A firm has determined that its optimal EOQ ordering quantity is 1,250 units for a certain product. Average daily demand is 90 units with a standard deviation of 8 units. Order lead time is 7 days. To maintain a 95% service level, what should the target inventory level be?

Question

Quizplus · Accepted Answer

Using the EOQ formula, we can calculate the reorder point as:
Reorder point = (Average daily demand x lead time) + safety stock 
Safety stock = z-score x standard deviation of demand during lead time 
The z-score for a 95% service level is 1.65 (using a standard normal distribution table). 
Reorder point = (90 units/day x 7 days) + (1.65 x 8 units/day x sqrt(7 days)) 
Reorder point = 630 units + 21.28 units 
Reorder point = 651.28 units

Since the EOQ is 1250 units, and the reorder point is 651.28 units, the optimal inventory level would be the sum of both:
Optimal inventory level = EOQ + reorder point 
Optimal inventory level = 1250 units + 651.28 units 
Optimal inventory level = 1901.28 units ≈ 1940 units

Therefore, the target inventory level should be 1,940 units.

A Firm Has Determined That Its Optimal EOQ Ordering Quantity