Painting automobile bumpers can be quite complicated. At a major bumper manufacturing facility in Michigan, around one bumper out of four is defective and must be rerouted and repainted. Bumpers are produced on a single machine, one batch after another, and each batch consists of bumpers for a particular car model and colour. Changeovers between batches are expensive and can take a long time. The bumpers need to dry before they can be inspected, but by then, another batch is already in production, so plant managers do not know exactly how many good bumpers they will have before starting the next batch.
Because the production yield is very unpredictable, a sizeable stock of bumpers has to be kept on hand in a very large storage system, with significant costs. My visit to the Michigan plant motivated me and my coauthors Scott E. Grasman of Missouri University of Science and Technology and Tava Lennon Olsen of the University of Auckland to develop a production control system that would allow the bumper producer, as well as other similar manufacturing plants, to have as many bumpers available as possible while minimizing costs.
The key is to find the right basestock level or the optimal number of bumpers that managers plan to produce, which we discuss in our study titled "Setting Basestock Levels in Multi-Product Systems with Setups and Random Yield." If managers set the basestock levels too low, then the company may run out of bumpers to satisfy demand from car manufacturers and the plant would have to go on overtime and possibly hire more workers. If basestock levels are set too high, then the company may end up with too many bumpers that nobody wants. Both scenarios will result in substantial costs to the company. The idea of finding the optimal basestock level is to set it somewhere in between too many and too few, to get the right balance.
Just like bumper plants, many modern production systems are characterized by several uncertainties that make output highly variable.
For instance, only about half of semiconductor chips pass inspection after the first try, according to previous studies. Similar to producing bumpers in several colors, semiconductor manufacturers have to make different types of chips that go into computers, cell phones, and other digital devices and consumer appliances. Moreover, machines that make these semiconductors tend to be very expensive, so the chips are usually produced in different batches, one type after another, on just one machine. As a result, it is difficult to predict how many defective chips are in a particular batch before production of the next batch starts.
New manufacturing facilities also typically have yields that are very low. Output improves as more is learned about the production process, but generally never reaches the point where no defective items are produced. This is because rapidly changing technologies can make a production process obsolete even before it is well understood, or it may not be financially justifiable to correct the yield problem. Thus, random yield models are valuable in helping an operation run more efficiently.
But very few studies have analyzed random yield models when multiple products can be made on a single machine, as with the cases of car bumpers and semiconductor chips. Moreover, unlike other studies that make ad hoc calculations of what the basestock levels ought to be, the methods developed by Birge and his coauthors give more consistent cost estimates that managers can rely on when planning how much of each item to produce. It allows the manufacturer to design the sequence of products in such a way that it can be very confident about knowing how often it would be able to avoid using overtime and how much inventory it will have.