Masoud Rabbani - School of Industrial Engineering, College of Engineering, University of Tehran
Moeen Sammak Jalali - School of Industrial Engineering, College of Engineering, University of Tehran
Babak Javadi - Department of Industrial Engineering, Faculty of Engineering, College of Farabi, University of Tehran Qom
Reza Tavakoli-Moghaddam - School of Industrial Engineering, College of Engineering, University of Tehran

Proposing a graph representation of hybrid manufacturing systems, we use graph-coloring in order to solve the potential conflicts among various workstations and present an upper bound for the chromatic number of hybrid manufacturing environments. We prove that the graphs’ chromatic numbers in such systems are less than or equal to the total number of dummy nodes applied to the system by means of our proposed algorithm. Two examples of hybrid manufacturing systems are propounded in small and medium sizes and our proposed heuristic approach is applied. Finally, to ensure the rectitude of our methodology, the performance of the systems is assessed in terms of their chromatic numbers.

Graph coloring; Heuristics; Conflict recognition; Hybrid Make-To- Stock/Make-To-Order