<p>Various factories have been successfully distributed by their planning machines. The execution of tasks is made easier, the speed of execution is increased, and the delay time is reduced due to successful distribution. In the Distributed Flexible Job shop Scheduling Problem with transportation time that we study in this work, the processing time of each operation is dependent on the used machine and can be done on different machines. This is done in a collection of factories that are distributed geographically. m machines are present in each factory, and they are responsible for processing n jobs. One or several transport robots transport jobs between machines. The Distributed Flexible Job shop Scheduling Problem with transportation time (DFJSPT) is not studied in the literature, so it is presented for the first time in this paper. Three NP-Hard problems are combined in the DFJSPT: the issue of assigning jobs to machines, distributing jobs to factories, and routing robots. Our study focuses on the DFJSP with transportation time using a single robot in each factory. The mixed-integer linear programming formulation, which encompasses both oriented and non-oriented disjunctive graphs, was first presented by us. Then, we validate our formulation with CPLEX and we tested our TS algorithm by solving two categories of instances to minimize the maximum completion time (makespan): The first category is composed of instances of Flexible Job shop Scheduling Problem with transportation time which we have integrated the constraints of jobs distribution between factories, and the second category is composed of instances of Distributed and Flexible Job shop Scheduling Problem which we have integrated the constraints of transportation time.</p>

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Modeling and solving the distributed flexible job shop scheduling problem with transportation time

  • Bilel Marzouki,
  • Olfa Belkahla Driss,
  • Khaled Ghédira

摘要

Various factories have been successfully distributed by their planning machines. The execution of tasks is made easier, the speed of execution is increased, and the delay time is reduced due to successful distribution. In the Distributed Flexible Job shop Scheduling Problem with transportation time that we study in this work, the processing time of each operation is dependent on the used machine and can be done on different machines. This is done in a collection of factories that are distributed geographically. m machines are present in each factory, and they are responsible for processing n jobs. One or several transport robots transport jobs between machines. The Distributed Flexible Job shop Scheduling Problem with transportation time (DFJSPT) is not studied in the literature, so it is presented for the first time in this paper. Three NP-Hard problems are combined in the DFJSPT: the issue of assigning jobs to machines, distributing jobs to factories, and routing robots. Our study focuses on the DFJSP with transportation time using a single robot in each factory. The mixed-integer linear programming formulation, which encompasses both oriented and non-oriented disjunctive graphs, was first presented by us. Then, we validate our formulation with CPLEX and we tested our TS algorithm by solving two categories of instances to minimize the maximum completion time (makespan): The first category is composed of instances of Flexible Job shop Scheduling Problem with transportation time which we have integrated the constraints of jobs distribution between factories, and the second category is composed of instances of Distributed and Flexible Job shop Scheduling Problem which we have integrated the constraints of transportation time.