Question

historically, demand has averaged 1282 units with a standard deviation of 708. the company currently has 2556 units in stock. what is the service level?

Answer 1

Calculating the service level requires additional information such as lead time or reorder point. It is a measure of the inventory's ability to meet demand and involves a trade-off between holding costs and the risk of stockouts.

Step-by-step explanation:

The service level is a measure of how well a company's inventory can meet customer demand. To calculate the service level, we would typically use historical demand data and the company's inventory levels. In this scenario, the historical demand averages at 1282 units with a standard deviation of 708 units. With 2556 units in stock, we would need additional information such as the lead time, reorder point, or desired service level percentage before the actual service level can be determined. Service level calculations often involve determining the probability that demand will not exceed supply before the next replenishment or, in other terms, the likelihood that a stockout will not occur.

In inventory management, setting a higher service level typically means keeping more stock on hand to meet demand, which reduces the risk of stockouts but increases holding costs. Conversely, a lower service level might reduce holding costs but increase the risk of stockouts. The choice of service level will depend on the company's inventory strategy and how much risk of a stockout they are willing to accept.

Answer 2

To calculate the service level, we use the Z-score formula and the provided average demand and standard deviation. The Z-score for a stock of 2556 units given the average demand of 1282 with a standard deviation of 708 is 1.80. The corresponding service level would be the cumulative probability associated with a Z-score of 1.80.

Step-by-step explanation:

The service level is a measure of the probability that demand will not exceed supply during a certain period. In this scenario, the student has mentioned that the demand has historically averaged 1282 units with a standard deviation of 708. The company has 2556 units in stock. To calculate the service level, we need to find the probability that the demand is less than or equal to the number of units in stock. This can be done using the Z-score formula: Z = (X - μ) / σ, where X is the number of units in stock, μ is the mean, and σ is the standard deviation. Plugging in the given values gives us:

Z = (2556 - 1282) / 708 = 1.80. We then look up this Z-score in a standard normal distribution table or use statistical software to find the corresponding probability. Assuming a normal distribution of demand, this Z-score corresponds to a service level, which is the cumulative probability up to that Z-score.

The exact figure would depend on the property of the standard normal distribution, but based on this calculation, the service level would be the probability associated with a Z-score of 1.80.