Swarm Baed Truck-Shovel Dpatchg Sytem Ope Pt Me Operato Yaah Br, W. Scott Dubar ad Alla Hall Departmet of Mg ad Meral Proce Egeerg Uverty of Brth Columba, Vacouver, B.C., Caada Emal: br@mg.ubc.ca Abtract The dpatch of truck ad hovel ha alway bee a mportat compoet the ucce of ope pt me operato. Dpatch ytem have evolved from maual to today automatc wth almot o huma terveto. Although dpatchg ytem avalable today are peudo real tme ad effcet, the optmal dpatchg realzed over ubet of the fleet whe dealg wth large fleet. Th approach certaly rae the queto of optmalty. I fact decompog the fleet to ub-fleet ad the optmzg each oe doe ot guaratee optmalty for the etre fleet. Moreover the ytem ot flexble to chage the operato evromet uch a emergecy breakdow ad atcpated dow tme. The warm tellgece approach troduced th paper a ew techque that ue the behavour of ocal ect to model ad mulate a dpatchg ytem. Socal ect are flexble that they repod to ay chage ther evromet, partcularly thoe that threate ther urvval. Th flexblty occur repoe to chemcal or phycal cue produced the evromet ether by the ect themelve or by exteral fluece. Ug aaloge to thee chemcal ad phycal cue, a flexble dpatchg ytem ca be developed that ca effcetly dpatch truck of the etre fleet ad that ca adapt to chage the truck/hovel/mateace evromet. Smulato of dpatchg ytem baed o thoe cocept are preeted ad decrbed. Itroducto Dpatchg ytem for ope pt me have attracted coderable atteto the lat year due to ubtatal ga productvty acheved through ther mplemetato. Haul truck ad hovel are oe of the key reource, whch repreet a gfcat captal ad operatg cot, of urface mg. Due to the hgh operatg ad mateace cot, a lot of effort ha bee drected to cot avg hovel-truck haulage whch ha prove to be mprovg term of relablty over the tme. But the creae of equpmet ad fleet ze ha reduced the flexblty of the hovel-truck haulage procedure. The allocato of the equpmet become more delcate a a deco o oe pece of equpmet ca have a huge mpact o the etre operato. For example whe hould oe decde to ed a hovel or a truck to mateace wth repect to cotrat uch a target requremet (mll requremet), equpmet cheduled ad/or ucheduled mateace, tre wear off, etc. Wth the advet of larger ze equpmet coupled wth creag haul dtace, deepeg pt ad a more compettve meral market, there a urget eed to develop a dpatchg procedure that ot oly relable term of allocatg reource real tme but ca alo be flexble ad adapt to ay chage that occur wth the operato evromet. Dpatchg procedure avalable today rage from mple heurtc rule to complex mathematcal programmg baed method. Mathematcal programmg (more ofte lear programmg) baed dpatchg ytem have motly bee two part. The frt part ormally baed o the hort rage plag objectve, ad the ecod part ued to mplemet the frt part real tme [1]. Today may author agree that heurtc dpatchg procedure are formulated rule that do ot guaratee optmalty, epecally whe dealg wth large fleet. The heurtc et of rule cot geerally of maxmzg truck ad hovel ue baed o earet avalable truck to dpatch. Boate [2] ad Lzotte [3] oberved that ot oly optmalty ot guaratee, but alo grade requremet caot be met by th approach.
The geeral approach of mathematcal procedure are baed o ug mathematcal tool uch a lear or a o-lear programmg that are ued to optmze truck or toage flow rate betwee hovel ad cruher/dump wth repect to ome qualty cotrat ad the truck are dpatch accordgly [4]. I order to accout for ucertate that may occur durg, ome mathematcal method ue tochatc lear or o-lear programmg or geetc algorthm. The later model although effcet do ot guaratee adequate adaptablty whe omethg goe wrog durg operato. Stochatc lear programmg for tace couple lear programmg method wth mulato techque that may ot decrbe the real evromet whch the equpmet are operated. Geetc algorthm ue the proce of mutato ad croover to determe a et of populato wth whch the problem hould be optmze. But becaue of the hgh cot related to the equpmet, omttg a part of the etre populato may have a mpact o the optmzato procedure. The procedure propoed th paper baed o the behavour of ocal ect uch a at coloe. The procedure ue local optmzato approach whle guarateeg a real tme dpatch ytem that adapt to varato wth the operato evromet to eure that optmzato atfed. Lke at react to ay chage wth ther evromet to guaratee ther urvval by adoptg flexble behavour, the method propoed th paper lead to a procedure that make truck ad hovel react to ay uforeee chage (uch a extreme weather codto, breakdow, etc) ad take acto to eure that the target are met uder ay gve cotrat. Backgroud Stude coducted by etomologt have how that at take dvdually are almot bld wth o memory ad they do ot have drect commucato wth ther coloy. At yet take together, thee ect are able to performed amazg thg uch fdg the hortet path from ther et to a food ource llutrated by Fg. 1, fdg ther way back to et after a log trp that rage from klometer, harvetg leave to produce fugu that ued for ther utrto, orgazg themelve a well tructured maer, etc. The very queto oe mght ak f at do ot have drect commucato ad are ot tellget the huma ee, how do they orgazed themelve ad perform all thee amazg tak? The ame tude have cofrmed that at commucate drectly through a chemcal hormoe, called pheromoe, whch they releae o ther route. A at travelg from a pot A to aother pot B wll releae a tral of pheromoe that eed by other at precedg hm (Th procedure called recrutmet ). The precedg at wll follow path AB f t pheromoe cocetrato the hghet amog the other path. The proce of recrutg ad uccefully repodg to the recrutmet called tgmergy. I Fg. 1A decrbe at travelg betwee a food ource ad ther et. Suddely ad obtacle placed ther path (Fg. 1B). At frt they react quckly by gog radomly aroud the obtacle (Fg. 1C), after a hort perod of tme, the at uccefully fgure out the hortet path betwee the food ource ad ther et (Fg. 1D). Fg. 1. Illutrato of pheromoe tral The pheromoe cocetrato became troger o the hortet a t take le tme for at o that porto of the path to travel. The frt at that traveled o the upper porto of Fg. 1D have therefore recruted the ret of the at a very radom way.
Aother behavour of at that are ued the propoed model ther ablty to react to ay codto ew to ther evromet. Wlo (5) coducted a expermet that upport the dea ad propoed a theory that expla the adaptable ature of at. The expermet cot of two categore (major ad mor) of at wth the ame coloy, each performg a tak allocated to t category. The rato of major to mor wa altered. After a hort perod of tme, ome major joed the remag mor to perform tak that were tally allocated to mor. The Wlo expermet well llutrated by Fg. 2. Tak 1 S 1 + S 1 Tak 2 S 2 S 1 At 1 At 2 θ θ 2 At 3 1 R 1 R 2 θ 3 R 3 Fg. 2. Illutrato of the Wlo expermet Accordg to Wlo, every tak releae ome pheromoe, called tmulu S, whch determe the tety wth whch t eed to be performed order to guaratee the urvval of the at the hort term. A at wll the perform a tak baed o t age, morphology ad/or cat detfed a the threhold level θ. A at caddate to perform a gve tak f the tmulu tety S greater tha t threhold θ. I the Wlo expermet the fact of reducg mor performg tak 1 created a demad for that tak tralated to the creae t tmulu tety (S 1 + S 1 ). Provded wth a hgher tmulu, tak 1 ca ow attract major that where ot prevouly egaged performg tak 2. A mathematcal model wa developed by Wlo to upport h expermet. Gve a tak wth a tmulu tety S ad gve at wth a threhold θ, the lkelhood of the at performg the tak gve by a fucto called the repoe fucto R (, θ ). The repoe fucto llutrate the fact eve though the tmulu tety of tak greater tha the threhold of at, that at wll ot ecearly perform the tak but a caddate to perform the tak. The at wll perform the tak f ad oly f t repoe fucto the greatet amog the other at. The dyamc repoe fucto gve below R θ j j = + θ = threhold of = etvty factor j jth at wth repect to th tak at tme t = tmulu tety dplayed by th tak at tme t 1. The repoe repreet fact the probablty that a at that caddate for performg a tak wll perform the tak. It geerate value betwee 0 ad 100%. The etvty of the repoe fucto decrbed Fg. 3 ad Fg. 4.
θ R θ 0 + R(t) 1 0 Fg. 3. Setvty wth repect to threhold Fg. 3 how that the repoe fucto decreae from 0 to 1 a the value of the threhold creae. Th ugget that at wth low threhold value are more lkely to perform a gve tak at a gve tme Fg. 4 however ugget that at expoed to tak wth larger tmulu tety are more lkely to perform the tak at a gve tme becaue the repoe a creag fucto of creag tmulu. 0 + R R (t) 1 0 Fg. 4. Setvty wth repect to Stmulu I the cae of at however, the oto of pecalzato added to the model to jutfy why the tmulu tety of tak 2, the hghet, dd ot attract mor. I at coloe ome member ca perform tak allocated to other. It called relece or elatcty of at. For example major that uually perform grdg tak ca carry food ad mud tally allocated to mor. The elatcty factor ca be accouted the model a follow: R j = e j j j +θ j 2. e j (t) the elatcty factor of the j th wth repect to the th tak. I the Wlo expermet, the elatcty factor ca be choe to 1 whe a tak aocated to a at category bd o a at of that category ad 0 otherwe.
It th cocept that appled to the truck-hovel dpatch procedure to develop a ytem of truck ad hovel that capable of recogzg future upet durg operato ad react to uppre them. Aalogy of ore body-truck-hovel-mateace wth At coloy The model propoed th paper decrbed Fg. 5. Ore block bd o hovel baed o ther prorty o the hort term. Shovel bd o truck baed o the hort-term producto requremet (target) ad fally mateace ad emergecy repar bd o both hovel ad truck baed o cheduled ad/or atcpated mateace program. I th paper however, focu wll be o the teracto betwee a fleet of hovel ad truck. By aalogy wth a at coloy, hovel are compared to tak ad truck to at. The ame approach ca be exteded to other compoet of the module. Block 1 Block2 Target Block Mateace/ Emergecy repar Fg. 5. Model decrpto The ma challege ug the behavour of at to model the teracto betwee hovel ad truck are to defe what a tmulu for a hovel, what a threhold cot of for a truck ad fally how a truck react to the bd of a hovel. Thee fucto are defed wth oly three purpoe that are: Satfacto of operato requremet Be a "real tme a poble" Guaratee optmalty Shovel-truck teracto The teracto betwee hovel ad truck decrbed Fg. 6. Shovel are tally et to dfferet locato (ore block) of the ore body baed o the hort term me pla ad truck warm betwee hovel, tockple, cruher ad wate dump. A hovel demad or bd for truck wll deped o the geometry of the ore body, the ature of the block the hovel allocated to, the prorty gve to the block the hort term pla, the loadg tme of the hovel ad the legth of the queue at the hovel. The repoe of a truck to a hovel demad wll deped o the locato of the truck to that hovel, the truck capacty f dfferet type of truck are ued, the peed of the truck the dumpg tme of the truck ad the tatu of the truck (loaded veru uloaded).
Block1 V 1 (t) = volume of block 1 at tme t V e 1(t) = expected volume of block at tme t 7 Statu of truck at tme t: loaded or uloaded Dtace to hovel at tme t Truck capacty N 1 (t) = queue legth of hovel at tme t P 1 (t) = prorty gve to block 1 the hort tme pla at tme t Block t 1 = loadg tme Fg. 6. Shovel-truck teracto I th model, each dvdual hovel bd o each truck at ay tme ad a deco to deco to dpatch a truck to a gve hovel wll deped o how jutfed, term of target ad requremet atfacto, th hovel eed a truck. A hovel wth a hgher tmulu (demad) doe ot ecearly bd uccefully o a truck, oly the value of the repoe fucto of the truck wth repect to the hovel determe whether or ot a bd ucceful. Fg. 7 how a hovel bddg o dfferet truck. Aumg the truck have the hghet tmulu tety t wll uccefully bd o the truck wth the hghet repoe value at the tme the bddg occur. S 1 7 Truck # 1 θ 11 R 11 ( t 7 ) Truck # 2 Shovel # 1 12 R 12 ( t θ ) 7 Truck # θ 1 R 1 Fg. 7. Repreetato of the bdg proce of a hovel
The bdg proce decrbed Fg. 7 duplcated by each hovel ad for a gve hovel that ha to acqure a truck, the ucceful caddate atfe the followg codto: l uch that R t d l ( t d = dpatch tme ) = max( R j j ( t d )) 3. Stmulu tety of a hovel The tmulu tety of a gve hovel hould be dyamc ad reflect the behavour of the target (optmzato). The followg parameter decrbed below are ued the defto of the dyamc tmulu tety. The update fucto eure that the ytem dpatche a truck to hovel baed o a real eed to meet the target whle atfyg the cotrat. It value potve f o truck dpatch ad egatve whe a truck uccefully dpatched. Aumg the followg parameter: V e = expected cumulatve = umber of truck queued at hovel at tme t C = capacty of volume of materal removed by hovel # at tme t V = actual cumulatve volume of materal removed by hovel # at tme t truck queued at hovel (aumg ame truck) p = prorty gve to materal med by hovel The tmulu tety of hovel # ca be defed a: e [ V V ] S p = where f (, C) a fucto of the queue legth ad the capacty f (, C) aumed to be o zero. 4. Example: f (, C) = ( C + ξ where 0 < ξ << 1 The tmulu tety defed above eure that the toage requremet met gve the prorty of each block wth the hort-term pla. However the dyamc of the tmulu requre t be updated order to reforce a o gog bddg procedure. A update fucto added a follow: S ( t + t) = S + Ψ( t) where Ψ( t) the updatefucto 5. The goal of the update fucto to mata dpatch tablty durg operato. For example f after a certa perod, aother truck ha already bee dpatched to the hovel, the update fucto trgger t tmulu tety to decreae, freeg the truck for aother hovel. If however ot truck ha prevouly dpatched to the hovel, the the update fucto wll creae the value of the tmulu to eure that the truck effectvely clamed by that hovel ule a dramatc chage occur. The update fucto gve a better chace to a hovel that ha uccefully clamed prevouly to hold o to t clam, ule major chage happe. Threhold value of a truck The dyamc threhold fucto of a truck decrbed Fg. 8. The threhold value a fucto of the tatu of a truck (loaded or uloaded), the dtace betwee the truck ad the hovel. Itutvely t ca be ee from the repoe fucto the Wlo model that for a gve tmulu tety, the repoe fucto creae wth decreag threhold value. Fg. 8 how that a loaded truck ha a very hgh tal threhold value (lower repoe) whe t at the hovel level. A the truck drve toward a cruher or a wate dump t threhold value decreae (hgher repoe) to reflect the fact t may be avalable oo.
@hovel Cycle @ cruher or dump tme Fg. 8. Profle of threhold fucto for a loaded truck A uloaded truck however wll have a lower threhold value at the cruher or wate dump level to reflect t avalablty. The threhold value wll the creae the truck returg to the ame hovel or reallocated to aother oe. Ulke the tadard defto of a cycle for a truck, a cycle the model defed a the tme pa betwee the begg of t frt dpatch ad the ed of the ext oe. A truck doe ot ecearly have to retur to the ame hovel. ε d j j = tatu = dtace of of truck j at tme t 1f = -1f truck j to hovel at tme t truck loaded truck uloaded 6. 7. The threhold fucto ca bedefeda : dj ε j( t) [ ] dk θj = e k 8. Although the profle dcate that the threhold cotuou, t uffce for the fucto to be pecewe cotuou to atfy the modelg requremet wth dcotuty pot at each ed of the cycle tme (Whe a truck chage tatu). Cocluo A ew model for truck-hovel dpatch procedure developed th paper. The model adapt the equpmet to the evromet of the operato. Ulke the prevou model, t mple ad take to accout every apect of the operato. However, the ucce of the model rele o the defto of the threhold ad tmulu fucto that cottute the ma challege of th model. The ue of mulato techque ca be helpful determg ew fucto that ca lead to better optmzato of the teracto betwee hovel ad truck.
The model preeted th paper aume that the optmalty of truck ad hovel fleet ze are predefed ad therefore focue more o the effcet ue of the equpmet. However, the model ca further be adjuted to take to accout the target. The target, whch mot operato to optmze the toage of ore delvered to the cruher, ca play a very mportat role reforcg the tmulu geerated by each hovel. For example the demad for more load at the cruher level ca force truck that were aged to ore group operatg a wate zoe to jo the oe that operate a ore zoe. Th later remark wll be elaborated a future paper. Referece 1. Temeg Vctor A., 1997, A computerze Model For Truck Dpatchg I Ope Pt Me, PhD dertato, Mchga Techologcal Uverty. 2. Lzotte Y. ad Boate E., 1986, Truck ad hovel dpatch rule ad Aemet Ug Smulato, Mg Scece ad Techology, 5, Elever, Amterdam, 45-58. 3. Boate E. ad Lzotte Y., 1988, A combed Approach to olve Truck Dpatchg Problem, Computer Applcato the Meral Idutry, Fyta, Coll & Sghal (ed), Balkema, Rotterdam, 403-412. 4. Boate E., 1992, PhD the. Uverdade Federal Da Paraba. Departmeto De Meracao Geologa. 5. Boabeau, Erc et al, 1999, Swarm Itellgece, from atural to artfcal ytem, 109-147.