Bicriteria robotic cell scheduling with controllable processing times

The current study deals with a bicriteria scheduling problem arising in an m-machine robotic cell consisting of CNC machines producing identical parts. Such machines by nature possess the process flexibility of altering processing times by modifying the machining conditions at differing manufacturing costs. Furthermore, they possess the operational flexibility of being capable of processing all the operations of these identical parts. This latter flexibility in turn introduced a new class of robot move cycles, called pure cycles, to the literature. Within the restricted class of pure cycles, our task is to find the processing times on machines so as to minimise the cycle time and the manufacturing cost simultaneously. We characterise the set of all non-dominated solutions for two specific pure cycles that have emerged as prominent ones in the literature. We prove that either of these pure cycles is non-dominated for the majority of attainable cycle time values. For the remaining regions, we provide the worst case performance of one of these two cycles.