Which one of the following statements is best?

Question

BlackTom AI · Accepted Answer

When evaluating statements about safety stock and inventory levels, it helps to unpack the underlying concepts and check each claim against standard inventory theory.

Option 1: The level of safety stock maintained decreases when the standard deviation of demand during lead-time increases.
- Why this seems wrong: Safety stock is typically used to buffer against variability in demand during lead time. As the standard deviation (a measure of variability) increases, the required safety stock usually increases, not decreases, to maintain the same service level. Therefore this statement contradicts the conventional relationship between demand variability (lead-time variability) and safety stock, making it incorrect.

Option 2: The level of safety stock maintained decreases when the desired cycle-service level increases.
- Why this seems wrong: The cycle-service level (the probability of not stocking out in a cycle) is directly linked to how much safety stock you hold. A higher service level generally requires more safety stock to reduce the risk of stockouts. Thus, claiming that safety stock decreases as the target service level increases contradicts standard practice and is incorrect.

Option 3: The level of safety stock maintained is greater if mean absolute deviation (MAD) is used rather than standard deviation in estimating forecast errors.
- Why this seems questionable: In practice, safety stock calculations for service levels commonly use the standard deviation of lead-time demand because it aligns with the normal distribution assumptions used in many safety stock formulas (e.g., safety stock = z * sigma_LT). MAD is another dispersion measure, but using MAD typically does not yield the same results as using standard deviation, and the statement that Safety stock is necessarily greater when MAD is used is not a universal truth. The claim depends on the specific model and conversion between MAD and sigma, but as stated, it is not a standard or universally correct assertion, making it questionable.

Option 4: When no safety stock is maintained, stockouts will occur during approximately 50% of the cycles.
- Why this could be considered plausible: If safety stock is zero and demand during lead time is symmetrically distributed around the mean, the probability of stockout in a cycle is tied to how often demand during lead time exceeds the on-hand inventory. If the on-hand equals the mean demand, roughly half the cycles would see demand exceed on-hand under a symmetric distribution, leading to stockouts in about 50% of cycles. While this is a simplification and relies on distributional assumptions (e.g., symmetric distribution around the mean and on-hand equal to the mean), it aligns with a common heuristic that zero safety stock yields a substantial, often around-50% stockout rate under typical symmetric demand distributions. This makes the statement the most defensible among the four, given standard simplifying assumptions in introductory inventory theory.

Summary: Options 1, 2, and 3 conflict with standard relationships between safety stock, demand variability, and service level, or rely on nonstandard interpretations of MAD versus standard deviation. Option 4 expresses a commonly taught simplification about stockouts when safety stock is zero, making it the best-fitting statement among the four under typical introductory frameworks.

Which one of the following statements is best? 单项选择题

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