simulation experiment using random sampling or according to the given sets of random numbers.
The probability of getting R-type call is 0.42, assign 42 random numbers, 0.0 to 0.41 (but less than 0.42) to R-type call. Similarly, the probability of C-type call is 0.27, the next 27 numbers from 0.42 to 0.68 would be assigned to this level. Similarly other RN intervals are identified as follows:
Nature of Call
Frequency
Probability
Cumulative Probability
Random Number Intervals
R
42
0.42
0.42
0 but less than 0.42
C
27
0.27
0.69
0.42 but less than 0.69
A
14
0.14
0.83
0.69 but less than 0.83
P
7
0.07
0.90
0.83 but less than 0.90
O
10
0.10
1.00
0.90 but less than 0.99
100
If two digit random number is required, then following intervals will be assigned:
Nature of Call
Frequency
Probability
Cumulative Probability
Random Number Intervals
R
42
0.42
0.42
00 but less than 42
C
27
0.27
0.69
42 but less than 69
A
14
0.14
0.83
69 but less than 83
P
7
0.07
0.90
83 but less than 90
O
10
0.10
1.00
90 but less than 99
100
Example of simulation:
Simulation Trials
Random Number
Simulated call type
1
67
C
2
12
R
3
90
O
If the generated random number if 90, then the number is included in range of 90 but less than 99. Thus, simulated call type is O.
Nature of Call
Frequency
Probability
Cumulative Probability
Random Number Intervals
R
42
0.42
0.42
0 but less than 0.42
C
27
0.27
0.69
0.42 but less than 0.69
A
14
0.14
0.83
0.69 but less than 0.83
P
7
0.07
0.90
0.83 but less than 0.90
O
10
0.10
1.00
0.90 but less than 0.99
100
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