1. At what point should Anna and Joachim be ordering if they desire a stock out risk of 4% ? A. 142 kits B. 224 kits C. 133 kits 2. What would be their level of safety stock with that stock out risk? A. 25 kits B. 29 kits C. 52 kits 3. At what point should they be ordering if they desire a stock out risk of 7.5% ? A. 128 kits B. 120 kits C. 137 kits 4. What would be their level of safety stock with that stock out risk of 7.5% ? A. 21 kits B. 24 kits C. 12 kits 5. At what point should they be ordering if lead time was constant and stable (no standard deviation)? A. 121 kits B. 113 kits C. 104 kits Final answer: The re-order points for 4% and 7.5% stock-out risks are 142 kits and 137 kits respectively. The associated safety stocks are 29 kits and 24 kits. If lead time had no variations, re-order point would simply be average lead time demand, which is 104 kits.

Question

1. At what point should Anna and Joachim be ordering if they desire a stock out risk of 4% ? A. 142 kits  B. 224 kits  C. 133 kits  2. What would be their level of safety stock with that stock out risk? A. 25 kits  B. 29 kits  C. 52 kits  3. At what point should they be ordering if they desire a stock out risk of 7.5% ? A. 128 kits  B. 120 kits  C. 137 kits  4. What would be their level of safety stock with that stock out risk of 7.5% ? A. 21 kits  B. 24 kits  C. 12 kits  5. At what point should they be ordering if lead time was constant and stable (no standard deviation)? A. 121 kits  B. 113 kits  C. 104 kits  Final answer: The re-order points for 4% and 7.5% stock-out risks are 142 kits and 137 kits respectively. The associated safety stocks are 29 kits and 24 kits. If lead time had no variations, re-order point would simply be average lead time demand, which is 104 kits.

Ana · Answer

Explanation: This question relates to inventory management and safety stock calculation, based on a constant demand, variable lead time, and given risk of stockout. In this case, Anna and Joachim are concerned with lead time demand which is how many units will be needed during the replenishment lead time. For a constant rate of demand but variable lead time, lead time demand is a random variable with a mean and standard deviation.  1. To calculate the re-order point with a 4% stock-out risk, you would need to consider the average lead time demand (demand rate x average lead time) and safety stock (z-score for the desired service level x standard deviation of lead time demand). Taking demand as 81 kits/week, lead time as 9 days, and the z-score for 4% stock-out risk as 1.75 gives: Re-order Point = (81 kits/week x 9/7 weeks) + (1.75 x √(9/7 x 1.3)) resulting in approximately 142 kits.  2. The level of safety stock with a 4% stock-out risk is just the second part of the above calculation. Safety stock = 1.75 x √(9/7 x 1.3) ≈ 29 kits.  3. For a 7.5% stock out risk, the z-score is approximately 1.44. When calculating using this z-score, we get roughly 137 kits for the re-order point.  4. Safety stock with a 7.5% stock out risk would be 1.44 x √(9/7 x 1.3) ≈ 24 kits.  5. If lead time was constant and stable with no standard deviation, there would be no need for a safety stock. Re-order point then would simply be average lead time demand = (81 kits/week x 9 days/7) = 104 kits.

Inventory Management: Calculating Re-order Points and Safety Stock

1. At what point should Anna and Joachim be ordering if they desire a stock out risk of 4% ?

2. What would be their level of safety stock with that stock out risk?

3. At what point should they be ordering if they desire a stock out risk of 7.5% ?

4. What would be their level of safety stock with that stock out risk of 7.5% ?

5. At what point should they be ordering if lead time was constant and stable (no standard deviation)?

Final answer:

Explanation:

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