The intention of the scheduling system developed at the Fraunhofer-Institute for Material Flow and Logistics is the support of a scheduler working in a job-shop. Due to the existing requirements for a job-shop scheduling system the usage of flexible knowledge representation and processing techniques is necessary. Within this system the attempt was made to combine the advantages of symbolic AI-techniques with those of neural networks

Bayat-Sarmadi, Fahid

Hellingrath, Bernd

Marx, Andreas

Robbach, Peter

English

NASA Technical Reports Server

= ,
= ,
i
N 93 -A a o
A Hybrid Job-Shop Scheduling System /J_
Bo nd H_rath
Peter Ro_ach
Fa_ Bayat-Sm'madi
Andre.as Marx
Fraunhofer-Insthute for Material Flow and Logistics
Emil-l_gge-Str. 75
D-4600 Dorunund 50
-- F.R.G.
/
J
Abstract
The intention of the scheduling system devel_ at the Fraunhofer-Institute for Material Flow and
Logistics is the support of a schedulerworking in a job-shop. Due to the exirdng requirements for a
job-shop scheduling system the usage of flexible knowledge representation and processing techniques
is necessary. Within this system the attempt was made to combine the advantages of symbolic AI-
techniques with those of neural networks.
E
B
m
E
System structure
The scheduling system is situated below a
MRP system giving the relevant data for the
schedule generation. _is data contains
information about the ordors, work plans and
resources, the optimization goals and the
strategies. Out of this data local, global and
suategic camralnts aregenemed.
The local constraints describe the strict
 nts thescheduiehas  ese ....
are the sequence of _tions'_ _"for
re_, the capacity restriction of resources,
and the duc dates. Beside the strict
req_nts global optimization goals have to
be considered within the schedule. An
optimization goal consists of an optimization
criterion whose value describes certain costs
(throughput time. resource utilization,
inventory, tardiness) and a goal description
(minimizationof eh-oughputime,minlmi,_tlon
of weighted resource utilization, ...). These
global consualnts represent the optimization
goals aspreferences. Strategies for buildingup
and refining a schedule are formulated as
strategicumsuxtnts.
contains a description about when certain
strategies can be used, where the schedule can
be mademore dcmilled, how specific simmions
_ 145
https://ntrs.nasa.gov/search.jsp?R=19930009501 2020-03-17T07:50:26+00:00Z
can be detected and what kind of actions have
to take place, how the data of the schedule can
be aggregated tO make the detection of
situations possible, and how specific
requirements of the factory can be taken into
account. All three type of consuaints arc used
Generation of the schedule
For the generation of the schedule all three
schedulers work on it while the information
between them is exchanged through the
partially det_lled schedule. The process of the
m
Io_l
Constraints
L
m
tm
ml
Scheduler
m
g
m
i
Z
U
m
m
Control
F_. I: Stngnnc of the Scheduling System
by the different schedulcn (local, global,
su'atcgic) to bu,__dup a schedule. The structmc
of the scheduling system is shown in Fig. 1.
schedule generation can be described as
follows. In a first phase _C local scheduler
makes a pruliminaryanalysisof the starting
time for every operation. This analysis is done
146
W
m|
R
m
m
_-...-
i
g
|
i
"lmm
L,
m
I
w
mm
w
m
E
m
m
Meet
with respect to the strict requirements and
preferences the schedule should fulfill. The
possible starting times are determined through
the propagation of the local constraints within
so called suitability functions [JOHNSTON 89].
Suitability functions describe for every
operation how desirable it is to start it at a
certain time, so they can be described as
functions over the dine (Fig. 2). When the
value of a suitability function for an operation
is zero this operation cannot be started at that
time. The local scheduler generates a schedule
in which all times where an operation cannot
start are excluded. The propagation of the local
consuaints arc based onto Allen's time relations
[ALLEN 83], the values of the constraints being
suitability functions (Tqg. 3).
opl
op2
op3
t
4_.- t
mint
Fig. 2: Example of suitability function before
pmpagatm
Each time relation is expressed by a utility
function (Fig. 4). This type of function
represen_ a relative measure for the preference
of the starting time of an operation. In an
extention _ the time relations static constraints
for the first possible start time, the least
possible end time, and the capacity of •
resomcc are built.
147
el: opl after op2
pplbeforeop3
Fig. 3: Constraints as utility functions
In each propagation step an operation is chosen
and for each constraint to another operation a
sub-suitability function is being built. The
result is a suitability that shows the possible
starting times of this operation under a
consmLint.
C1
t
C2
t
Fig. 4 : Resuldngsub-sultabifity run.ons
At each propagation step the new suitability
function is formed out of the product of all sub-
suitabilites and the stadc suitabilities. Within
this new suitability all constraints have bccn
taken into account (Fig. 5). If the sui_bility
function has changed all suitabilities of a
constrained operation must be uIxlated. When
no suitability changes anymore the propagation
ends. In the CSP - notation this propagation
creates an arc consistent graph.
nfw
opl I_
mtt eild t
Fig.S: Suitability Function after propagation
Besides the s_ct requirements the global
optimization goals should also be considered
within the schedule. This is done by the global
schedulerwhich refines the possible starting
times of every operation by using a neural
network.
This neural network is built up based upon the
possible starting times determined through the
local scheduler. The neural network is a
Guarded-Discrete-Stoc_ Network (GDS) a
special type of Hopfield net [JOHNSTON/
89], [MncroN _ AL. 90], [HO_
T,,,_ 85], [HOPHFzLDPr,_C 86]. The main
i_ isa unit_gasubset of no_ uni_
so that it is guaranteed that one unit is active. In
the scheduling domain it helps to generate
schedules for all operations and resources and
not for a subset what would only be possible
with Hopfield-nets [JOHNSTON/ADORP 89].
The netisdividedintotwo parts,theoperation
net and the resource net. The weights between
the units of the operation net are cxplicidy set
by the goals of the optimization (minimization
of throughput time, weighted resource
u_zation,tardiness_ workinprogress).All
units have a bias which isbased on theresults
of the local scheduler, thus representing the
suitability functions. The activation of the units
of the operation net corresponds to it's
_ferredsu_ _ m_rv_ "h_c_ _on
of the resource units represent the remaining
capacityin _ timeinterv_
The net is arranged in a matrix-like manner.
While the rows represent the operations and
resources, the columns contain the time
intervals in which the suit_li'ty _ns of all
operations are constant. The updateof all units
of both nets is done synchronically with the
same probability and regarding the state of the
guarding units. The convergence of GDS-
networks is not guaranteed, and so we impose
148
a restriction on the number of epochs
[JOHNSTON/ADORP 89]. The result of a stable
state of the neural network is an optimized
schedule with respect to the different
optimization goals.
The local and the gio_ scheduler work on the
schedule as a whole, i.e. changes in the
schedule affect all operations. These changes
are generally rather coarse. The strategic
scheduler on the other hand selects one
operation out of the schedule for which it does
a detailled planning. The strategies the
scheduler uses for this are described within the
strategic constraints. Strategic constraints arc
formulated as rules on four levels of
• mct_ulcs
These rules describe which strategies are
adequate at certain states of the schedule.
• sumgies
The strategies describe how to refine the
schedule (e.g. scheduling the critical
operations fh'sO taking into account the
stateof all operationsandresomces.
• situation & action
These rules are used to detect situations
(e.g. when an operation is critical) and to
suggest actions (e.g. sch_uling an
operation in it's preferred lime interval).
The view of these rules is local, looking
at the actual state of an operation or
resotnce within the schedule.
mm
qm
r
D
m
M
im
mm
qm
mm
w
mm
i
a_
C
• transformation & reduction
With these rules the actual state of the
current schedule can be reduced to the
relevant informations (e.g. the preferred
At the moment the system described above is in
the state of implementation. So a judgement
_tthe quality of=the _h_g System can't
be done yet. But the parts implemented so far
time interval for starting an operatiOn) _ show promising results, so that we are rather
............... hopeful about fulfilling the objectives the
used by the rules of the higher abstraction
levels.
As a first step the strategic scheduler selects an
adequate strategy by using the metarules. The
strategies suggest detailled changes for the
scheduling of a selected operation. This
selection is done by the strategic cons_ts
describing the situation & action and
transformation & reduction. The suggestions
are based upon the actual schedule containing
the possible and the preferred starting times for
each _tion as a result of the local and_the
global scheduler. The suggestion which seems
to have the most promising effects on the
schedule is integrated into the schedule and the
effects are propagated through the suitability
functions using the local scheduler. This cycle
0oud. gioha]- mn=gicscheduling)conanues
until all operations are scheduled. In the case
flint the decision of the strategic scheduler leads
to an inconsistent sch__ _ion __ ....
it's effects have tO be retracted and an
alive has to be chosen. This work is done
bya control componentThework0f .......
schedulers can be seen as a stepwise refinement
of the schedule. The possible starting times for
each operation are repeatedly restricted until a
sufficient exact starting _nt or a sufficient
small interval for-the starting-fim-e_:i_s .........
de_
system should meet concerning the quality of
the schedule.
Literature
[Ax2J_ 83]
James F. Allen ; "Maintaining
Knowledge about Temporal Intervals", In :
Commumcations of the ACM, 26, 832-843,
1983
[JOtmSTON/ADOP_ 89]
Mark D. Johnston, Hans-Martin Adorf;
"Learning in stochastic neural networks for
Constraint Satisfaction Problems" ; In: Proc
NASA Cont" on Space Telerobotics, Pasadena
CA, 1989
[JOHNSTON 89]
Johnston, Mark D.; "Reasoning with
Scheduling Constraints and Preferences"
SPIKE Technical Report 1989-2, Space
Telescope Science Institute, Baltimore, MD,
1989
[Homm , T ,,rzs5]
Hopfiel& John T.; Tank, David W.;
"'Neural' Computation of Decisions in
Optimization Problems", in: Biological
Cybernetics, 52, pp. 141-152, 1985
[H_, TANK 86]
.... Hopfield, John T; Tank, David W;
"computing with Neural Circuits: A Model",
in: Science_ 233, pp. 625-633, 1986
[MeCmNFr.AX.90]
Steven Minton, Mark D. Johnston,
Andrew B. Philips, Philip Laird; "Solving
Large-Scale Constraint Satisfaction and
Scheduling Problems Using_aHeuristicRepalr
Method"; In : Prec. _ 90, pp. 17-24, 1990
149


A hybrid job-shop scheduling system

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server