A METIST Review Meeting, Brussels, 13 November 2005 The Axxom Case Study state of the art Ed...
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Transcript of A METIST Review Meeting, Brussels, 13 November 2005 The Axxom Case Study state of the art Ed...
Review Meeting, Brussels, 13 November 2005
AMETIST
The Axxom Case Studystate of the art
Ed Brinksmajoint work with
Gerd BehrmannMartijn HendriksAngelika Mader
Review Meeting, Brussels, 13 November 2005
AMETIST
Contents
case study description information transfer modelling heuristics extended case study results evaluation & current work
Review Meeting, Brussels, 13 November 2005
AMETIST
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
Review Meeting, Brussels, 13 November 2005
AMETIST
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
Review Meeting, Brussels, 13 November 2005
AMETIST
An Axxom Recipe
13
12 15
13
13
13
13
98
VORDISP.UNI.85
DISP.UNI.85
DK.UNI.85
PRUEFEN1.UNI.85
KORREKTUR.UNI.85
PRUEFEN2.UNI.85
MISCH.UNI.85
offset 0-4h
offset 6h
offset 2-4h
Review Meeting, Brussels, 13 November 2005
AMETIST
The recipesin an alternativerepresentation
Review Meeting, Brussels, 13 November 2005
AMETIST
A Basic Processing Step
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
time<=processing_time
resource>0resource --time:=0
time==processing_timeresource++
Review Meeting, Brussels, 13 November 2005
AMETIST
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
Review Meeting, Brussels, 13 November 2005
AMETIST
Heuristics
We distinguish:
“nice” heuristics
do not remove best remaining schedule
“cut-and-pray” heuristics
may remove best remaining schedule
Review Meeting, Brussels, 13 November 2005
AMETIST
Nice Heuristics
non-overtakingorders of the same recipe cannot overtake each other
non-lazinessa process that needs an available resource will not waste time if its is not claimed by others (a.k.a. active scheduling)
Review Meeting, Brussels, 13 November 2005
AMETIST
A Non-Lazy Processing Step
time<=processing_time
resource>0urgent!resource --time:=0
time==processing_timeresource++
resource>0time:=0
resource==0urgent!
time<processing_time
Review Meeting, Brussels, 13 November 2005
AMETIST
Cut-and-Pray Heuristics
greedinessa process that needs an available resource will claim this resource immediately
reducing active ordersthe number of concurrent orders is restricted (number of critical resources can give an indication)
Review Meeting, Brussels, 13 November 2005
AMETIST
Experimental Results
#jobs heuristicmax.
ordersterm.time
29 - - -
29 nl - 1 s
73 nl, no - -
73 nl, no 3 7 s
219 g, no 4 8 s
uses clock optimization &optimized successor
calculation
Review Meeting, Brussels, 13 November 2005
AMETIST
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.
Review Meeting, Brussels, 13 November 2005
AMETIST
Results Availability Factors
#jobs heuristicmax.
ordersterm.time
29 nl, no - 1 s
29 g - <1 s
73 nl, no - -
73 nl, no 4 3 s
73 g, no 4 3 s
Review Meeting, Brussels, 13 November 2005
AMETIST
Storage, Delay, and Setup Costs
use cost-extended Uppaal CORA cost optimization problem delaying earliest starting time heuristic
(cut-and-pray)
time<=processing_timecost’==late[id]*dcf
resource>0resource --time:=0
time==processing_timeresource++
cost’==late[id]*dcf cost’==late[id]*dcf
Review Meeting, Brussels, 13 November 2005
AMETIST
Working Hours
Taken into account through an extra automaton that calculates the effective processing time “online”.
This increases the size of the model considerably
Review Meeting, Brussels, 13 November 2005
AMETIST
Results Extended Case
#jobsworkhrs
heuristicmax.
ordersmin. cost
found in 60 s
29 - es, no, nl - 530,771
29 - es, no, g - 647,410
29 avail. es, no, nl - 1,714,875
29 avail. es, no, g - 2,263,496
29 expl. no 4 192,881,129
competitivewith
Orion-piresults
Review Meeting, Brussels, 13 November 2005
AMETIST
Evaluation
successful extension of core scheduling problem to 73 and 219 ordersall results obtained < 10 s (PC 512MB, 1GHz)
generic patterns for processing steps, resources, and heuristics
first results for inclusion of costs and working hoursresults competitive with Orion-pi
information transfer was a non-trivial problem
Review Meeting, Brussels, 13 November 2005
AMETIST
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