yazid mati & xiaolan xie crf club, 04/07/2004 scheduling automated manufacturing systems with...

CRF Club, 04/07/2004 Yazid Mati & Xiaolan Xie

Scheduling Automated Manufacturing Systems

with Transportation and Storage Constraints

Yazid MATI Ecole des Mines de [email protected]

Xiaolan XIE INRIA / MACSI Team & LGIPM / AGIP Team

Ile du Saulcy, 57045 Metz, [email protected]


1. Scope of the scheduling model

2. A case study in which new features really count

3. Backgrounds

4. A generic scheduling model

5. Solving the scheduling model

6. Numerical performances

7. Extensions

PLAN


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.

Scope of the scheduling model


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

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)



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



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.

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.

Background


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.

A generic scheduling modelMulti-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.



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.



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


J1 (1h) J2 (2h)

M1 M2

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

J1 (1h) J2 (1h)

M1 M2


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, ij) (M+T, pij).


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 on a conveyor as Oij = (, )

• transportation with an AGV as Oij = (AGV, )

• transportation with a robot R as Oij = (R, ).



Solving the scheduling model : two-job case

Geometric method

D

Cx

Cy

vi vi

F

O

SE

NW

F

3

3 3

3

Representation in the plane

Successors

The resulting network

J1

J2

F

O M1 M2 M3

M3

M2

M1

NW

SE

J1 = (M1M4, 1), (M2, 2), (M3, 1),J2 = (M3, 2), (M2, 1), (M1, 2),


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

Solving the scheduling model :general case

A Greedy algorithm

Job sequence : J1 J2 J3 … JN-1 JN

Jcom J3Geometric approach

geometric approach

between Jcom and J3


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.


Construction of the combined job

M2

M3

M1

t

t

t

O11 O23

O21

O12

O13

O22

1

2

3 4

6

Jcom = M1 M3 (1) M2 M3 (1)

M2 (1) M3 M2 (1) M1 (2)


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].


Improving the greedy algorithm


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.


Numerical performances

Test on special cases

Robotic cell (Ramaswamy & Joshi [1996]) : 4 jobs, 3 machines, one robot under various buffer size constraints at machines.

• Optimal solutions

• Computation timeComputation time : 0.1 CPUs

Randomly generated examples (Damasceno et Xie [1999])

• 9 bestbest solutions overs 9 instances

• Computation timeComputation time : 8 CPUs

Robot

chargement/déchargement

M4

M3 M2

M1

PPii

PPjj


EXTENSIONS

The proposed approach has been extended to the following cases:

1. operations with alternative resource requirements

2. products with multiple manufacturing processes

Future extensions include:

3. assembly/disassembly operations

4. jobs with no-wait operations

5. jobs with limited-wait operations.

yazid mati & xiaolan xie crf club, 04/07/2004 scheduling automated manufacturing systems with...

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