Question

Average stock level required to maintain the inventory is calculated as

• A. Minimum stock level + half of the reorder cost
• B. Maximum stock level + half of the reorder cost
• C. Minimum stock level + one fourth of the reorder cost
• D. Maximum stock level + one fourth of the reorder cost

Hint:

Remember the two standard expressions for Average Stock Level: 1. $\text{Minimum Level} + \frac{1}{2}(\text{Reorder Quantity})$ 2. $\frac{\text{Minimum Level} + \text{Maximum Level}}{2}$ This makes it simple to spot the correct structure on a test.

Answer 1

The Correct Option is A

Concept: In traditional inventory control systems, stock levels fluctuate dynamically between a peak upper boundary and a base lower boundary. To estimate annual holding costs, managers determine an average inventory level. The standard formula configurations for average stock level are: \[ \text{Average Stock Level} = \text{Minimum Stock Level} + \frac{1}{2}(\text{Reorder Quantity}) \] Alternatively, it can be approximated as the midpoint between boundaries: \[ \text{Average Stock Level} = \frac{\text{Minimum Stock Level} + \text{Maximum Stock Level}}{2} \] *Note: In the provided question options, the term "reorder cost" is used in place of "reorder quantity/size" due to varied regional terminology or semantic error in exam drafting. Treating it as the reorder quantity factor resolves the structural expression.*

Step 1: Evaluating the mathematical derivation of average inventory.
Consider a classic inventory sawtooth wave diagram where safety stock represents the absolute baseline floor (Minimum Stock Level). When a shipment arrives, the inventory spikes by the total reorder size ($Q$). Thus, the maximum height reached is: \[ \text{Maximum Stock} = \text{Minimum Stock} + Q \] As inventory is consumed at a constant rate, the average quantity held above the safety floor is exactly half of the incoming batch size, $\frac{1}{2}Q$.

Step 2: Matching with the given options.
Expressing this mathematically gives: \[ \text{Average Stock} = \text{Minimum Stock Level} + \frac{1}{2}(\text{Reorder Quantity}) \] Reviewing the multiple-choice options, Option (1) reads: $\text{Minimum stock level} + \text{half of the reorder cost}$. Swapping "reorder quantity" into the placeholder term confirms Option (1) as the intended correct answer.