ORIGINAL ARTICLE Trade-off between process scheduling and production cost in cyclic flexible robotic cells Mazyar Ghadiri Nejad 1 & Seyed Mahdi Shavarani 1 & Béla Vizvári 1 & Reza Vatankhah Barenji 2 Received: 31 July 2017 /Accepted: 3 January 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract In this study, a bi-objective scheduling problem of a flexible robotic cell is considered aiming to a trade-off between cell’ s processes scheduling and the production cost. At the cell, machines are identical and parallel and in line. There is an input buffer for the raw materials and an output buffer for the products. A robot is in charge of loading and unloading of the items from the input buffer to machines and from machines to the out put buffer. The system is cyclic means repeats the same processes in every cycle. It is assumed that each machine processes one part in each cycle. A bi-objective mathematical model is presented to solve the problem, and as an alternative, an NSGAII is developed for large-sized problems. Several numerical examples are solved for examining the proposed mathematical model and NSGAII method. Keywords Flexible manufacturing . Flexible robotic cell . Cyclic scheduling . Metaheuristics . Multi-objective . NSGAII 1 Introduction A flexible robotic cell (FRC) is a manufacturing unit in which CNC machines perform all the processes of a product, and the robot is in charge of loading and unloading of the parts to the machines and from the machines. FRC is more welcomed by the firms working under mass customization paradigm since the system is more flexible, agile and the production rate, as well as the quality, is much fine comparing with job shops. In an FRC, the same group of processes is performed on all the machines. Hence, each item is processed only on one ma- chine. Depends on order of the input parts, the state of a cell (i.e., machines and robots) might be reversible. Thus, in a reversible FRC, the state of the cell’ s components can always get back to the initial state or might back to some home state, which will appear as the initial state. The duration of the re- versible cycle is called cycle time, and the scheduling problem is cyclic [1]. In a cycle, each machine processes one part and as a fact, declining the cycle time of a cyclic production system means increasing the production rate [2]. The cycle time depends on the order of the actions. Thus, determining the order of the actions to minimize the cycle time is an opti- mization problem. Some researchers contribute the cyclic scheduling problem of FRC. Crama and Van de Klundert [3] used an in-line layout FRC and developed a dynamic programming approach to produce identical parts. The result was a shortest cyclic sched- ule for the robot moves. Brauner and Finke [4] considered an m-machine FRC, and employed algebraic approach and proved that the optimality of a one-unit cycle is valid only for two or three machine cells but not more. Abdekhodaee et al. [5] studied parallel machines FRCs and scheduled two- operation and non-preemptible jobs with same processing and set up times. Dawande et al. [6] considered a one-unit cycle of an FRC with multiple robots including a single and dual grip- per and proposed a lower bound for cycle time. Gultekin et al. [7] recommended a new cycle that performs better in compar- ison with the classical robot move cycles for two-machine cells. Yildiz et al. [8] proposed two pure cycles and showed that these two cycles jointly dominate all other pure cycles for a wide range of the processing times. They also presented the worst case for minimizing the cycle time. Ghadiri Nejad et al. [9] suggest an MTZ based TSP model for scheduling problem of the flexible robotic cell with m machines and a robot. They provide a reduced version for their model by excluding waiting time variables and reported that, the reduced model * Reza Vatankhah Barenji reza.vatankhah@hacettepe.edu.tr 1 Department of Industrial Engineering, Eastern Mediterranean University, Mersin 10, TRNC, Turkey 2 Department of Industrial Engineering, Hacettepe University, Ankara, Turkey The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-1577-x