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A firm sells bulk rolls of newsprint.

The daily demand is given by the following probability distribution:

Daily Demand (Rolls) 3 4 5 6
Probability 0.20 0.35 0.30 0.15

Lead time is a random variable given by the following distribution:

Lead Time (Days) 1 2 3
Probability 0.36 0.42 0.22

Determine the lead-time demand for 5 cycles of simulation. Random digits for lead time and demand are as follows:

R.D for Lead Time 46 75 86 27 63
Probability 4 5 4 5 6 3 4 4 6 4
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Using the probability of demand, we can assign random digits to demand, similarly, we can assign random digits to lead time by using the probability to lead time.

Table A: Random Digit Assignment for Daily Demand

Daily Demand Probability Cumulative Prob Random Digit Assignment
3 0.20 0.20 1 - 20
4 0.35 0.55 21 - 55
5 0.30 0.85 56 - 85
6 0.15 1.00 86 - 00

Table B: Random Digit Assignment for Lead Time

| Lead Time | Probability | Cumulative Prob | Random Digit Assignment | | 1 | 0.36 | 0.36 | 1- 36 | | 2 | 0.42 | 0.78 | 37 - 78 | | 3 | 0.22 | 1.00 | 79 - 00 |

The random digit for lead time for first cycle is given by 46. Mapping it (46) to table B gives a lead time of 2 days. Hence two random digits are required for demand (4,5)

R.D. for lead time 46 75 86 27 63 - - - - -
R.D. for demand 4 5 4 5 6 3 4 4 6 4

After mapping, these R.D. for demand from table A, if gives demand of '3' for both random digits. So, lead time demand for first cycle is b(3+3). In this way, lead time demand is calculated for remaining cycles and given Table 'C'.

cycle Random
Digit
for Lead
Time
Lead
Time
Random
Digit
Demand
Daily
Demand
Lead
Time
Demand
1 46 2 4
5
3
3
6
2 75 2 4
5
3
3
6
3 86 3 6
3
4
3
3
3
9
4 27 1 4 3 3
5 63 2 6
4
3
3
6

Table 'C': Simulation table for Lead Time Demand

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