Two-phase branch and bound algorithm for robotic cells rescheduling considering limited disturbance

This paper addresses a robotic cell rescheduling problem and focuses on trade-off between the total completion time of all jobs and the disturbance of a reschedule. We first define and measure the disturbance of a reschedule as the deviation of completion time of the jobs already scheduled between the reschedule and the initial schedule. To guarantee the steady performance of the system, we consider a special case that the processing sequence of the jobs already scheduled cannot be changed. The addressed rescheduling problem is transformed into a series of deterministic local scheduling problems with the objective of minimizing the total completion time of all jobs provided that the disturbance is within a given limit. A two-phase branch and bound algorithm is developed to efficiently solve the local scheduling problems. To improve the efficiency of the search procedure, a dynamic enumeration mechanism is applied to eliminate redundant constraints. Furthermore, two search strategies are proposed to direct the search procedure toward finding an optimal solution and a near-optimal solution. Finally, computational results demonstrate the efficiency of our algorithm.