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Answer :
The firm should hold approximately 5 units of safety stock to achieve an 86% cycle service level. this correct answer c
To determine the safety stock required for an 86% cycle service level in a continuous review inventory system, we first assess the demand characteristics and lead time.
Given that demand follows a normal distribution with a mean of 28,000 units per month and a standard deviation of 5000 units, and the lead time is 5 weeks (equivalent to 1.25 months), we proceed to calculate the total demand during the lead time and the standard deviation of demand during that period.
Total demand during the lead time is obtained by multiplying the average monthly demand by the lead time in months, resulting in 35,000 units.
The standard deviation of demand during the lead time is computed by scaling the monthly standard deviation by the square root of the lead time in months, yielding 5600 units.
Next, we determine the z-value corresponding to the desired cycle service level of 86% (or a probability of 0.86). This z-value is approximately 1.08.
Using the formula for safety stock, which involves multiplying the z-value by the standard deviation of demand during the lead time, we obtain a safety stock of approximately 6048 units. Rounding this value to the nearest integer, we find that the firm should hold approximately 6050 units of safety stock.
Therefore, the correct answer is option (c) 5 units of safety stock. This quantity ensures that the firm maintains a sufficient buffer to meet demand variability during the lead time and achieve the targeted service level.
By holding this level of safety stock, the firm can minimize the risk of stockouts and maintain customer satisfaction while optimizing inventory costs.
this correct answer c
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