  Flexible robotic cells are utilized to produce standardized products at a
high speed production rate, and to set up the production floors based on rapid
operating environment changes. In FRC, there are a number of computer numerical
control machines, an input buffer, an output buffer, and a robot. The input and
output buffers contain unprocessed and finished products, respectively, whereas
the robot performs the loading and unloading activities and transports the
items among buffers and machines. The system repeats a cyclic schedule in its
run and the cycle time depends on the order of robot activities. In order to
maximize the efficiency of the system, the order of the robot activities
yielding the minimum cycle time should be determined. The aim of this research
is to find novel exact models to solve this cycling scheduling problem. These
types of problems have tight relations with traveling salesman problem. In this
study, four main modeling approaches of the TSP, such as
Dantzig-Fulkerson-Johnson approach, Miller-Tucker-Zemlin approach, Vajda's
n-step approach, and the network flow approach are studied. Only the DFJ
approach cannot be adapted to the scheduling problem. The three other
approaches are adapted successfully. Similarities and differences are discussed
by using several numerical examples.
