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Suppose we are considering the selection of the reorder point, R, of a (Q, R) inventory policy. With this policy, we order up to Q when the inventory level falls to R or less. The probability distribution of daily demand is given in Table.
Daily Demand (units) |
Probability |
12 |
.05 |
13 |
.15 |
14 |
.25 |
15 |
.35 |
16 |
.15 |
17 |
.05 |
The lead time is also a random variable and has the distribution in Table.
Lead Time (days) |
Probability |
1 |
.20 |
2 |
.30 |
3 |
.35 |
4 |
.15 |
We assume that the “order up to” quantity for each order stays the same at 100. Our interest here is to determine the value of the reorder point, R, that minimizes the total variable inventory cost. This variable cost is the sum of the expected inventory carrying cost, the expected ordering cost, and the expected stockout cost. All stockouts are backlogged. That is, a customer waits until an item is available. Inventory carrying cost is estimated to be 20¢/unit/day and is charged on the units in inventory at the end of a day. A stockout costs $1 for every unit short. The cost of ordering is $10 per order. Orders arrive at the beginning of a day. Develop a simulation model to simulate this inventory system to find the best value of R.
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