Robotic Cells: Configurations, Conjectures and Cycle Functions

Summary Robotic cells consist of a flow-shop with a circular layout and a single transporter, a robot, for the material handling. A single part is to be produced and the objective is to minimize the production rate. Different cell configurations have been studied, depending on the travel times of the empty robot: additive, constant or just triangular. A k-cycle is a production cycle where exactly k parts enter and leave the system. Consider the set S K of all k-cycles up to size K where S K contains, for every instance, an optimal solution and K is minimal. The cycle function K depends on the cell configuration and the number of machines. Some of these functions are known and there are conjectures about others. We give new results invalidating in particular the so-called Agnetis’ Conjecture for the classical robotic cell configuration.