Question

Cyber Chemicals uses liquid nitrogen on a regular basis. Average daily demand is normally distributed with a mean of 175 gallons and a standard deviation of 43. Cyber operates Six days a week and orders from its supplier once each week. The supplier takes one week to deliver Cyber's order. a. Suppose an order-up-to level of 4000 is used. What is the average order quantity?

Answer 1

To compute the average order quantity for Cyber Chemicals, considering a two-week usage period and an order-up-to level of 4000 gallons, it is calculated to be 1900 gallons.

Step-by-step explanation:

Cyber Chemicals uses liquid nitrogen with a daily demand that is normally distributed with a mean of 175 gallons and a standard deviation of 43. Ordering once a week with a supplier lead time of one week, they aim to determine the average order quantity given an order-up-to level of 4000 gallons.

To calculate the average order quantity, we need to consider the average usage over the two-week period (one week for usage and one week for supplier lead time). This is the average daily demand multiplied by the number of operating days in two weeks, which is 175 gallons/day × 12 days = 2100 gallons on average for two weeks.

Since Cyber Chemicals wants to maintain a stock level up to 4000 gallons, we subtract the average demand over the reorder period from the order-up-to level to get the average order quantity. This gives us 4000 gallons - 2100 gallons = 1900 gallons. Therefore, the average order quantity for Cyber Chemicals is 1900 gallons.