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Scheduling of sequence-dependant jobs on parallel multiprocessor systems using a branch and bound-based Petri net

This paper presents a new branch-and-bound algorithm for minimizing the make-span of a job-shop scheduling problem where n jobs must be scheduled on m machines. It is assumed that the jobs are available at time zero and have sequence-dependent setup times on machines. For solving the scheduling problem we develop a new branch and bound system which constructs its search tree gradually and does not need a large size memory. An upper-bound cost (UBC) is introduced to initialize the root node in search tree which reduces Branch and Bound computations. For modeling the manufacturing system and applying the desired sequence-dependent schedule on it, a supervisor Petri net is introduced. The proposed methods are verified through a computational experiment