Question

An auto repair shop orders cleaning rags in batches of 160 boxes. This inventory is depleted at a constant rate and new rags are ordered to arrive exactly when the on-hand inventory of rags reaches zero boxes. What is the average inventory level over time?

Answer 1

The average inventory level for the auto repair shop's cleaning rags, calculated using a standard inventory management model, will be 80 boxes over time.

Step-by-step explanation:

The question describes a standard inventory model where the auto repair shop orders a fixed quantity of inventory, and this inventory is used up at a constant rate until it reaches zero, at which point a new order arrives to replenish the stock. This scenario represents a simple inventory management problem that aims to calculate the average inventory level over time.

Assuming that the inventory depletes at a constant rate and there are no delays in replenishment, the average inventory level can be calculated as the maximum inventory level divided by two. When the inventory is at its maximum level (160 boxes), it will linearly decrease to zero before replenishment. This forms a triangle if you were to plot the inventory level over time until replenishment. Therefore, the formula for the average inventory level is:

Average Inventory Level = (Maximum Inventory Level) / 2

Average Inventory Level = (160 boxes) / 2

Average Inventory Level = 80 boxes

So, over time, the average inventory level of the cleaning rags will be 80 boxes.

Answer 2

80

Step-by-step explanation:

Given that number of orders = 160 boxes , On hand inventory = 0

The formula for Average inventory level is given below:

Average inventory level = (Number of orders + On hand inventory) / 2

Average inventory level = 160 + 0 / 2

Average inventory level = 160 / 2

Average inventory level = 80

Therefore, the average inventory level over time is 80