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# Mathieu BECART , Philippe LACOMME, Aziz MOUKRIM, Nikolay TCHERNEV - PowerPoint PPT Presentation

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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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

• FMS presentation

• Objectives and assumptions

• MILP formulation

• Benchmarks

• Concluding remarks

• M stations

• One or more vehicles

• Each job follows a given sequence of operations

• Limited input buffer capacity

• Limited output buffer capacity

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

• Objectives

• Exact resolution for small and medium scale instances

• Mixed Integer Linear Programing formulation

• Constraints of interest

• Only one vehicle

• Nonpreemptive operations

• Limited input/output buffers capacity

• Management rule of buffers (FIFO)

Global optimization between job processing and job transportation

Notations:

• 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

(d)

(d)

Processing order of operations according to each job sequence of treatement

No more than one job processed on the same station at the same time

FIFO for both input and output buffers

(Bilge and Ulusoy, 1995) (Liu and MacCarthy, 1997)

LAYOUT 2

150

135

Station 3

Station 2

90

75

Station 1

Station 4

0

station

30

60

0

Bilge and Ulusoy instances

4 Layouts, 10 Jobsets

< 1min

 30min

Sun Entreprise 450 with 4 Ultra Sparc II processors 450 MHz under Sun Solaris 7 OS with 2 Go of central memory

• 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

• Cutting plane approach

• Extend the model for more than one vehicle

• Extend the model to stochastic transportation times (robustness)

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

This requires