An automobile company assembles cars in a plant and purchases batteries from a vendor in china. the average cost of each battery is $45. the automobile company takes ownership of the batteries when they arrive at the plant. it takes exactly 12 hours to make a car in the plant and the plant assembles 200 cars per 8-hour shift (currently the plant operates one shift per day). each car uses one battery. the company holds on average 8,000 batteries in raw material inventory at the plant as a buffer.

There are three questions in this problem:

First, what is the total number of batteries in the plant for both work in process and raw materials inventory.

Second, how much are the batteries worth?

And lastly, how many days of supply are held in the raw material inventories on average?

1. So we know that there are two inventories namely work-in-process and raw material.

For the work-in-process, Little’s law can be straightly applied to look for the amount ofwork-in-process inventory:

Little’s law is Inventory = Throughput × Flow time

Where:

Throughput is the production rate of the plant which is 200 cars per 8-hour shift or 25 cars per hour.

Since we use one battery per car, our throughput rate for the batteries is 25 per hour.

Flow time is 12 hours, so the work-in-process is:

Work-in-process inventory = 25 batteries per hour × 12 hours = 300 batteries

Given from the problem that there are 8,000 batteries in raw materials inventory;

so the total number of batteries in the pipeline on average is computed by:

Total inventory = 8,000 + 300 = 8,300 batteries

2. The worth of this batteries is computed by 8,300 × $45 = $373,500.

3. Remember, that the days of supply in raw material inventory is always the same to the “Flow time” for a battery in raw material inventory.

At this point, we need to assume that the batteries are used in the similar order when they reach the plant. So we need to reorder our Little’s law formula to:

Flow time = Inventory/Throughput

Therefore, flow time = 8,000 batteries / (200 batteries/day) = 40 days

This represents a 40-day supply of inventory.