12. ZMW Motorwerks buys its car seats from Slippery Seats, Inc. Slippery puts 10 different fabrics on the same seats delivered to one of ZMW’s assembly plants. Slippery sells and delivers each seat to ZMW in batches of 500, which ZMW orders when its inventory on a particular seat reaches 100 units—the expected use by ZMW during the two-week lead time (guaranteed as a maximum by Slippery). Every day, the particular 100 seats expected to be used the next day are removed from the inventory at ZMW and transported to the line where the seats are installed (at a rate of 10/hour during a 10-hour day (100/day, 250 days/year). As the cars pass through the seat section, the workers pick the right seat to go with the particular car. In the event that a seat is damaged, another of the same fabric is used (there is a safety stock of five seats in each fabric, which is replenished each day as needed).

Slippery tries to maintain a finished goods inventory of one batch of each seat-fabric combination.

This allows it to almost always be able to ship a batch of seats quickly when ordered by ZMW. The lead time required to make a batch of 500 seats is three weeks, and Slippery has promised to deliver in two weeks at a maximum. The lead time is based on one week to make the frames, one week to order/receive the fabric, which is cut and sewn in week 2, with the final seats assembled in week 3

(when all the other materials have been ordered and delivered). A new batch is started whenever an order is received, which will replenish the batch removed from inventory to fill the order.

a. What is the expected inventory level (average) of seats at ZMW?

b. What is the expected inventory level (finished goods) at Slippery?

c. What is the expected inventory level (work-in-process) at Slippery?

d. What are the hidden factory costs in both companies?