Question

**Answers are provided in Question 1 and 2, see below for more details**

Western Pharmaceuticals

Once George has initiated the supply chain design project, his next task was to investigate the firm's inventory management capability relative to the refined supply chain. The integration of the Western and Atlantic Medical distribution systems required a refinement of the firm's inventory management system.

Although the firm wanted to have a comprehensive inventory analysis, the information available was limited due to the merger and a simultaneous move to an Enterprise Resource Planning system. In fact, in terms of quickly available data, there was only a limited sample from the Atlantic Medical Sales and Inventory records.

For a sample of 100 stock keeping units (SKUs), the data base includes the average and standard deviation of weekly sales, average order cycle time (OCT), replenishment order quantity (OQ), and the average inventory. Based on history, the current standard deviation in the replenishment cycle time is 1 week. The sales, order quantities, and inventory are recorded in cases. The historical information is provided for each of the three existing distribution centers.

Question 1:

What should the case fill rate be for each product given the current uncertainty levels and order quantities? I have provided the answers BELOW but I need to understand HOW it was calculated. What is or are the formulas to get those two answers below?

The answer is 96.31 percent fill rate by value and 96.10 percent fill rate in terms of units.

Question 2:

What are the safety stock and average inventory levels for each product necessary to achieve 95 percent case fill rate for reach product? I have provided the answer BELOW but I need to understand HOW it was calculated. What is or are the formulas to get the answer below?

The answer is $7.5 million to achieve a 95 percent fill rate, while the existing situation only yields a 96 percent with twice the inventory.