Daily demand for a product is 60 units with a standard deviation of 10 units. The review period is 10 days, and lead time is 2 days. At the time of review, there are 100 units in stock. If 98 percent service probability is desired, how many units should be ordered?
To calculate the number of units that should be ordered, we need to consider several factors: daily demand, standard deviation, review period, lead time, current stock, and the desired service probability.
Here's how we can determine the number of units to order:
1. Determine the demand during the review period:
- The daily demand is 60 units, and we have a review period of 10 days.
- So, the demand during the review period is 60 units/day * 10 days = 600 units.
2. Calculate the safety stock:
- Safety stock is used to account for the uncertainty in demand and lead time.
- We can calculate the safety stock using the following formula:
Safety stock = Z * √((Lead time * Variance of demand) + (Review period * Variance of demand))
where Z is the Z-value corresponding to the desired service probability.
- In this case, the desired service probability is 98 percent, which corresponds to a Z-value of 2.05.
- Lead time is 2 days.
- Variance of demand can be calculated as the square of the standard deviation: (10 units)^2 = 100 units.
- Review period is 10 days.
- Plugging in these values, we get:
Safety stock = 2.05 * √((2 * 100) + (10 * 100))
= 2.05 * √(200 + 1000)
= 2.05 * √1200
= 2.05 * 34.64
= 70.98 units (rounded to the nearest whole number).
3. Calculate the reorder point:
- Reorder point is the level of inventory at which a new order should be placed to avoid stockouts.
- It is calculated by adding the safety stock to the average demand during lead time.
Reorder point = Safety stock + (Average daily demand during lead time * Lead time)
Average daily demand during lead time = (Demand during review period) / (Review period + Lead time)
= 600 units / (10 days + 2 days)
= 600 units / 12 days
= 50 units/day.
- Plugging in the values, we get:
Reorder point = 70.98 units + (50 units/day * 2 days)
= 70.98 units + 100 units
= 170.98 units (rounded to the nearest whole number).
4. Calculate the order quantity:
- The order quantity is the number of units to order to bring the stock back to the desired level.
- It can be calculated by subtracting the current stock from the reorder point.
Order quantity = Reorder point - Current stock
= 170.98 units - 100 units
= 70.98 units (rounded to the nearest whole number).
Therefore, the number of units that should be ordered is 71 units (rounded to the nearest whole number) to achieve a 98 percent service probability.