ABB: An Anytime Branch and Bound Algorithm for Scheduling of Deadlock-Prone Flexible Manufacturing Systems

This work investigates a scheduling problem of deadlock-prone flexible manufacturing systems modeled by place-timed Petri nets. It proposes an anytime branch and bound (ABB) algorithm for it to minimize system makespan based on the branch tree of a net model and a highly permissive deadlock controller. The proposed algorithm searches a sequence of transitions in the branch tree that evolves the model from the initial marking to the final one. In order to prune the branch tree and increase search speed, this work develops two pruning rules, a lower bound of makespan, and a novel branching strategy. Their usage ensures ABB's high search efficiency. Experimental results demonstrate that the proposed algorithm surpasses the state-of-the-art ones. Note to Practitioners - In practice, scheduling is one of the most important issues for production managers to address. Existing approaches to deadlock-prone flexible manufacturing system (FMS) scheduling have multiparameters. Their settings can impact the scheduling results greatly. Since their turning is a challenging task, it is difficult to find the best parameter settings. This article proposes an anytime branch and bound (ABB) algorithm for minimizing the makespan of deadlock-prone FMSs. It has only one parameter, i.e., maximal CPU time, which needs no turning. When it is highly tight, ABB can output a feasible and decent schedule. If it is larger and larger, ABB can output a better and better schedule. Comparison studies show that ABB outclasses existing ones significantly. It is suitable for real-time scheduling cases in which satisfied schedules must be offered in a very short time.