LIMOS CNRS UMR 6158
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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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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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Summary

  • FMS presentation

  • Objectives and assumptions

  • MILP formulation

  • Benchmarks

  • Concluding remarks


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Flexible Manufacturing System

  • M stations

  • One or more vehicles

  • One load/unload station

  • Each job follows a given sequence of operations


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

FMS: station

  • Limited input buffer capacity

  • Limited output buffer capacity


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Deadlock phenomenon


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

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)


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Problem formulation

Global optimization between job processing and job transportation

Notations:


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Set of constraints


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Precedence constraints

(d)

(d)

Processing order of operations according to each job sequence of treatement


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Sequencing constraints

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Transport constraints

Only one loaded/deadheading move of the vehicle at the same time


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Storage constraints for input buffers


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Storage constraints for output buffers


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Limited number of jobs simultaneously allowed


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Buffers management rule constraints

FIFO for both input and output buffers


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Evaluation of the model

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Computational experiments

< 1min

ï‚£ 30min

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Future research

  • Cutting plane approach

  • Extend the model for more than one vehicle

  • Extend the model to stochastic transportation times (robustness)


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Transport constraints

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


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Buffers management rule constraints (FIFO)


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Storage constraints for input buffers

Theorem:


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

Proof


Mathieu becart philippe lacomme aziz moukrim nikolay tchernev

This is impossible since

This requires


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