The reorder point [see equation 14.6] is defined as the lead-time demand for an item. In cases of long lead times, the lead tie demand and thus the reorder point may exceed the economic order quantity Q*. In such cases, the inventory position will not equal the inventory on hand when an order is placed, and the reorder point may be expressed in terms of either the inventory position or the inventory on hand. Consider the economic order quantity with D = 5000, C0 = 32, Ch = 2, and 250 working days per year. Identity the reorder point in terms of the inventory position and in terms of the inventory on hand for each of the following lead times.

Equation 14.6?

To calculate the reorder point in terms of inventory position and inventory on hand for different lead times, we need to first find the economic order quantity (Q*) using the given values of D, C0, Ch, and the number of working days per year.

The formula to calculate the economic order quantity (Q*) is as follows:

Q* = sqrt((2*D * C0) / Ch)

where:
- D is the demand per year (5000)
- C0 is the fixed cost per order ($32)
- Ch is the holding cost per unit per year ($2)

Let's substitute the values and calculate Q*:

Q* = sqrt((2 * 5000 * 32) / 2)
= sqrt(160000)
= 400

Now, let's calculate the reorder point in terms of inventory position and inventory on hand for different lead times.

1. Lead time = 2 working days:

Reorder point in terms of inventory position:
Reorder point = Lead time demand
= D * (Lead time / Number of working days per year)
= 5000 * (2 / 250)
= 40

Reorder point in terms of inventory on hand:
Reorder point = Reorder point in terms of inventory position - Q*
= 40 - 400
= -360

2. Lead time = 5 working days:

Reorder point in terms of inventory position:
Reorder point = D * (Lead time / Number of working days per year)
= 5000 * (5 / 250)
= 100

Reorder point in terms of inventory on hand:
Reorder point = Reorder point in terms of inventory position - Q*
= 100 - 400
= -300

3. Lead time = 10 working days:

Reorder point in terms of inventory position:
Reorder point = D * (Lead time / Number of working days per year)
= 5000 * (10 / 250)
= 200

Reorder point in terms of inventory on hand:
Reorder point = Reorder point in terms of inventory position - Q*
= 200 - 400
= -200

Therefore, the reorder points in terms of inventory position and inventory on hand for each lead time are as follows:

- For a lead time of 2 working days: Inventory position - 40, Inventory on hand - (-360)
- For a lead time of 5 working days: Inventory position - 100, Inventory on hand - (-300)
- For a lead time of 10 working days: Inventory position - 200, Inventory on hand - (-200)