Question

For a given inventory item, demand averages 70 units per week, with a standard deviation of 5 units. Lead time for this item is 2 weeks. If we wanted to set a reorder point for this item that exposes to not more than a 2.5% risk of a stockout, that reorder point would be units. (Round to 2 decimal places and report only the number.)

Answer 1

The reorder point for an item with an average demand of 70 units per week, a standard deviation of 5 units, and a lead time of 2 weeks to have not more than a 2.5% risk of stockout is 153.86 units.

Step-by-step explanation:

To calculate the reorder point with not more than a 2.5% risk of stockout, we need to consider the demand and its variability (standard deviation) during the lead time. Assuming a normal distribution, we can use the z-score corresponding to the desired service level. Here, the service level is 1 - 0.025 because we're looking at the top 2.5% of the probability, and we want to find the 97.5th percentile.

The z-score for the 97.5th percentile is approximately 1.96. The formula for the reorder point (ROP) is given by:

ROP = (Average demand per unit of time) × (Lead time) + (z-score) × (Standard deviation of demand) × (Square root of Lead time)

Plugging in the given numbers:

ROP = (70 units/week) × (2 weeks) + (1.96) × (5 units/week) × (√2)

ROP = 140 units + (1.96) × (5 units/week) × (1.414)

ROP = 140 units + (1.96) × (5 units/week) × (1.414)

ROP = 140 units + 13.86 units

ROP = 153.86 units

The reorder point that exposes us to not more than a 2.5% risk of stockout is 153.86 units, rounded to two decimal places.