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**Module-based architecture for a periodic job-shop scheduling problem.**
*(English)*
Zbl 1252.90021

Summary: We address the Petri net (PN) based design and modeling approach for a periodic job-shop scheduling problem. Asynchronous synthesis for net-modules of the jobs is suggested in this paper for optimal allocation of shared resources to different operations. To make sure the completion of all the jobs in a single iteration of a production cycle and the correct calculation of a makespan, the synchronization problem among jobs is tackled by introducing the special synchronizing transition in the model. A timed-place PN is adopted for the purpose of finding the feasible schedule in terms of the firing sequence of the transitions of the PN model by using the heuristic search method. Further, the characterization of the PN model is performed and it is shown that the PN model for a periodic job-shop scheduling problem is equivalent to a class of PN known as parallel process net with resources (PPNRs). The modeling approach is demonstrated with a practical example and a makespan is calculated for the example.

### MSC:

90B35 | Deterministic scheduling theory in operations research |

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\textit{F. Ahmad} and \textit{S. A. Khan}, Comput. Math. Appl. 64, No. 1, 1--10 (2012; Zbl 1252.90021)

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### References:

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