Inventory control (EOQ context): if safety stock is 6 units and the economic order quantity (EOQ) is 50 units, what is the average inventory level assumed under a continuous review system?

Introduction / Context:
Average inventory is a key performance and cost driver in inventory management. Under the classic EOQ model with continuous review and steady demand, on-hand inventory cycles between a maximum level and a minimum level. When safety stock is maintained to protect against uncertainty, the average on-hand amount increases by the safety buffer. Knowing how to compute average inventory is important for holding-cost estimation and service-level planning.

Given Data / Assumptions:

• Safety stock s = 6 units.
• Economic order quantity Q = 50 units.
• Standard EOQ assumptions: constant demand and lead time, immediate replenishment of Q, and continuous review.

Concept / Approach:
In the basic EOQ framework with safety stock, the cycle (or “cycle stock”) component averages to Q/2 over time because inventory depletes linearly from Q down toward zero during each cycle. Safety stock is a constant buffer added to whatever cycle stock remains. Therefore, average on-hand inventory equals safety stock + average cycle stock. In symbols: Avg_Inventory = s + Q/2.

Step-by-Step Solution:

Verification / Alternative check:
If demand or lead-time variability were modeled differently, the safety stock value might change, but with s = 6 and Q = 50 the EOQ average inventory formula yields 31 consistently. Cross-checking with inventory textbooks confirms Avg_Inventory = s + Q/2 under standard assumptions.

Why Other Options Are Wrong:

• 80, 85, 86, 90: each implies either a much larger safety stock or a different modeling assumption. None matches the standard calculation using the given numbers.

Common Pitfalls:
Confusing “maximum inventory” (s + Q) with “average inventory;” forgetting to add safety stock to the cycle-stock average; or using end-of-period rather than time-weighted averages.

Final Answer:
None of the above