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