Robust scheduling for three-machine robotic cell using interval data

Document Type: Research Paper


Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran


In reality, due to the lack of adequate environmental information, uncertainty is a common practice. In order to provide good and acceptable solutions, development of systematic methods for solving problems of uncertainty is important. One of these methods is based on robust optimization. This type of planning is to find a solution that is not sensitive to parameter fluctuations. In this article, a new way is represented to solve a three-machine robotic cell problem. An intervallic processing time is concerned as the problem being discussed. Different scenarios are defined by using robust optimization; afterwards, applying min-max regret method, robust counterpart of original problem is specified. Since the problem is NP-hard, a metaheuristic is applied to solve it. Genetic Algorithm (GA) as a population-based metaheuristic is employed. Cycle time and program operating time are calculated for different number of parts. It is demonstrated that by increasing the part numbers, gap between the robust and original cycle time increases. It is observed that both the cycle time and algorithm operating time increase.


Agnetis A. (2000), Scheduling No-Wait Robotic Cells with Two and Three Machines; European Journal of Operational Research 123;303–314.

Aytug H., Lawley M.A., McKay K., Mohan S., Uzsoy R. (2005), Executing production schedules in the face of uncertainties: A review and some future directions; European Journal of Operational Research161;86–110.

Bedini R., Lisini G.G., Sterpos P. (1979), Optimal Programming of Working Cycles for Industrial Robots; Journal of Mechanical Design. Transactions of the ASME 101; 250–257.

Che A., Chu C., Chu F. (2002), Multicyclic Hoist Scheduling with Constant Processing Times;   IEEE Transactions on Robotics and Automation18; 69–80.

Che A., Chu C., Levner E.(2003), A Polynomial Algorithm for 2-degree Cyclic Robot Scheduling; European Journal of Operational Research 145;31–44.

Chen H., Chu C., Proth J. (1998), Cyclic Scheduling with Time Window Constraints; IEEE Transactions on Robotics and Automation 14;144–152.

Claybourne B.H. (1983), Scheduling Robots in Flexible Manufacturing Cells; CME Automation 30;36–40.

Kondoleon A.S. (1979), Cycle Time Analysis of Robot Assembly Systems; Proceedings of the Ninth Symposium on Industrial Robots;575–587.

Lei L., Wang T.J. (1994), Determining Optimal Cyclic Hoist Schedules in a Single- Hoist Electroplating Line; IIE Transactions 26;25–33.

Levner E., Kats V., Levit V. (1997), An Improved Algorithm for Cyclic Flowshop Scheduling in a Robotic Cell; European Journal of Operational Research 97;500–508.

Luce R.D., Raiffa H. (1957), Games and Decisions: Introduction and Critical Survey; Dover Publications Inc.

Maimon O.Z., Nof S.Y. (1985), Coordination of Robots Sharing Assembly Tasks; Journal of Dynamic Systems Measurement and Control. Transactions of the ASME 107; 299–307.

Roy B. (2010), Robustness in operational research and decision aiding: A multi-faceted issue; European Journal of Operational Research200; 629–638.

Sabuncuoglu I., Goren S. (2009), Hedging production schedules against uncertainty in manufacturing environment with a review of robustness and stability research. International Journal of Computer Integrated Manufacturing22; 138–57.

Wilhelm W.E. (1987), Complexity of Sequencing Tasks in Assembly Cells Attended by One or Two Robots; Naval Research Logistics 34; 721–738.