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Mathieu BECART , Philippe LACOMME, Aziz MOUKRIM, Nikolay TCHERNEV

LIMOS CNRS UMR 6158. HeuDiaSyC CNRS UMR 6599. Mixed Integer Linear Model for FMS scheduling based on AGVs: Job-Shop with a Single Transport Robot. Mathieu BECART , Philippe LACOMME, Aziz MOUKRIM, Nikolay TCHERNEV. Summary. FMS presentation Objectives and assumptions MILP formulation

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Mathieu BECART , Philippe LACOMME, Aziz MOUKRIM, Nikolay TCHERNEV

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  1. LIMOS CNRS UMR 6158 HeuDiaSyC CNRS UMR 6599 Mixed Integer Linear Model for FMS scheduling based on AGVs: Job-Shop with a Single Transport Robot Mathieu BECART, Philippe LACOMME, Aziz MOUKRIM, Nikolay TCHERNEV

  2. Summary • FMS presentation • Objectives and assumptions • MILP formulation • Benchmarks • Concluding remarks

  3. Flexible Manufacturing System • M stations • One or more vehicles • One load/unload station • Each job follows a given sequence of operations

  4. FMS: station • Limited input buffer capacity • Limited output buffer capacity

  5. Deadlock phenomenon

  6. FMS: Job Type Job 1: L/U (M1,10) (M3,20) (M4,6) L/U Job 2: L/U (M2,5) (M1,14) (M3,12) L/U FMS: Management rules • Management policy of the vehicle: FIFO, STT, MOQS, … • Management rule for buffers: FIFO • Maximal number of jobs simultaneously allowed to avoid deadlock

  7. Scope and purpose • Objectives • Exact resolution for small and medium scale instances • Mixed Integer Linear Programing formulation • Constraints of interest • Only one vehicle • Nonpreemptive operations • Deadheading transport times • Limited input/output buffers capacity • Management rule of buffers (FIFO)

  8. Problem formulation Global optimization between job processing and job transportation Notations:

  9. Set of constraints

  10. Set of constraints • Precedence constraints • Sequencing constraints • Transport constraints • Storage constraints for input buffers • Storage constraints for output buffers • Maximal number of jobs simultaneously allowed • Buffers managements rule constraints

  11. Precedence constraints (d) (d) Processing order of operations according to each job sequence of treatement

  12. Sequencing constraints No more than one job processed on the same station at the same time

  13. Transport constraints Only one loaded/deadheading move of the vehicle at the same time

  14. Storage constraints for input buffers

  15. Storage constraints for output buffers

  16. Limited number of jobs simultaneously allowed

  17. Buffers management rule constraints FIFO for both input and output buffers

  18. Evaluation of the model (Bilge and Ulusoy, 1995) (Liu and MacCarthy, 1997)

  19. Benchmarks LAYOUT 2 150 135 Station 3 Station 2 90 75 Station 1 Station 4 0 Load/Unload station 30 60 0 Bilge and Ulusoy instances 4 Layouts, 10 Jobsets

  20. Computational experiments < 1min  30min Sun Entreprise 450 with 4 Ultra Sparc II processors 450 MHz under Sun Solaris 7 OS with 2 Go of central memory

  21. Concluding remarks • MILP for FMS with one vehicle • Great number of management constraints taken into account: limited input/output buffers capacity, managing rule of buffers (FIFO), maximal number of jobs in the system • Instances of Bilge and Ulusoy, 1995 • Optimal resolution for small and medium scale instances

  22. Future research • Cutting plane approach • Extend the model for more than one vehicle • Extend the model to stochastic transportation times (robustness)

  23. Transport constraints Deadheading vehicle move from L/U station to stations in the system taken into account

  24. Buffers management rule constraints (FIFO)

  25. Storage constraints for input buffers Theorem:

  26. Proof

  27. This is impossible since This requires

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