Review Meeting, Brussels, 13 November 2005

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The Axxom Case Studystate of the art

Ed Brinksmajoint work with

Gerd BehrmannMartijn HendriksAngelika Mader

Review Meeting, Brussels, 13 November 2005

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Contents

case study description information transfer modelling heuristics extended case study results evaluation & current work

Review Meeting, Brussels, 13 November 2005

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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

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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

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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

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The recipesin an alternativerepresentation

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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++

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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

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Heuristics

We distinguish:

“nice” heuristics

do not remove best remaining schedule

“cut-and-pray” heuristics

may remove best remaining schedule

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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)

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A Non-Lazy Processing Step

time<=processing_time

resource>0urgent!resource --time:=0

time==processing_timeresource++

resource>0time:=0

resource==0urgent!

time<processing_time

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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)

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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

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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.

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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

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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

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Working Hours

Taken into account through an extra automaton that calculates the effective processing time “online”.

This increases the size of the model considerably

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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

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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

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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