In this video, I'll talk about the economic order quantity (EOQ) inventory model with
nonzero lead time and deterministic demand.
The lead time is a known constant number.
We denote it with a capital letter L. If the lead time L is greater than zero, we
will receive the products L years after the order is placed.
Usually, L is a fraction of 1 year so it is less than 1.
The annual ordering cost and the annual holding do not change.
Hence, the EOQ still minimizes the total cost.
To prevent shortages and minimize the holding cost, each order must be placed L years ahead
of time so that the inventory level is decreased to zero when the products arrive.
The inventory level y at which an order should be placed is the reorder point.
To determine the reorder point y, we must consider two cases.
Case 1: L ≤ x/D. It means the lead time is shorter than a cycle.
We must order at this point so that after the lead time, the products will arrive exactly
when the inventory is reduced to 0.
In this case, we have two similar triangles, this small one and this large one.
Because the lengths of corresponding sides are proportional, the ratio of this side to
this side, that is, y to x*, must be equal to the ratio of this side to this side, that
is, L to x*/D.
This equation leads to this result: the reorder point occurs when the inventory level equals
LD.
Case 2: L is greater than k cycles but less than or equal to k+1 cycles, k is equal to
1, 2, 3, and so on.
For example, if the lead time is longer than one cycle but shorter than two cycles, k=1.
We must order at this point so that after the lead time, the products will arrive exactly
when the inventory is decreased to 0.
Let L' be the lead time that is beyond k cycles.
In this case, the ratio of this side to this side, that is, y to x*, must be equal to the
ratio of this side to this side, that is, L' to x*/D.
From this equation, we get this result, the inventory level equals L'D.
Let's revisit the car dealer example that was introduced in a previous video.
The EOQ is 21.9 cars per order.
The cycle time is 0.073 years, or 26.7 days.
If the lead time L is 1 week, 7 days, then the reorder point is L times D is equal to
5.7.
It means, when there are 5.7 cars left in the inventory, we need to place the next order
for 21.9 cars.
If the lead time L is one month, then k=1.
It means, the lead time is longer than one cycle but less than 2 cycles.
After calculation, L' is equal to 0.01 years.
The reorder point is L' times D is equal to 3.
It means, when there are 3 cars left in the inventory, we need to place the next order
for 21.9 cars.
Okay, that is about the EOQ inventory model with nonzero lead time and deterministic demand.
Thanks for watching.