Consider a single machine that can do operations on 3 part types. The operation time for part i is i, i = 1,2,3. The set-up time from part i to part j i is S, independent of i and j. Assume that the machine is perfectly reliable and operated as follows: The lot size of type i parts is Qi. Parts are produced in the following sequence: 1, 2, 3, 1, 2, 3, ... That is, a lot of type 1 is worked on, followed by a set-up change from 1 to 2, followed by work on a type 2 lot, followed by a set-up change from 2 to 3, followed by work on a type 3 lot, followed by a set-up change from 3 to 1, etc. (This is called a round-robin sequence.) In this example, a set-up cycle is a period in which 1 batch of each part type is produced, and in which there are 3 set-ups. The machine is never allowed to be idle.