Transcript Slide 1
The Axxom Case Study
state of the art
Ed Brinksma
joint work with
Gerd Behrmann
Martijn Hendriks
Angelika Mader
AMETIST
Review Meeting, Brussels, 13
November 2005
Contents
case study description
information transfer
modelling
heuristics
extended case study
results
evaluation & current work
AMETIST
Review Meeting, Brussels, 13 November 2005
Case Study Description
lacquer production scheduling
3 recipes
for uni/metallic/bronce lacquers
use of resources, processing times,timing
29 (73, 219) orders:
start time, due date, recipe
extensions:
delay costs, storage costs, setup costs
weekends, nights
AMETIST
Review Meeting, Brussels, 13 November 2005
Information Transfer
Stumbling blocks:
interpretation of terminology
creation of a dictionary
implicit knowledge
late modification of models
biased model description
based on Orion-pi features
non-standard notation
AMETIST
Review Meeting, Brussels, 13 November 2005
An Axxom Recipe
VORDISP.UNI.85
offset 0-4h
DISP.UNI.85
offset 6h
12
DK.UNI.85
13
15
MISCH.UNI.85
13
PRUEFEN1.UNI.85
13
KORREKTUR.UNI.85
13
98
offset 2-4h
PRUEFEN2.UNI.85
13
AMETIST
Review Meeting, Brussels, 13 November 2005
The recipes
in an alternative
representation
AMETIST
Review Meeting, Brussels, 13 November 2005
A Basic Processing Step
time<=processing_time
resource>0
resource -time:=0
time==processing_time
resource++
timed automaton with 3 locations:
claiming a resource
processing
releasing a resource
template with parameter for processing_time
combined into recipies and composed with models for resources
AMETIST
Review Meeting, Brussels, 13 November 2005
Scheduling Synthesis
use real-time model checker (Uppaal) to
determine the reachability of states where
all orders have been processed in time
schedules can be extracted directly from
witness traces to such states
problem: state space explosion
use heuristics to prune search tree
AMETIST
Review Meeting, Brussels, 13 November 2005
Heuristics
We distinguish:
“nice” heuristics
do not remove best remaining schedule
“cut-and-pray” heuristics
may remove best remaining schedule
AMETIST
Review Meeting, Brussels, 13 November 2005
Nice Heuristics
non-overtaking
orders of the same recipe cannot overtake
each other
non-laziness
a process that needs an available resource
will not waste time if its is not claimed by
others (a.k.a. active scheduling)
AMETIST
Review Meeting, Brussels, 13 November 2005
A Non-Lazy Processing Step
time<processing_time
resource==0
urgent!
resource>0
time:=0
time<=processing_time
resource>0
urgent!
resource -time:=0
AMETIST
time==processing_time
resource++
Review Meeting, Brussels, 13 November 2005
Cut-and-Pray Heuristics
greediness
a process that needs an available resource
will claim this resource immediately
reducing active orders
the number of concurrent orders is
restricted (number of critical resources
can give an indication)
AMETIST
Review Meeting, Brussels, 13 November 2005
Experimental Results
#jobs
heuristic
max.
orders
29
29
73
nl
nl, no
-
term.
time
1s
-
73
nl, no
3
7s
219
g, no
4
8s
uses clock optimization &
optimized successor
calculation
AMETIST
Review Meeting, Brussels, 13 November 2005
Extending the Case Study
1. performance and availability factors
if a resource has an average availability factor f,
its processing time is multiplied by 1/f.
2. storage, delay and setup costs,
working hours
penalties for delivering orders too early, or too
late; costs for cleaning filling stations; work in
shifts, no work over weekends.
AMETIST
Review Meeting, Brussels, 13 November 2005
Results
Availability Factors
#jobs
heuristic
max.
orders
29
nl, no
-
1s
29
g
-
<1 s
73
nl, no
-
-
73
nl, no
4
3s
73
g, no
4
3s
AMETIST
Review Meeting, Brussels, 13 November 2005
term.
time
Storage, Delay,
and Setup Costs
use cost-extended Uppaal CORA
cost optimization problem
delaying earliest starting time heuristic
(cut-and-pray)
time<=processing_time
cost’==late[id]*dcf
cost’==late[id]*dcf
resource>0
resource -time:=0
AMETIST
cost’==late[id]*dcf
time==processing_time
resource++
Review Meeting, Brussels, 13 November 2005
Working Hours
Taken into account through an extra
automaton that calculates the effective
processing time “online”.
This increases the size of the model
considerably
AMETIST
Review Meeting, Brussels, 13 November 2005
Results Extended Case
heuristic
max.
orders
min. cost
found in 60 s
-
es, no, nl
-
530,771
29
-
29
avail.
29
avail.
es, no, competitive
g
with
es, no, nl
Orion-pi
es, no, g results-
29
expl.
#jobs
work
hrs
29
AMETIST
no
4
Review Meeting, Brussels, 13 November 2005
647,410
1,714,875
2,263,496
192,881,129
Evaluation
successful extension of core scheduling problem to
73 and 219 orders
all results obtained < 10 s (PC 512MB, 1GHz)
generic patterns for processing steps, resources,
and heuristics
first results for inclusion of costs and working hours
results competitive with Orion-pi
information transfer was a non-trivial problem
AMETIST
Review Meeting, Brussels, 13 November 2005
Current Work
scaling up the core problem to O(103) orders
seems feasible with active orders heuristic
relation between long-term feasibility and
short-term planning schedules
availability and performance factors are
approximative
irrelevance of cost factors and working hours for
long planning periods
searching for schedules in reverse time
minimize storage and delay costs
AMETIST
Review Meeting, Brussels, 13 November 2005