TASK ALLOCATION IN A TASK ALLOCATION IN A PRODUCTION CHAIN PRODUCTION CHAIN Swarm intelligence intelligence project project Swarm Yann Christinat Christinat Yann Matteo Thomas DeGiacomi Matteo Thomas DeGiacomi
Description of of the the problem problem Description � A A truck truck assembly assembly chain chain produces produces n n truck truck/ /hour hour � � A A set set of of paint paint booths booths has to has to color color every every truck truck in a in a � predetermined color color c c predetermined � Every Every booth booth is is charged charged with with one one color color � � Every Every booth booth needs needs t1 t1 minutes minutes to to paint paint a a truck truck � � A A booth booth can can change change color color t2 t2 minutes minutes � � If If a a truck truck can can‘ ‘t t be be handled handled, , it it‘ ‘s s considered considered as lost as lost � GOAL: assign assign the the trucks trucks to to the the paint paint booths booths as as GOAL: efficiently as as possible possible efficiently
Booth state state machine machine Booth New task, Changing color mismatch Waiting color New task, color matching Color Task changed completed Working
Involved parameters parameters Involved � Environment Environment parameters parameters: : � describe the the environment environment ( (throughput throughput of of describe the assembly assembly chain chain, time , time needed needed by by a a the booth to to change change a a color color or or perform perform a a task task). ). booth � Allocation Allocation parameters parameters: : � define the the way way allocation allocation is is performed performed. . define Depend on on adopted adopted strategy strategy. . Depend
The Market Market- -based based approach approach The � Booth Booth bid bid for for the the trucks trucks. . Assigned Assigned trucks trucks � are put put in a in a queue queue in front of in front of the the winner winner. . are b i = α α q q i + β β m m i : b i = i + � Bidding Bidding function function: � i ε {0,1} i ε (q q i : queue queue length length, , m m i {0,1} color color matching matching) ) ( i : � An An auctioner auctioner selects selects the the winner winner � : T(t T(t) = ) = min( min(b b i (t)) )) i (t � Global Global objective objective function function: �
Enhancing specialisation specialisation Enhancing � If If more more than than a a winner winner is is found found: : � Select the the one one with with the the color color of of the the last last Select truck in in queue queue matching matching the the one one of of the the truck current truck truck. . current � If If still still more more than than one one truck truck is is found found: : � random selection selection random
The Threshold Threshold- -based based approach approach The � New New trucks trucks are are put put in a in a set set ( ( environment ) environment ) � � The The quantity quantity of of trucks trucks of a of a given given color color c c in in � the environment environment represent represent the the stimulus[c the stimulus[c] ] � booths booths have have a a threshold[c ] for for every every color color threshold[c] � � A A booth booth activates activates if if threshold[c] < stimulus[c] � � The distance booth-truck depends on the color (0 if match, 1 if mismatch)
Dynamic threshold threshold Dynamic Prize for for a a booth booth receiving receiving a a task task and and � Prize � already having having the the right right color color c: c: lower lower already threshold[c] ( ] (- -1) 1) threshold[c � If If a a prize prize is is given given, a , a penalty penalty is is assigned assigned to to � a randomly randomly selected selected booth booth: : higher higher a threshold[c] (+1) ] (+1) threshold[c IDEA: enhancing enhancing specialisation specialisation. . IDEA:
Market- -based based parameters parameters Market � Best Best performances performances for for the the market market based based � approach: : α α =0.2, =0.2, β β =1.0 =1.0 approach In successive successive benchmarks benchmarks we we used used those those values values In
Market- -based based performances performances Market
Threshold- -based based performances performances Threshold
Conclusions Conclusions : balanced balanced workload workload on on each each � Market Market- -based based: � booth, , equal equal quantity quantity of of change change color color. . booth unbalanced workload workload, , : unbalanced � Threshold Threshold- -based based: � working booths booths change change color color less less often often. . working Globally threshold threshold- -based based performs performs better better! ! Globally
References References � Campos Campos, , Mike Mike; ; Bonabeu Bonabeu, , Eric Eric; ; � Thé éradulaz radulaz, , Guy Guy; ; Denembourg Denembourg, , Jean Jean- - Th Louis. . Dynamic Louis Dynamic Scheduling Scheduling and and Division Division of of . Adaptative Adaptative Labor in Social in Social Insects Insects. Labor Behavior 2001, pag 2001, pag.83 .83- -92 92 Behavior
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