Calculate the optimal number Minimum and maximum stock level to maintain in the store

We need the average weekly demand to determine stock levels over time.

$$\text{Average Weekly Demand} = \frac{\text{Annual Demand}}{\text{Number of weeks in a year}}$$

Assuming 52 weeks in a year:

$$\text{Average Weekly Demand} = \frac{600\,000 \text{ units}}{52 \text{ weeks}} \approx 11\,538.46 \text{ units/week}$$

The "Unit security margin 75%" is interpreted as 75% of the average weekly demand, which serves as the safety stock to cover unexpected demand or delays.

$$\text{Safety Stock (SS)} = 0.75 \times \text{Average Weekly Demand}$$ $$\text{SS} = 0.75 \times 11\,538.46 \text{ units} \approx 8\,653.85 \text{ units}$$

Rounding to the nearest whole unit, the minimum stock level is 8,654 units.

The optimal number refers to the reorder point (ROP), which is the inventory level at which a new order should be placed.

$$\text{Reorder Point (ROP)} = (\text{Average Demand during Lead Time}) + \text{Safety Stock}$$

First, calculate the average lead time:

$$\text{Average Lead Time} = \frac{3 \text{ weeks} + 5 \text{ weeks}}{2} = 4 \text{ weeks}$$

Next, calculate the demand during the average lead time:

$$\text{Demand during Lead Time} = \text{Average Weekly Demand} \times \text{Average Lead Time}$$ $$\text{Demand during Lead Time} = 11\,538.46 \text{ units/week} \times 4 \text{ weeks} \approx 46\,153.84 \text{ units}$$

Now, calculate the Reorder Point:

$$\text{ROP} = 46\,153.84 \text{ units} + 8\,653.85 \text{ units} \approx 54\,807.69 \text{ units}$$

Rounding to the nearest whole unit, the optimal number (reorder point) is 54,808 units.

The maximum stock level is typically the safety stock plus the Economic Order Quantity (EOQ), assuming a new order arrives when the stock level has reached the safety stock.

$$\text{Maximum Stock Level} = \text{Safety Stock} + \text{EOQ}$$ $$\text{Maximum Stock Level} = 8\,653.85 \text{ units} + 4\,000 \text{ units} \approx 12\,653.85 \text{ units}$$

Rounding to the nearest whole unit, the maximum stock level is 12,654 units.

• The optimal number (Reorder Point) is $\boxed{54\,808 \text{ units}}$.
• The minimum stock level is $\boxed{8\,654 \text{ units}}$.
• The maximum stock level is $\boxed{12\,654 \text{ units}}$.