Enumerating Split-Pair Arrangements

In robotic scheduling, a single robot arm moves identical product along through a predetermined sequence of machines labelled M1,M2,. ..,Mn,Mn+1. The first machine M1 is an unlimited supply of the raw product, the last machine Mn+1 is unlimited storage for the finished product, while the remaining machines can only support one product at a time. In going from the raw product to the finished product, each machine must be visited in turn. Associated to each machine there is a time for processing the product and in addition there is a time cost in moving the robotic arm between machines.