Question

A warehouse supplies a single retailer with a product. The warehouse's purchasing lead time is 3 weeks and the lead time for the retailer (from the warehouse) is 1 week. Assume that forecast errors are normally distributed with the σ for 1 week being 70 units, and that σ t ​ = t ​ σ 1 ​ . The annual demand rate is 12,000 units, and the following data have been gathered: v W ​ =$32/ unit, v R ​ =$38 /unit, r=0.22$/$ year, n=2, or the warehouse orders two batches of the retailer's order quantity at one time. The retailer's order quantity is Q R ​ =500 units. Finally, suppose that the fractional charge per unit short, B 2 ​ , is set at 0.65. Find the reorder point for both locations.

Answer 1

To find the reorder point for both the warehouse and retailer, we need to consider the lead times, forecast errors, and demand rates.

1. Reorder point for the warehouse:

The warehouse's lead time is 3 weeks. To determine the reorder point, we need to consider the lead time demand, which is the demand during the lead time period.

Lead time demand = Lead time × Demand rate = 3 weeks × 12,000 units/year = 36,000 units

Since the forecast errors are normally distributed, we need to account for safety stock. Safety stock is used to cover unexpected demand fluctuations. To calculate safety stock, we multiply the lead time demand by the safety factor.

Safety stock = Lead time demand × Safety factor

The safety factor is determined based on the desired service level. However, since the question doesn't provide information about the service level, we can't calculate an exact value for the safety factor.

Assuming a standard normal distribution, we can estimate the safety factor for a 95% service level to be approximately 1.65.

Safety stock = 36,000 units × 1.65 = 59,400 units

Reorder point for the warehouse = Lead time demand + Safety stock = 36,000 units + 59,400 units = 95,400 units

2. Reorder point for the retailer:

The retailer's lead time is 1 week. Similar to the warehouse, we need to calculate the lead time demand and safety stock.

Lead time demand = Lead time × Demand rate = 1 week × 12,000 units/year = 12,000 units

Safety stock for the retailer can be calculated using the same formula as above, but with a different safety factor. Again, since the question doesn't provide information about the service level, we can't calculate an exact value for the safety factor.

Assuming a standard normal distribution, we can estimate the safety factor for a 95% service level to be approximately 1.65.

Safety stock = 12,000 units × 1.65 = 19,800 units

Reorder point for the retailer = Lead time demand + Safety stock = 12,000 units + 19,800 units = 31,800 units

Therefore, the reorder point for the warehouse is 95,400 units, and the reorder point for the retailer is 31,800 units.

Step-by-step explanation: