Several Types of Products on One Machine

Abstract

In Chapter 4 we have observed that in a situation with no capacity restrictions a rather simple production rule can be used, the (x,T)—rule. In the (x,T)—rule the dimension of the state space is largely reduced before the production decision is made. This reduction allows a simple production rule. We are interested whether in a more complex situation such a type of rule can also be used. In this chapter and in the next chapter, we will consider a situation in which several types of products are produced on one machine. The amount of work that can be done on the machine is restricted, due to the machine speed and to the time the machine is available for production. If the production is changed from one type of product to another, a set-up is needed. By performing a set-up, capacity is lost. Loosing too much capacity due to set-ups will lead to large delivery times for the ordered goods, but on the other hand, waiting too long with a set-up will also lead to large delivery times. By controlling the production, a balance has to be found such that the clients can be satisfied by limiting the number of late orders or by limiting the lateness of the orders, while on the other hand also the manufacturer can be satisfied by limiting the set-up costs, the holding costs and in some situations also the costs for working overtime.