Question

A factory buys N95 masks in bulks for daily usage of its employees. It is estimated that the weekly usage of N95 masks at the factory is normally distributed with a mean of 27 cases and a standard deviation of 5 cases. The factory operates 45 weeks in a year. The factory orders the masks directly from a supplier who takes 1 week to fulfill an order. The cost of preparing, placing, and shipping an order sums up to $10 per order. The annual holding cost of the masks is $75 per case. The factory adopts a Fixed-Order Quantity Model to manage the inventory of its N95 masks.

If the factory would like to achieve a service level of 98%, what is the minimum reorder point (in cases) it can use? Please write your answer as an integer.

Answer 1

To achieve a 98% service level for ordering N95 masks, the factory must have a minimum reorder point of 38 cases, calculated using the mean, standard deviation, and lead time with the appropriate Z-score for the desired service level.

Step-by-step explanation:

To calculate the minimum reorder point (ROP) with a service level of 98%, we need to take into account the normal distribution of weekly usage, the lead time for orders, and the desired service level. The weekly usage of N95 masks at the factory is normally distributed with a mean (μ) of 27 cases and a standard deviation (σ) of 5 cases. The factory has a lead time of 1 week to fulfill an order.

To achieve a 98% service level, we look at the Z-score that corresponds to this probability in the standard normal distribution. For a 98% service level, the Z-score is approximately 2.05. The reorder point can be calculated using the formula:

ROP = μ + Z * σ * √(Lead Time)

ROP = 27 + 2.05 * 5 * √(1)

ROP = 27 + 10.25

ROP = 37.25

Since the reorder point must be an integer, and we cannot have a fraction of a case, we round up to the next whole number. Therefore, the minimum reorder point that the factory can use is 38 cases.