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Scheduling Automated Manufacturing Systems with Transportation and Storage Constraints Yazid MATI Ecole des Mines de Nantes yazid.mati@emn.fr Xiaolan XIE INRIA / MACSI Team & LGIPM / AGIP Team Ile du Saulcy, 57045 Metz, France xie@loria.fr . PLAN. Scope of the scheduling model

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slide1

Scheduling

Automated Manufacturing Systems

with Transportation and Storage Constraints

Yazid MATI

Ecole des Mines de Nantes

yazid.mati@emn.fr

Xiaolan XIE

INRIA / MACSI Team & LGIPM / AGIP Team

Ile du Saulcy, 57045 Metz, France

xie@loria.fr

CRF Club, 04/07/2004

slide2

PLAN

  • Scope of the scheduling model
  • A case study in which new features really count
  • Backgrounds
  • A generic scheduling model
  • Solving the scheduling model
  • Numerical performances
  • Extensions

CRF Club, 04/07/2004

slide3

Scope of the scheduling model

  • The new scheduling model includes most existing production scheduling models as special cases:
  • Job-shop and flow-shop models
  • Robotic cell
  • Production line with intermediate buffers
  • Hybrid flow shops
  • Flow shop without intermediate buffers
  • Flexible manufacturing systems with AGVs.

CRF Club, 04/07/2004

slide4

Case study in which new features really count

  • Algorithms developed in our research have been selected and are being implemented for the production planning of :
    • A French company that produces large and heavy parts for the aerospace industry
  • Plant:
    • Plant layout arranged in line
    • 6 types of workstations : 2 idem workstations for 2 types
    • A single transportation device
    • No buffer area

CRF Club, 04/07/2004

slide5

Case study in which new features really count

  • Characteristics of the demand:
    • Around 10 part types (25 to 60 units per year)
    • Manufacturing processes : 8 to 13 operations (re-entrance)
    • An operation needs a machine, a tool and an operator
    • Processing times range from 1 to 23 hours
  • Additional constraints:
    • Transportation device cannot held workpieces and wait
    • Workpieces are loaded on palettes (high prices)

CRF Club, 04/07/2004

slide6

Case study in which new features really count

  • Main objective (realized):
    • Determine the minimum number of palettes
    • Determine a schedule that minimizes the completion time
  • Second step (realized):
    • Any workstation can serve as a buffer
    • Scheduling model with resources flexibility
  • Future work :
    • Operational software that takes into account the work-in-process

CRF Club, 04/07/2004

slide7

Background

High productivity of automated manufacturing systems is achieved through use of modern production resources for machining, transportation and storage.

Economic pressure requires high utilization of all resources and makes all resources nearly critical.

There is a need to coordinate the use of all resources for efficient production planning/scheduling.

CRF Club, 04/07/2004

slide8

Background

Mainstream literature in production scheduling only considers machining resources, treats other resources as “secondary resources” and focuses on oversimplified models such as job-shop, flow-shop models.

Practical approach to deal with this problem is to (i) first derive a production plan with machining resources and then (ii) adjust the planning by taking into account the availability of other resources.

This approach is unsatisfactory if the so-called “secondary resources” are nearly critical.

CRF Club, 04/07/2004

slide9

A generic scheduling model

Multi-resource Job-Shop with Blocking (MJSB)

The system is composed of m resources {R1, R2, …, Rm} and has n jobs (or customer orders) {J1, J2, …, Jn}

Each job Ji requires a sequence of operations Oi1Oi2…OiN(i).

The processing time pik of each operation Oik is given.

The goal is to complete all jobs in the minimum time.

CRF Club, 04/07/2004

slide10

A generic scheduling model

Multi-resource Job-Shop with Blocking (MJSB)

Resource availability:

Each resource is available in several units.

Resource requirement of an operation:

Each operation might require simultaneously more than one resource and more than one unit of each resource.

Example: Oik = (2OP+TR, 10 min) corresponds to an operation performed by 2 operators OP with one transportation device TR during 10 minutes.

CRF Club, 04/07/2004

slide11

A generic scheduling model

Multi-resource Job-Shop with Blocking (MJSB)

Resource release after an operation :

At the completion of an operation Oik, its resources are held and cannot be released till resources needed for the next operation of the same job are available.

This constraint is called Hold-While-Wait constraint.

CRF Club, 04/07/2004

slide12

A generic scheduling model

Multi-resource Job-Shop with Blocking (MJSB)

M1

M2

J1 (1h)

J2 (2h)

A production line without intermediate buffer where M1 is blocked during one hour after the completion of J1 on it.

A job-shop without intermediate buffer where M1 and M2 are deadlocked after the completion at time 1.

M1

M2

J1 (1h)

J2 (1h)

CRF Club, 04/07/2004

slide13

A generic scheduling model

Multi-resource Job-Shop with Blocking (MJSB)

One remarkable feature of our scheduling model is its flexible modeling granularity of resource requirements of operations thanks to multi-resources operations and the hold-while-wait constraint.

  • Example :
  • Operation with machine requirement only : Oij = (M, pij).
  • Machine+operator + tools, Oij = (M+O+T, pij).
  • If the operator is only needed to mount the tool and to load the product, then Oij = (M+O+T, Dij) (M+T, pij).

CRF Club, 04/07/2004

slide14

A generic scheduling model

Multi-resource Job-Shop with Blocking (MJSB)

  • Some common operations can be modeled as follows special MJSB operations:
  • waiting in a buffer of unlimited capacity as Oij = (, 0),
  • waiting in a buffer B of size n as Oij = (B, 0)
  • transportation delay D on a conveyor as Oij = (, D)
  • transportation with an AGV as Oij = (AGV, D)
  • transportation with a robot R as Oij = (R, D).

CRF Club, 04/07/2004

slide15

Solving the scheduling model : two-job case

Geometric method

J1 = (M1M4, 1), (M2, 2), (M3, 1),

J2 = (M3, 2), (M2, 1), (M1, 2),

Successors

Representation in the plane

The resulting network

CRF Club, 04/07/2004

slide16

Solving the scheduling model :general case

A Greedy algorithm

  • Jobs are scheduled one after another according to a job sequence,
  • The two first jobs are scheduled using a geometric approach,
  • Jobs already scheduled are grouped into a combined job,
  • A new job and the combined job are scheduled bythe geometric approach.

Job sequence : J1 J2 J3 … JN-1 JN

geometric approach

between Jcom and J3

Jcom

J3

Geometric approach

CRF Club, 04/07/2004

slide17

Solving the scheduling model :general case

Construction of the combined job

  • Determine the Gantt diagram of the resulting schedule,
  • Decompose [0, makespan] into sub-intervals according to the

finishing time of operations,

  • Processing time : the length of the sub-interval,
  • The required machines are machines occupied in the

corresponding sub-interval.

Jcom = M1 M3 (1) M2 M3 (1)

M2 (1) M3 M2 (1) M1 (2)

CRF Club, 04/07/2004

slide18

Solving the scheduling model :general case

Improving the greedy algorithm

  • The performance of the greedy algorithm strongly depends on the order, called job sequence, in which jobs are scheduled.
  • A taboo search is used to identify the job sequence with which the greedy algorithm leads to the shortest makespan, i.e.

Min Cmax(J[1]J[2] …J[n])

where Cmax is the makespan of the schedule given by the greedy algorithm with job sequence J[1]J[2] …J[n].

CRF Club, 04/07/2004

slide19

Numerical performances

Benchmark test

  • There is no test problems in the literature with features of our scheduling model.
  • For existing benchmarks (over 100 test cases) for the job shop problem, the proposed approach is in general very competitive with best known heuristics.

CRF Club, 04/07/2004

slide20

Numerical performances

Test on special cases

Pj

M3

M2

Pi

Robot

M4

M1

chargement/déchargement

  • Robotic cell (Ramaswamy & Joshi [1996]) : 4 jobs, 3 machines, one robot under various buffer size constraints at machines.
      • Optimal solutions
      • Computation time : 0.1 CPUs
  • Randomly generated examples (Damasceno et Xie [1999])
      • 9 best solutions overs 9 instances
      • Computation time : 8 CPUs

CRF Club, 04/07/2004

slide21

EXTENSIONS

  • The proposed approach has been extended to the following cases:
  • operations with alternative resource requirements
  • products with multiple manufacturing processes
  • Future extensions include:
  • assembly/disassembly operations
  • jobs with no-wait operations
  • jobs with limited-wait operations.

CRF Club, 04/07/2004