Simulation of inventory problem

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Simulation of inventory problem

A dealer of electrical appliances has a certain product for which the probability distribution of demand per day and the probability distribution of the lead-time, developed by past records are as shown in Table

Probability Distribution of Lead Demand

Demand (Units)
2
3
4
5
6
7
8
9
10
Probability
0.05
0.07
0.09
0.15
0.20
0.21
0.10
0.07
0.06
Probability Distribution of Lead Time
Lead Time (Days)
1
2
3
4
Probability
0.20
0.30
0.35
0.15
The various costs involved are,
Ordering Cost = `  50 per order
Holding Cost = `  1 per unit per day
Shortage Cost = `  20 per unit per day
The dealer is interested in having an inventory policy with two parameters, the reorder point and the order quantity, i.e., at what level of existing inventory should an order be placed and the number of units to be ordered. Evaluate a simulation plan for 35 days, which calls for a reorder quantity of 35 units and a re-order level of 20 units, with a beginning inventory balance of 45 units.
Assigning of random number intervals for the demand distribution and lead-time distribution is shown in Tables
Random Numbers Assigned for Demand Per Day
Demand per Day
Probability
Cumulative Probability
Random Number Interval
2
0.05
0.05
00-04
3
0.07
0.12
05-11
4
0.09
0.21
12-20
5
0.15
0.36
21-35
6
0.20
0.56
36-55
7
0.21
0.77
56-76
8
0.10
0.87
77-86
9
0.07
0.94
87-93
10
0.06
1.00
94-99
Table 9.26: Random Numbers Assigned for Lead-time
Lead Time (Days)
Probability
Cumulative Probability
Random Number Interval
1
0.20
0.20
00-19
2
0.30
0.50
20-49
3
0.35
0.85
50-84
4
0.15
1.00
85-99
Reorder Quantity = 35 units, Reorder Level = 20 units, Beginning Inventory = 45 units