A MultiHeuristic GA for Schedule Repair in Precast Plant Production


 Alexandra Bradford
 2 years ago
 Views:
Transcription
1 From: ICAPS03 Procdings. Copyright 2003, AAAI ( All rights rsrvd. A MultiHuristic GA for Schdul Rpair in Prcast Plant Production WngTat Chan* and Tan Hng W** *Associat Profssor, Dpartmnt of Civil Enginring, National Univrsity of Singapor, 0 Knt Ridg Crscn Singapor 9260; TEL ; **Rsarch Scholar, Dpartmnt of Civil Enginring, National Univrsity of Singapor, 0 Knt Ridg Crscn Singapor 9260; TEL ; Abstract A multihuristic schdul rpair modl for schdul conflict rsolution is prsntd and its application in rpairing th schduls of a prfabrication plant is dscribd in this papr. Th modl combins huristic stratgis with Gntic Algorithms to rpair schduls with rsourc constraints. Th GA dtrmins th bst squnc of rsolving schdul disturbancs using huristic ruls slctd from a library of huristics commonly usd in industry. W compar quantitativly th advantags of using this modl for schdul rpair against xisting singlhuristic schdul rpair tchniqus with a multicritria valuation function. Rsults on th macroscopic and microscopic lvls ar prsntd to undrstand th strngths and waknsss of th modl. Ky words: application of planning and schduling; dynamic schduling. Introduction Our rsarch is basd on a rallif application of production planning and (r)schduling in prfabrication plants. In Singapor, th incrasd us of prfabricatd building componnts and industrializd building mthods has bn idntifid as th mans of improving both th ovrall productivity at th construction sit and th quality of th construction facility. Th dmand for diffrnt typs of prfabricatd building componnts has bn on th incras, spcially in public housing and transport infrastructur projcts. As a rsul th prfabrication plants and th gnral contractors using ths prfabricatd componnts in thir projcts form a short but conomically significant construction supply chain. Th typs of prfabricatd componnts usd in a construction projct and th rat of th projct s progrss significantly influnc th production schdul of th prfabrication plant supplying thos componnts. Mor spcifically, th plant nds to schdul th production of spcific componnts rquird by th gnral contractor and Copyright 2003, Amrican Association for Artificial Intllignc ( All rights rsrvd. dlivr thm to th construction sit by th du dats dtrmind largly by th pac of th construction sit schdul. Du to this intimat rlationship, a chang in componnt spcifications, th quantitis rquird or th du dats by th contractors invitably lads to a rviw of th prfabrication plant s production schdul. Conflicts in production schduls aris whn th rviw shows that production rsourcs ar ovrcommittd to mt nw dlivry du dats. At last on of th production oprations has to b rschduld and this is calld a (schdul) disturbanc. Rschduling is furthr complicatd as prfabrication plants usually supply diffrnt htrognous componnts to a numbr of construction projcts simultanously at any on tim. In updating th production schdul, plant oprators tnd to utiliz thir own prfrrd huristic, usually th on that had provn asy to apply and rasonably fficint from past xprinc. Morovr, th sam huristic is likly to b applid to rsolv all schdul disturbancs. Howvr, huristics ar known to b problm spcific and cannot guarant good solutions for all cass. W propos to lt an volutionary sarch dcid th bst huristic to apply to a particular disturbanc, as wll as th ordr of rsolving disturbancs by combining th us of huristics and gntic algorithms (GA) in a mthod w call th Multihuristics Schdul Rpair Modl. A custom chromosom rprsntation is proposd to ncod th dcisions involving th ordr of rsolving disturbancs and th huristic bst suitd to rsolv disturbancs. Th GA volvs th chromosoms to dtrmin both th optimal rpair squnc as wll as th bst combination of huristics from a pool of slctd huristic stratgis. W invstigat th fficincy of th proposd schdul rpair modl in gnrating highquality rpaird schduls, and compar th schduls gnratd with th us of this modl against thos gnratd by th singlhuristic approachs currntly usd in th industry. This comparison is basd on a multicritria valuation function drivd from factors prtinnt to industry practics. 236 ICAPS 2003
2 2 Litratur Rviw Th widr us of prfabricatd building componnts has ld to rsarch on planning and schduling mthods in th prcast industry. Warszawski (982, 990 and 999) providd a gnral framwork of th main faturs to a proposd information for planning, cost and quality control in prfabricatd plant oprations, basd on a mathmatical prcast schduling modl dfind in trms of dcision variabls. Furthrmor, Warszawski (984) proposd a modl for short and longrangd production planning of componnts in maktoordr manufacturing systms. Dawood and Nal (993) dvlopd a computrbasd capacity basd modl using th backward schduling tchniqu to hlp managrs crat long trm capacity plan, mak bttr planning dcisions and xplor options. In th gnral application of GA for schduling optimization, Chan t al. (996) proposd a gnric GA modl suitabl for schduling and rsourc allocation problms. Th random kys concpt (Ban 994) was usd in th modl to nsur that thr was no illgal schdul. On th application for GA to th optimization of production schduling of prfabricatd componnts, Chan and Hu (998, 999 and 2002) dvlopd a flow shop squncing modl for spcializd prcast production schduling, and a hybrid gntic algorithm constraint programming (GA CP) approach to solv comprhnsiv prcast schduling. Lu and Hwang (200) proposd th usag of GA to obtain optimal rsourcconstraind production schduls for rptitiv prfabricatd componnts. On dvlopmnt that is prtinnt to industrial practic is that of ractiv schduling from artificial intllignc rsarch. Much rsarch on schdul coordination and rpair in th manufacturing industry has bn don using this schduling concpt (Zwnbn t al. 990; Smith 994 and Sadh 994). Howvr, thr has not bn much application of such concpts in th construction industry. Similaritis btwn th production procsss in th prcast factory and th assmbly lin in th manufacturing procss opns th possibility of th transfr of rsarch findings and practical xprinc of schdul rpair btwn ths two aras. Extrnal factors causing schduling disturbancs Architct Gnral contractor Nw businss opportunity Chang in spcification Chang in quantity Chang in du dats Rjctd lmnts for quality Nw lmnts rquird Mold modification Rsourc shortag Storag/production spac shortag Mod of transport Inhous factors causing schduling disturbancs Machin maintnanc and claning Mandatory chang Potntial changs in production schdul Accommodativ chang X Y Dnots factor X has a dirct influnc on factor Y Figur : Extrnal and Inhous factors causing schdul disturbancs ICAPS
3 3 Schdul Disturbancs and Huristic Stratgis Important background information on how schdul disturbancs occur and th varity of huristic stratgis usd was obtaind through intrviws with industry practitionrs during th cours of this study. 3. Schdul disturbancs Thr ar svral common causs of schdul disturbancs, ranging from quantity and dsign spcification changs to poor quality and machin brakdowns. Ths causs hav bn catgorizd as ithr inhous factors or xtrnal factors, dpnding on whthr th caus is within th control of th factory or not. Schdul changs may or may not b rquird in rspons to ths disturbancs. For xampl, th plant oprator may choos to forgo nw ordrs and not disrupt xisting schduls but is complld to chang his schduls if this involvs contractual obligations. Figur illustrats th spcific xtrnal and inhous factors causing schdul disturbancs, as wll as thir influncs on on anothr. 3.2 Huristic stratgis for rpairing schduls Production schduling is carrid out for a fixd planning horizon (usually 30 days ahad) according to an agrd schdul for dlivring componnts. Among th huristic ruls usd by plant oprators to rschdul disturbancs and rpair thir production schduls includ: () Right shift (RS): rsolvs conflicts by pushing th production forward in tim until th disturbanc is rsolvd (Fig. 2.); (2) Lft shift (LS): a similar stratgy that shifts an opration backwards in tim. It is particularly usful whn a hard constraint that prviously prohibitd th commncmnt of th opration is softnd or rmovd (Fig. 2.2); (3) Opportunistic insrtion (OI): maks us of idl days in th schdul to accommodat a disturbanc by braking it into smallr parts and fitting ths smallr parts into th schdul in an opportunistic first fit mannr. Th fficincy of this huristic rul largly dpnds on th initial utilization lvl of th production facilitis (Fig. 2.3); (4) Dtrministic Insrtion (DI): similar to opportunistic insrtion but th disturbancs hav priority ovr alrady schduld production and displac thm from th schdul. Th lattr ar rschduld using OI (Fig. 2.4); (5) Assoonaspossibl (ASAP) / Backward Schduling (BS): th ASAP mthod schduls th disturbanc basd on th arlist start tim (EST); th BS mthod Bfor rsolution Start of disruption Rsolution by RS Bfor rsolution Rsolution by LS Disturbanc Rvisd arlist start dat Bfor rsolution Disturbanc Aftr rsolution Production lin End of disruption Figur 2.: Right shifting Figur 2.2: Lft shifting Initial arlist start Figur 2.3: Opportunistic insrtion Point of insrtion Figur 2.4: Dtrministic insrtion Idl stat for production lin Occupid stat for production lin Disturbanc Figur 2: Illustrations of som huristic ruls schduls th disturbancs basd on th latst start tim (LST); (6) Multipl mold approach: rsolvs th disturbanc by assigning similar componnts within th sam group of componnts to any on of svral molds capabl of producing th componnts using a OI or DI stratgy; (7) Subcontracting: this stratgy outsourcs production to othr oprators and is usd whn th plant is alrady producing at its pak capacity or it is conomically mor bnficial to do so. Th huristic ruls mntiond abov wr solicitd from xprincd plant oprators through prsonal intrviw. Th plant oprators dpndd on prvious xprinc whn choosing ruls to rsolv disturbancs and did not 238 ICAPS 2003
4 sm to hav a formal quantitativ way of dciding on how bst to rpair schduls. Tim prssur oftn prvntd thm from trying altrnativ ways of rsolving disturbancs or considring th ffct of rsolving svral disturbancs togthr. Th multihuristics schdul rpair modl could hlp addrss ths dficincis and provid altrnativ high quality rpaird schduls. 4 Multihuristic Schdul Rpair Modl Our proposd modl supports th dtrmination of priority for conflict rsolution using huristic stratgis that ar bst suitd to incorporat th conflictcausing disturbancs into an xisting schdul. Th rpair actions ar also likly to caus furthr disturbancs which thn hav to b rsolvd. Thrfor, it is ncssary to considr not only how to rsolv th conflict but also th ordr in which th conflicts ar to b rsolvd as both hav a baring on th dsirability of th final rpaird schdul. Th proposd modl supports this important considration by sarching for th bst combination of conflictrsolving squnc (ordr) and huristics usd (how) from many possibl combinations using GA. Gntic algorithms ar stochastic sarch mthods basd on th mchanism of slction and volution, and hav bn succssfully applid in schduling problms including that of prcast lmnt production. Dtails of a GA adaptation for our proposd modl ar dscribd as follows. 4. Constraints Production schduling rquirs allocating rsourcs ovr tim to a st of jobs whil satisfying a varity of constraints and objctivs. Hard constraints must always b satisfid for a (rpaird) schdul to b valid. Soft constraints on th othr hand, could b rlaxd whn ncssary. Basd on th rsults of th industry study, w hav catgorizd th hard constraints in our proposd modl as functional, capacity and availability constraints, whil th soft constraints ar dlivry and invntory constraints. Th rprsntation of ths constraints in mathmatical trms is ncssary for thir us in GA. Th following sction discusss th mathmatical formulation of ths constraints in trms of binary dcision variabls dfind in Tabl. Functional constraint: to maintain th production intgrity of th prfabrication plant by limiting th typs of lmnts that a spcific mold can produc. Although it is possibl for a mold to produc svral diffrnt typs of lmnts, w hav rstrictd this capability to lmnts within a mold group within which thr ar only minor variations in mold dtails. This is ncssary as convrting a mold to a diffrnt mold group is rarly don in practic du to substantial convrsion tim and costs incurrd. 5 4 = 4 m= 3 6 = m= 5 x = 0 for all t () m, x = 0 for all t (2) m, Capacity constraints: Following industry norms, ach Paramtrs x m, T M E S o, S S S R D N m L L,r T T n Dscription A binary dcision variabl, whr x m, = mans that mould m is assignd to produc lmnt on day whilst x m, =0 will man th opposit; t = 0,, 2 T, schduling priods in days; m = 0,, 2 M, mould srial numbrs; = 0,, 2 E, typs of lmnts to b producd; Initial stock of lmnt typ at th bginning of th schduling priod (t = 0); Numbr of lmnt typ in stockyard on day t; Maximum allowabl storag lvl of lmnt in stockyard; Minimum buffr storag lvl of lmnt in stockyard; Numbr of lmnt typ rquird to b dlivrd on day t; Numbr of lmnt typ dlivrd on day t; Numbr of changovrs for mould m in th schduling priod; Lad tim of lmnt typ btwn production and dlivry; Minimum lad tim rquird for lmnt typ btwn production and dlivry; Prsnt tim; Total numbr of working days, obtain by subtracting th numbr of Sundays from T. Tabl. Paramtrs for mathmatical rprsntations ICAPS
5 mold is limitd to produc only on lmnt pr working day (Equation 3). Thrfor th daily maximum capacity of th prcast yard is qual to th total numbr of molds (Equation 4). W hav furthr assumd that thr is no production during Sundays and public holidays (Equation 5). E = M x (0,) for all m,t (3) m, = E m= = x m, M for all t (4) x m, = 0 for t Sundays and public holidays (5) Availability constraint: spcifis th tim rquird for ach producd lmnt to b rady for dlivry. A minimum lad tim btwn production and dlivry must b obsrvd for th componnts to attain approximatly 70% of thir 28day strngth, which rfrs to th spcific strngth that concrt gains as it stiffns from an initial plastic stat aftr a stting tim of 28 days. Traditional curing taks up to svn days, although th local practic of controlld acclratd curing in a curing chambr rducs this lad tim to just two days. L L, r whr L, r = 48 hours (6) Dlivry constraint: spcifis th dlivry rquirmnts of th componnts to th construction sits. Du to th larg sizs of th prfabricatd lmnts and th shortag of storag spac on th construction sits, plant oprators ar usually not allowd to dlivr th lmnts any arlir than th stipulatd dat of dlivry, nor dlivr mor than what is rquird (Equation 7). Furthrmor th sum of th initial stock lvl and th total production of any lmnt bfor ach dlivry dat should b at last as many as th numbr of lmnts rquird to b dlivrd (Equation 8). D t Rt, for all, whr t t2 (7), 2 T M t= m= T S0, + x,, R, for all (8) t m t= t Invntory constraint: limits th numbr of prfabricatd componnts to b stord in th invntory. It also spcifis th lvl of buffr invntory. In shor th invntory constraint srvs to dfin th oprating rang for stock lvls of ach prfabricatd componnt. Du to spac constraints, th total numbr of producd componnts that can b kpt in a plant s stockyard is limitd. Howvr, plant oprators ar highly rsourcful in sking nw avnus for storing invntory and hav bn known to stor lmnts tmporarily on transportation trailrs. Thy also kp a minimum numbr of various componnts to srv as buffrs to unxpctd or urgnt dmand. Thrfor th cumulativ numbr of any producd componnts lss dlivrd in any priod should b lss than th maximum allowabl storag limit but mor than th minimum buffr lvl. T M T S S + x D S 0, m, t= m= t= for all (9) 4.2 Objctiv functions Local prcast plants produc prfabricatd componnts mainly on a contractual basis, apart from producing som standard lmnts for anticipatd dmand. Plant oprators hav to mt contractual du dats for dlivris whil kping an accptabl lvl of invntory in th stockyard to buffr any unanticipatd dmand. Counting th numbr of lmnts that was not dlivrd on tim and th numbr of ovr or undrstockd lmnts in th invntory will thn rflct on th fficincy of th (rpaird) schduls. Plant oprators also try to mak full us of thir molds and minimiz th numbr of changovrs rquird. Efficint lmnt to mold assignmnt is thrfor important to fficint schduling, as that will minimiz th cost of changovrs. Hnc, th numbr of changovrs incurrd bcoms our third paramtrs for valuating (rpaird) schdul fficincy. Plant oprators tnd to minimiz th numbr of idl days during th planning horizon, as it is sn as a wast of rsourcs. Howvr, thy hav to balanc btwn th costs and ffcts of xcssiv production. Production of any particular lmnt on a prmannt basis will kp th numbr of mold changs down and improv th mold utilization rat. Howvr it will also incras th ovrstocking of th lmnt thrby affcting th production of othr componnts, which can rsult in lat dlivris for th lattr. It is clar thn that th oprators hav to sk a balanc btwn th diffrnt objctivs of mting du dats, minimizing mold changs, maintaining optimum invntory lvls and kping nonproductiv working days to th minimum. Th mathmatical rprsntations of ths paramtrs ar as follows: Numbr of lmnts in xcss/inadquat invntory lvl: th invntory lvl of any lmnt is bst maintaind at an optimum rang for spatial and buffr considrations. Thrfor th total numbr of lmnts in xcss of or blow dsird invntory lvls should b minimizd T E + + Min Z = {( S S ) + ( S S ) } S t= = ( + whr S S ) = max{0,( S S )} 240 ICAPS 2003
6 ( S S, ) + t = max{0,( S S )} (0) DGn HGn Numbr of mold changs: in ordr to produc diffrnt lmnts of th sam mold group, a mold must undrgo minor modification, thrby incurring both cost and tim. Thrfor, fficint lmnt to mold assignmnt is ndd to minimiz th total numbr of mold changovrs. Min M Z M = N m m= () Numbr of lmnts not dlivrd on du dats: failur to dlivr th stipulatd numbr of lmnts on tim would incur financial pnaltis and bring dtrimnts to th rputation of plant oprators. Thrfor th total numbr of lmnts not dlivrd on tim should also b minimizd. Min Z D = T E t = = ( R D ) (2) Numbr of ffctiv idl days: th maximum numbr of lmnts that can b producd pr day is M, and th total production capacity within a planning horizon cannot b mor than MT n. A mor accurat rflction of th numbr of idl days would thrfor b rprsntd by: T M E Min Z I = MTn xt, m, (3) M t = m= = Du to th diffrnt units of masurmnt of th 4 valuation paramtrs, it would not b maningful to add thm dirctly; hnc, thr is a nd to normaliz thm into a dimnsionlss quantity. On approach is to divid ach paramtr by a constant (.g. th man valu of a distribution) and thn sum up th numbrs into an fficincy indx. Howvr this would rsult in a biasd analysis favoring paramtrs which xhibit high variability thus rsulting in high normalizd valus, as ths tnd to dominat th fficincy indx. W hav usd 4 planning ruls and th intgr programming approach to gnrat 25 psudoschduls at various rsourc utilization lvls. Th hard constraints wr obsrvd in th cration of ths schduls to b usd for our rpair algorithms. Ths schduls wr thn valuatd sparatly using ach of th four paramtrs, rsulting in a rang of prformanc valuations for ach of th four paramtrs. Th raw valuation valus wr mappd onto a rang btwn 0 and 0.25 by mans of linar rgrssion. Doing so mant that w assumd that ach of th 4 paramtrs was qually important. Th summation of th four paramtrs cratd a dimnsionlss objctiv function which minimizd th dominanc of any paramtr. This normalizd objctiv function gav an indication of th rlativ prformanc on ach paramtr D D2 D3 D4 D5 H H2 H4 H3 H3 Figur 3: Chromosom rprsntation DGn HGn D5 D4 D3 D D2 H H2 H4 H3 H H H2 H4 H3 H3 Figur 4: Dcoding of chromosom Th highr th indx valu, th poorr was th prformanc ranking. Th objctiv function is thrfor dfind as: Min Z = Z S Z M Z D Z I (4) 4.3 GA rprsntation As shown in Fig. 3, th chromosom string is mad up of qual numbr of Dgns (disturbanc gn) and Hgn (huristic gns). Each conflict to b rsolvd is rprsntd by a pair of D and Hgns. Th Dgns ncod ral numbrs that srvs as sort kys to dtrmin priority of rsolution, whilst th Hgns ncod th ordinal valu of th huristics usd to rsolv th conflict. Th proprtis of ach disturbanc and th rsolving algorithm for ach huristic ar dfind on thir rspctiv tabu. To dcod th chromosom, th squnc of rsolving conflicts is dtrmind by sorting th disturbancs in incrasing ordr of th Dgn valus. Th corrsponding huristics dfind in th Hgns ar thn usd to incorporat th disturbancs into an xisting schdul, as illustratd in Fig. 4. In this cas, th squnc of conflict rsolution with corrsponding huristics is: D5 (H) D4 (H2) D3 (H4) D (H3) D2 (H3). Thr ar svral paramtrs that can dtrmin th prformanc of GA but thir optimal valus cannot b ascrtaind by applying fixd ruls. In fac optimal GA paramtrs ar known to b notoriously difficult to dtrmin (Myrs and Hancock 200). Ths paramtrs includ th population siz, th numbr of itrations prformd, th crossovr ra th mutation rat and th trmination critrion. ICAPS
7 Disturbanc Elmnt Typ Quantity Du Dat for Dlivry Natur of Disturbanc D E Day 5 To rplac a rjctd lmnt D2 E2 2 Day 7 Dsign chang to E2 lmnt D3 E3 2 Day 9 Dsign chang to E3 lmnt D4 E3 2 Day 5 To rplac a rjctd lmnt D5 E2 2 Day 7 To rplac a rjctd lmnt Tabl 2. Charactristics of disturbancs Original production schdul Rpaird production schdul Day Day L E E E E E E E E E N E E E E E E E E E E Production lins L2 E E N N N N N N N N Schdul Rpair E E N N N N N E3 E3 E3 L3 E3 E3 E3 E3 E3 E3 E3 E3 E3 N E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 L4 N N N N N N N N N N E2 E2 N N N N N N E2 E2 Th Multihuristic Schdul Rpair Modl dtrmins th optimal squnc (D D2 D4 D3 D5) and th bstsuitd huristic to incorporat ach disturbanc dfind in Tabl 2 into th original schdul. Each cll rprsnts an lmnt typ schduld to b producd in a spcific production lin on a particular day. For xampl, production lin L is schduld to produc lmnt typ E on th first day of th original production schdul. "N" dnots no production; thrfor production lin L4 is not schdul for any production in th original schdul. Gry clls in th rpaird production schdul rprsnt th incorporatd disturbancs. Figur 5: Rpaird schdul dtrmind by GA In our proposd modl, a twopoint crossovr is usd to combin th gn valus of two chromosoms to crat a nw pair of chromosoms. Mutation oprats on a singl chromosom and producs a nw gnotyp by making a random chang to th valu of on or mor of th gns in th chromosom string. Th sttings for ths ky paramtrs ar: population siz (00), numbr of itrations (500), probability of crossovr (0.85) and mutation (0.00). Ths valus wr dtrmind by fintuning dfault valus ovr svral runs of th GA on a similar problm. Th PGAPack opratd on a Silicon Graphics workstation in th UNIX nvironmnt was adoptd as th GA softwar usd. It is a paralll gntic algorithm library that is intndd to provid most of th capabilitis ndd for ncoding GA applications in an intgratd, samlss and portabl mannr. 5 Exprimnts Th application of our proposd modl prsntd involvs th schdul rpair of four molds ovr a priod of two wks (0 work days). Th plant producs thr typs of lmnts, namly E, E 2 and E 3, which can b producd by any of th four molds with minimal modification. Fiv disturbancs occur during th planning priod and th charactristics of ths disturbancs ar shown in Tabl 2. Svn huristic ruls wr slctd to b includd in th huristics pool. Six of th huristics wr basd on th multipl mold approach whr mor than on mold could b usd to rsolv a conflict. Th sarch for th point of insrtion into th original schdul can b prformd in a paralll mannr across all mold schduls simultanously or for ach mold schdul in squnc. Th first ICAPS 2003
8 Mthod of Rsolution Multihuristic S/BS/OI P/ASAP/OI S/ASAP/OI P/BS/OI Low utilization lvl ( ) Total numbr of idl days (days) Total numbr of lat dlivris (lmnts) Total numbr of ovr/undr stocking (lmntdays) Total numbr of mould changs (tims) Bst Indx Multiplhuristic yild 0% 9.45% 3.4% 7.87% 0.63% Middl utilization lvl ( ) Total numbr of idl days Total numbr of lat dlivris Total numbr of ovr/undr stocking Total numbr of mould changs Bst Indx Multiplhuristic yild 0% 2.8% 2.45% 4.42% 4.42% High utilization lvl (>0.8) Total numbr of idl days Total numbr of lat dlivris Total numbr of ovr/undr stocking Total numbr of mould changs Bst Indx Multiplhuristic yild 0% 3.55% 2.59% 6.80% 5.60% Tabl 3. Bst prformanc of multihuristic approach compard to th singl huristics huristics ar dnotd as S/ASAP/OI, S/BS/OI, S/ASAP/DI, P/ASAP/OI, P/BS/OI, P/ASAP/DI. Th last huristic considrd is subcontracting. In th naming schm mployd, th first part of th nam squnc dnots th sarch squnc (paralll or squntial), th scond part dnots th dirction of sarch (from th bginning or from th nd), and th last part dnots th mannr of insrtion (opportunistic or dtrministic fit). To tst our proposd modl, 5 schduls wr artificially constructd using a random procss to giv mold utilization rats varying from 0.6 to 0.8; this rang was chosn to rflct th utilization rats commonly sn in local practic. Th initial invntoris for E, E2 and E3 ar assumd to b 6, 2 and 6 lmnts rspctivly. For ach of ths schduls, a tst was conductd using th baslin / original schdul as a basis within which to schdul th disturbancs shown in Tabl 2. Th GA procdur was thn usd to construct modifid schduls whrin th disturbancs had bn insrtd. Th rsult of on such tst is shown in Fig. 5 as spac dos not allow showing th rsults of all th tsts. Anothr 4 sts of xprimnts wr conductd, again using th sam baslin schduls but this tim allowing GA to apply only on of four huristics (S/ASAP/OI, S/BS/OI, P/ASAP/OI and P/BS/OI). Ths 4 huristics wr chosn bcaus thy ar industry s favorits. Th prformanc of our proposd multihuristic schdul rpair modl is compard to th singlhuristic approach at both th macro and microscopic lvl. At th macroscopic prspctiv, w compar th valuation indx valus obtaind by both approachs. Th improvmnt obtaind by th multihuristic approach is also discussd. At th microscopic lvl, w analyz th prformancs in trms of ach of th physical paramtrs that constitut th valuation indx. 5. Macroscopic analysis Having vrifid that th indx valus satisfy th normality and corrlation tsts, 4 sparat sts of pairdsampl t tsts wr prformd to valuat th significanc of th diffrnc btwn th man indx valus of our multihuristic modl with ach of th 4 singlhuristic approachs. Th tsts rvald rsults that wr vry ncouraging. Our multihuristics modl has, in all th 4 sparat ttsts, producd lowr man indx valus than ach of th 4 singlhuristic approachs with pvalus vry clos to ICAPS
9 Man valu Indx Lat dlivry Mould chang Nonoptimal invntory Singl huristic tstd against Altrnativ hypothsis Pvalu S/BS/OI < P/ASAP/OI < 0 0 S/ASAP/OI < 0 0 P/BS/OI < 0 0 S/BS/OI < P/ASAP/OI < S/ASAP/OI < P/BS/OI < S/BS/OI < P/ASAP/OI < 0 0 S/ASAP/OI < 0 0 P/BS/OI < 0 0 S/BS/OI > P/ASAP/OI not = S/ASAP/OI not = P/BS/OI > approach prformd bst against th 4 singl huristic at 3 diffrnt lvls of utilization. Th prformanc of th multihuristic approach vrsus that of th singl huristic appars marginal whn masurd on our valuation indx formulation. Howvr, th gains bcom mor tangibl whn translatd to ral physical masurs lik th numbr of lat dlivris or mould changs, which ar significant to th plant oprators. Th oprators would typically prfr not to incur any lat dlivris du to ithr contractual obligation or far of marring th plant s rputation. Thrfor, a yild of 5% on an indx valu of 0.3 would translat to an quivalnt (0.3*0.05/0.0042) 3.57 lmnts rduction in lat dlivris or a (0.3*0.05/0.0008) 8.75 lmntsdays rduction in xcss/inadquat invntory during th 0day rpair priod. 5.2 Microscopic analysis Th sam sts of statistic tsts wr prformd on 3 of th 4 paramtrs that constitutd th valuation indx. Th rlativ prformanc of th multihuristic approach is thn compard with ach of th 4 singlhuristic approachs. Th rsults of ths tsts ar summarizd in Tabl 4. Plant oprators prfr to kp both th numbr of lat dlivris and th numbr of mold changs during production to th minimum. Whil ovrstocking is also undsirabl, it can b rsolvd with rlativ as in comparison. From th tst rsults, it is obsrvd that th multihuristic modl xclld in producing rpaird schduls with a minimal numbr of mold changs. This fficint lmnt to mold assignmnt is significant as changs in th molds disrupt th workflow of th production lins and incurrd additional changovr costs. Tabl 4. Pvalus for paird sampl ttsts tsting th diffrnc of th multihuristics approach against th various sing huristics zro. Such pvalus allow us to conclud strongly that thr is significant statistical vidnc supporting our claim that th multihuristics modl prformd bttr than any of th singlhuristic approachs in schdul rpair. Rcalling that th indx valu is mad up of 4 diffrnt paramtrs, this suggsts that our modl gnratd solutions that dominatd thos obtaind with th singlhuristic approachs. In trms of th yild, our proposd modl outprformd any singl huristic by up to 3.09%. Th cas whr th multihuristic approach could only prform as wll as a singl huristic occurrd whn th molds xprincd high utilization rats. Th lack of idl days for schdul rpair in ths schduls limitd what any rpair stratgy could do. Tabl 3 illustrats th cass whr th multihuristic Having kpt th numbr of mold changs to a minimum, th multihuristic approach continud to prform rmarkably wll in minimizing th numbr of lat dlivris incurrd in th rpaird schduls it gnratd. Statistics rvald that th multihuristic modl producd rpaird schduls that hav a lowr man numbr of lat dlivris than 2 of th singlhuristic approach at 5% lvl of significanc and of thm at 0% lvl of significanc. Howvr, thr was not nough to show that th numbr of lat dlivris is lowr whn compard to th P/ASAP/OI huristic. Th multihuristic approach did not far as wll in minimizing th numbr of lmnts in xcss/inadquat invntory. In fac th multihuristic approach producd rpaird schduls that hav significantly highr man valus of xcss/inadquat invntory compard to two of th singl huristics (S/BS/OI and P/ASAP/OI). Howvr, this man valu is not significantly diffrnt from th man valus of th two othr singl huristics. 244 ICAPS 2003
10 This analysis indicatd that th multihuristic schdul rpair modl was abl to do bttr than any singlhuristic approach; th rpaird schduls achivd mor fficint mold utilization and fwr lat dlivris. Mor significantly, ths improvmnts wr attaind at only a sligh or no incras in th valu of xcssiv/inadquat invntory. 6 Conclusions W hav applid th multihuristic schdul rpair modl on a ralistic planning and (r)schduling problm for a prfabrication plant. Th initial xprimntal rsults indicat that this multihuristic approach is ffctiv in rsolving schdul disturbancs, dmonstrably mor so than th singlhuristic approachs currntly usd in industry. Th valuation indx usd as th objctiv function incorporats most of th paramtrs of concrn to industry practitionrs including fficint lmnt to mold assignmnt and minimal lat dlivris with littl or no compromis to th invntory lvl. It can b usd to gnrat nondominatd schduls in conjunction with th sarch procdur of th GA. Howvr, th scop of th modl is quit limitd and is rstrictd to schdul rpair. For xampl, it dos not addrss th nd for bttr schdul coordination btwn lmnts of th supply chain, particularly btwn th construction sit and th production plant. Furthr work is in progrss to look into this aspct of prcast production schduling. Idally, this will thn allow both th plant oprator and th construction managr to ngotiat th prfrrd outcom in a cooprativ rathr than advrsarial mannr. 7 Rfrncs Ban, J.C Gntic Algorithms and Random Kys for Squncing and Optimization. ORSA Journal on Computing, 6(2), pp Chan, W.T.; Chua, D.K.H.; and Kannan, G Construction Rsourc Schduling with Gntic Algorithms. Journal of Construction Enginring and Managmn 22(2), pp Chan, W.T., and Hu, H Production Schduling for Prcast Plants Using a Flow Shop Squncing Modl. Journal of Computing in Civil Enginring, 6(3), pp Dawood, N., and Nal, R.H A Capacity Planning Modl for Prcast Concrt Building Products. Building and Environmn 28(), pp Lu, S.S., and Hwang, S.T A GABasd Modl for Maximizing Prcast Plant Production undr Rsourc Constraints. Enginring Optimization, Vol. 33, pp Myrs, R., and Hancock, E.R Empirical Modling of Gntic Algorithms. Evolutionary Computation, 9(4), pp Sadh, N MicroOpportunistic Schduling: Th MicroBoss Factory Schdulr. Intllignt Schduling, pp San Francisco: Morgan Kaufmann Publishrs Inc. Smith, S.F OPIS: A Mthodology and Architctur for Ractiv Schduling. Intllignt Schduling, pp San Francisco: Morgan Kaufmann Publishrs Inc. Warszawski, A Managrial Planning and Control in Prcast Industry. Journal of th Construction Division, 8(CO2), pp Warszawski, A Production Planning in Prfabrication Plant. Building and Environmn 9(2), pp Warszawski, A Industrialization and Robotics in Building. Nw York: Harpr & Row. Warszawski, A Industrializd and Automatd Building Systms. London: E & FN Spon. Zwbn, M.; Daun, B.; Davis, E.; and Dal, M Schduling and Rschduling with Itrativ Rpair. Intllignt Schduling, pp San Francisco: Morgan Kaufmann Publishrs Inc. Chan, W.T., and Hu, H Procss Schduling Using Gnric Algorithms for Construction Industry. Proc. Third Intrnational Confrnc on Managmn CHEP and Springrvrlag, Shanghai, China. Chan, W.T., and Hu, H Procss Schduling of Prcast Production Using Gntic Algorithms. In Proc. Fifth Intrnational Confrnc on Application of Artificial Intllignc to Civil and Structural Enginring, Vol. C, pp Comp Prss, Oxford, U.K. ICAPS
EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS
25 Vol. 3 () JanuaryMarch, pp.375/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationAdverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wllsuitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of Cnts. Hnc, it can b rad by popl
More informationQUANTITATIVE METHODS CLASSES WEEK SEVEN
QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.
More informationby John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia
Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs
More informationWORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769
081685 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt
More informationGenetic Drift and Gene Flow Illustration
Gntic Drift and Gn Flow Illustration This is a mor dtaild dscription of Activity Ida 4, Chaptr 3, If Not Rac, How do W Explain Biological Diffrncs? in: How Ral is Rac? A Sourcbook on Rac, Cultur, and Biology.
More informationGold versus stock investment: An econometric analysis
Intrnational Journal of Dvlopmnt and Sustainability Onlin ISSN: 2688662 www.isdsnt.com/ijds Volum Numbr, Jun 202, Pag 7 ISDS Articl ID: IJDS20300 Gold vrsus stock invstmnt: An conomtric analysis Martin
More informationC H A P T E R 1 Writing Reports with SAS
C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd
More informationImproving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost
Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 5054 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin
More informationChiSquare. Hypothesis: There is an equal chance of flipping heads or tails on a coin. Coin A. Expected (e) (o e) (o e) 2 (o e) 2 e
Why? ChiSquar How do you know if your data is th rsult of random chanc or nvironmntal factors? Biologists and othr scintists us rlationships thy hav discovrd in th lab to prdict vnts that might happn
More informationA Project Management framework for Software Implementation Planning and Management
PPM02 A Projct Managmnt framwork for Softwar Implmntation Planning and Managmnt Kith Lancastr Lancastr Stratgis Kith.Lancastr@LancastrStratgis.com Th goal of introducing nw tchnologis into your company
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationA Derivation of Bill James Pythagorean WonLoss Formula
A Drivation of Bill Jams Pythagoran WonLoss Formula Ths nots wr compild by John Paul Cook from a papr by Dr. Stphn J. Millr, an Assistant Profssor of Mathmatics at Williams Collg, for a talk givn to th
More informationNonHomogeneous Systems, Euler s Method, and Exponential Matrix
NonHomognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous firstordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach
More informationAnalysis Of Injection Moulding Process Parameters
Analysis Of Injction Moulding Procss Paramtrs Mr. M.G. Rathi Assistant Profssor, partmnt of Mchanical Enginring, Govrnmnt Collg of Enginring Aurangabad, (MS), India. Mr. Manoj amodar Salunk Studnt, partmnt
More informationEntityRelationship Model
EntityRlationship Modl Kuanghua Chn Dpartmnt of Library and Information Scinc National Taiwan Univrsity A Company Databas Kps track of a company s mploys, dpartmnts and projcts Aftr th rquirmnts collction
More informationJune 2012. Enprise Rent. Enprise 1.1.6. Author: Document Version: Product: Product Version: SAP Version: 8.81.100 8.8
Jun 22 Enpris Rnt Author: Documnt Vrsion: Product: Product Vrsion: SAP Vrsion: Enpris Enpris Rnt 88 88 Enpris Rnt 22 Enpris Solutions All rights rsrvd No parts of this work may b rproducd in any form or
More informationAbstract. Introduction. Statistical Approach for Analyzing Cell Phone Handoff Behavior. Volume 3, Issue 1, 2009
Volum 3, Issu 1, 29 Statistical Approach for Analyzing Cll Phon Handoff Bhavior Shalini Saxna, Florida Atlantic Univrsity, Boca Raton, FL, shalinisaxna1@gmail.com Sad A. Rajput, Farquhar Collg of Arts
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. GangLn Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationSci.Int.(Lahore),26(1),131138,2014 ISSN 10135316; CODEN: SINTE 8 131
Sci.Int.(Lahor),26(1),131138,214 ISSN 1135316; CODEN: SINTE 8 131 REQUIREMENT CHANGE MANAGEMENT IN AGILE OFFSHORE DEVELOPMENT (RCMAOD) 1 Suhail Kazi, 2 Muhammad Salman Bashir, 3 Muhammad Munwar Iqbal,
More informationLecture 3: Diffusion: Fick s first law
Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th
More informationDeer: Predation or Starvation
: Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,
More informationParallel and Distributed Programming. Performance Metrics
Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:
More informationIncomplete 2Port Vector Network Analyzer Calibration Methods
Incomplt Port Vctor Ntwork nalyzr Calibration Mthods. Hnz, N. Tmpon, G. Monastrios, H. ilva 4 RF Mtrology Laboratory Instituto Nacional d Tcnología Industrial (INTI) Bunos irs, rgntina ahnz@inti.gov.ar
More informationKeywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.
Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud
More information7 Timetable test 1 The Combing Chart
7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing
More informationExponential Growth and Decay; Modeling Data
Exponntial Growth and Dcay; Modling Data In this sction, w will study som of th applications of xponntial and logarithmic functions. Logarithms wr invntd by John Napir. Originally, thy wr usd to liminat
More informationREPORT' Meeting Date: April 19,201 2 Audit Committee
REPORT' Mting Dat: April 19,201 2 Audit Committ For Information DATE: March 21,2012 REPORT TITLE: FROM: Paul Wallis, CMA, CIA, CISA, Dirctor, Intrnal Audit OBJECTIVE To inform Audit Committ of th rsults
More information811ISD Economic Considerations of Heat Transfer on Sheet Metal Duct
Air Handling Systms Enginring & chnical Bulltin 811ISD Economic Considrations of Hat ransfr on Sht Mtal Duct Othr bulltins hav dmonstratd th nd to add insulation to cooling/hating ducts in ordr to achiv
More information5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power
Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 1213)
con 37: Answr Ky for Problm St (Chaptr 23) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More information(Analytic Formula for the European Normal Black Scholes Formula)
(Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually
More informationPrinciples of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationStatistical Machine Translation
Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) 92.222  Linar Algbra II  Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial
More informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More informationGlobal Sourcing: lessons from lean companies to improve supply chain performances
3 rd Intrnational Confrnc on Industrial Enginring and Industrial Managmnt XIII Congrso d Ingniría d Organización BarclonaTrrassa, Sptmbr 2nd4th 2009 Global Sourcing: lssons from lan companis to improv
More informationForeign Exchange Markets and Exchange Rates
Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls
More informationCategory 7: Employee Commuting
7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil
More informationLecture 20: Emitter Follower and Differential Amplifiers
Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.
More informationFree ACA SOLUTION (IRS 1094&1095 Reporting)
Fr ACA SOLUTION (IRS 1094&1095 Rporting) Th Insuranc Exchang (301) 2791062 ACA Srvics Transmit IRS Form 1094 C for mployrs Print & mail IRS Form 1095C to mploys HR Assist 360 will gnrat th 1095 s for
More informationAnalyzing Product Attributes using Logical Framework of Quality Function Deployment (Phase I): Concept and Application
Intrnational Journal Enginring Rsarch & Tchnology (IJERT) Vol. 2 Issu 10, Octobr  2013 Analyzing Product Attributs using Logical Framwork Quality Function Dploymnt (Phas I): Concpt and Application Dvndra
More informationFACULTY SALARIES FALL 2004. NKU CUPA Data Compared To Published National Data
FACULTY SALARIES FALL 2004 NKU CUPA Data Compard To Publishd National Data May 2005 Fall 2004 NKU Faculty Salaris Compard To Fall 2004 Publishd CUPA Data In th fall 2004 Northrn Kntucky Univrsity was among
More informationRural and Remote Broadband Access: Issues and Solutions in Australia
Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity
More informationConstraintBased Analysis of Gene Deletion in a Metabolic Network
ConstraintBasd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFGRsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany
More informationLABORATORY 1 IDENTIFICATION OF CIRCUIT IN A BLACKBOX
LABOATOY IDENTIFICATION OF CICUIT IN A BLACKBOX OBJECTIES. To idntify th configuration of an lctrical circuit nclosd in a twotrminal black box.. To dtrmin th valus of ach componnt in th black box circuit.
More informationPerformance Evaluation
Prformanc Evaluation ( ) Contnts lists availabl at ScincDirct Prformanc Evaluation journal hompag: www.lsvir.com/locat/pva Modling Baylik rputation systms: Analysis, charactrization and insuranc mchanism
More informationRealTime Evaluation of Email Campaign Performance
Singapor Managmnt Univrsity Institutional Knowldg at Singapor Managmnt Univrsity Rsarch Collction L Kong Chian School Of Businss L Kong Chian School of Businss 102008 RalTim Evaluation of Email Campaign
More informationSUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* RostovonDon. Russia
SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* RostovonDon. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs
More informationSCHOOLS' PPP : PROJECT MANAGEMENT
Rport Schools' PPP Sub Committ 22 April 2004 2 SCHOOLS' PPP : PROJECT MANAGEMENT 1 Rason for Rport To provid Mmbrs with information on th structur of th Schools' PPP Projct Tam 2 Background 21 Dumfris
More informationUse a highlevel conceptual data model (ER Model). Identify objects of interest (entities) and relationships between these objects
Chaptr 3: Entity Rlationship Modl Databas Dsign Procss Us a highlvl concptual data modl (ER Modl). Idntify objcts of intrst (ntitis) and rlationships btwn ths objcts Idntify constraints (conditions) End
More informationSPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM
RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs
More informationAn Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore
Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 22502459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt
More informationPlanning and Managing Copper Cable Maintenance through Cost Benefit Modeling
Planning and Managing Coppr Cabl Maintnanc through Cost Bnfit Modling Jason W. Rup U S WEST Advancd Tchnologis Bouldr Ky Words: Maintnanc, Managmnt Stratgy, Rhabilitation, Costbnfit Analysis, Rliability
More informationKey Management System Framework for Cloud Storage Singa Suparman, Eng Pin Kwang Temasek Polytechnic {singas,engpk}@tp.edu.sg
Ky Managmnt Systm Framwork for Cloud Storag Singa Suparman, Eng Pin Kwang Tmask Polytchnic {singas,ngpk}@tp.du.sg Abstract In cloud storag, data ar oftn movd from on cloud storag srvic to anothr. Mor frquntly
More informationInstallation Saving Spaceefficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison
Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doublsidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation
More informationGOAL SETTING AND PERSONAL MISSION STATEMENT
Prsonal Dvlopmnt Track Sction 4 GOAL SETTING AND PERSONAL MISSION STATEMENT Ky Points 1 Dfining a Vision 2 Writing a Prsonal Mission Statmnt 3 Writing SMART Goals to Support a Vision and Mission If you
More informationFEASIBILITY STUDY OF JUST IN TIME INVENTORY MANAGEMENT ON CONSTRUCTION PROJECT
FEASIBILITY STUDY OF JUST IN TIME INVENTORY MANAGEMENT ON CONSTRUCTION PROJECT Patil Yogndra R. 1, Patil Dhananjay S. 2 1P.G.Scholar, Dpartmnt of Civil Enginring, Rajarambapu Institut of Tchnology, Islampur,
More information5.3.2 APPROACH TO PERFORMANCE MANAGEMENT
Chaptr 5: Prformanc Managmnt Systm 5. APPROACH TO PERFORMANCE MANAGEMENT Th Municipal Systms Act () rquirs municipalitis to dvlop a prformanc managmnt systm suitabl for thir own circumstancs. According
More informationLong run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange
Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity
More informationA Note on Approximating. the Normal Distribution Function
Applid Mathmatical Scincs, Vol, 00, no 9, 4549 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and
More informationL13: Spectrum estimation nonparametric and parametric
L13: Spctrum stimation nonparamtric and paramtric Lnnart Svnsson Dpartmnt of Signals and Systms Chalmrs Univrsity of Tchnology Problm formulation Larning objctivs Aftr today s lctur you should b abl to
More informationBasis risk. When speaking about forward or futures contracts, basis risk is the market
Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also
More informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationMETHODS FOR HANDLING TIED EVENTS IN THE COX PROPORTIONAL HAZARD MODEL
STUDIA OECONOMICA POSNANIENSIA 204, vol. 2, no. 2 (263 Jadwiga Borucka Warsaw School of Economics, Institut of Statistics and Dmography, Evnt History and Multilvl Analysis Unit jadwiga.borucka@gmail.com
More information606 EDUCATIONAL LEADERSHIP
606 EDUCATONAL LEADERSHP jl VCTOR W. DOHERTY AND LNDA B. PETERS O f th many aspcts of school systm planning and valua tion, prhaps th most critical and lusiv is that of goals and objc tivs. Until th aims
More informationMEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM. Hans G. Jonasson
MEASUREMENT AND ASSESSMENT OF IMPACT SOUND IN THE SAME ROOM Hans G. Jonasson SP Tchnical Rsarch Institut of Swdn Box 857, SE501 15 Borås, Swdn hans.jonasson@sp.s ABSTRACT Drum sound, that is th walking
More informationAsset set Liability Management for
KSD larning and rfrnc products for th global financ profssional Highlights Library of 29 Courss Availabl Products Upcoming Products Rply Form Asst st Liability Managmnt for Insuranc Companis A comprhnsiv
More informationDehumidifiers: A Major Consumer of Residential Electricity
Dhumidifirs: A Major Consumr of Rsidntial Elctricity Laurn Mattison and Dav Korn, Th Cadmus Group, Inc. ABSTRACT An stimatd 19% of U.S. homs hav dhumidifirs, and thy can account for a substantial portion
More informationAP Calculus AB 2008 Scoring Guidelines
AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a notforprofit mmbrship association whos mission is to connct studnts to collg succss and opportunity.
More informationVersion Issue Date Reason / Description of Change Author Draft February, N/A 2009
Appndix A: CNS Managmnt Procss: OTRS POC Documnt Control Titl : CNS Managmnt Procss Documnt : (Location of Documnt and Documnt numbr) Author : Ettin Vrmuln (EV) Ownr : ICT Stratgic Srvics Vrsion : Draft
More informationTheoretical aspects of investment demand for gold
Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is
More informationPolicies for Simultaneous Estimation and Optimization
Policis for Simultanous Estimation and Optimization Migul Sousa Lobo Stphn Boyd Abstract Policis for th joint idntification and control of uncrtain systms ar prsntd h discussion focuss on th cas of a multipl
More informationSigmoid Functions and Their Usage in Artificial Neural Networks
Sigmoid Functions and Thir Usag in Artificial Nural Ntworks Taskin Kocak School of Elctrical Enginring and Computr Scinc Applications of Calculus II: Invrs Functions Eampl problm Calculus Topic: Invrs
More informationSTATEMENT OF INSOLVENCY PRACTICE 3.2
STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationThe international Internet site of the geoviticulture MCC system Le site Internet international du système CCM géoviticole
Th intrnational Intrnt sit of th goviticultur MCC systm L sit Intrnt intrnational du systèm CCM géoviticol Flávio BELLO FIALHO 1 and Jorg TONIETTO 1 1 Rsarchr, Embrapa Uva Vinho, Caixa Postal 130, 95700000
More informationDeveloping Software Bug Prediction Models Using Various Software Metrics as the Bug Indicators
Dvloping Softwar Bug Prdiction Modls Using Various Softwar Mtrics as th Bug Indicators Varuna Gupta Rsarch Scholar, Christ Univrsity, Bangalor Dr. N. Ganshan Dirctor, RICM, Bangalor Dr. Tarun K. Singhal
More informationModule 7: Discrete State Space Models Lecture Note 3
Modul 7: Discrt Stat Spac Modls Lctur Not 3 1 Charactristic Equation, ignvalus and ign vctors For a discrt stat spac modl, th charactristic quation is dfind as zi A 0 Th roots of th charactristic quation
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationWhole Systems Approach to CO 2 Capture, Transport and Storage
Whol Systms Approach to CO 2 Captur, Transport and Storag N. Mac Dowll, A. Alhajaj, N. Elahi, Y. Zhao, N. Samsatli and N. Shah UKCCS Mting, July 14th 2011, Nottingham, UK Ovrviw 1 Introduction 2 3 4 Powr
More informationthe socalled KOBOS system. 1 with the exception of a very small group of the most active stocks which also trade continuously through
Liquidity and InformationBasd Trading on th Ordr Drivn Capital Markt: Th Cas of th Pragu tock Exchang Libor 1ÀPH³HN Cntr for Economic Rsarch and Graduat Education, Charls Univrsity and Th Economic Institut
More informationFleet vehicles opportunities for carbon management
Flt vhicls opportunitis for carbon managmnt Authors: Kith Robrtson 1 Dr. Kristian Stl 2 Dr. Christoph Hamlmann 3 Alksandra Krukar 4 Tdla Mzmir 5 1 Snior Sustainability Consultant & Lad Analyst, Arup 2
More informationElectronic Commerce. and. Competitive FirstDegree Price Discrimination
Elctronic Commrc and Comptitiv FirstDgr Pric Discrimination David Ulph* and Nir Vulkan ** Fbruary 000 * ESRC Cntr for Economic arning and Social Evolution (ESE), Dpartmnt of Economics, Univrsity Collg
More informationCPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.
Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by
More information14.3 Area Between Curves
14. Ara Btwn Curvs Qustion 1: How is th ara btwn two functions calculatd? Qustion : What ar consumrs and producrs surplus? Earlir in this chaptr, w usd dfinit intgrals to find th ara undr a function and
More informationEssays on Adverse Selection and Moral Hazard in Insurance Market
Gorgia Stat Univrsity ScholarWorks @ Gorgia Stat Univrsity Risk Managmnt and Insuranc Dissrtations Dpartmnt of Risk Managmnt and Insuranc 800 Essays on Advrs Slction and Moral Hazard in Insuranc Markt
More informationJob Description. Programme Leader & Subject Matter Expert
Job titl: Programm Ladr & Subjct Mattr xprt Arbitration Pathways, ducation and Training Dpartmnt Salary band: 47,500 to 56,500 (dpndnt upon xprinc) Hours: 35 hours a wk Trm: Full Tim, Prmannt Accountabl
More informationFar Field Estimations and Simulation Model Creation from Cable Bundle Scans
Far Fild Estimations and Simulation Modl Cration from Cabl Bundl Scans D. Rinas, S. Nidzwidz, S. Fri Dortmund Univrsity of Tchnology Dortmund, Grmany dnis.rinas@tudortmund.d stphan.fri@tudortmund.d Abstract
More informationProduction Costing (Chapter 8 of W&W)
Production Costing (Chaptr 8 of W&W).0 Introduction Production costs rfr to th oprational costs associatd with producing lctric nrgy. Th most significant componnt of production costs ar th ful costs ncssary
More informationModern Portfolio Theory (MPT) Statistics
Modrn Portfolio Thory (MPT) Statistics Morningstar Mthodology Papr May 9, 009 009 Morningstar, Inc. All rights rsrvd. Th information in this documnt is th proprty of Morningstar, Inc. Rproduction or transcription
More information10/06/08 1. Aside: The following is an online analytical system that portrays the thermodynamic properties of water vapor and many other gases.
10/06/08 1 5. Th watrair htrognous systm Asid: Th following is an onlin analytical systm that portrays th thrmodynamic proprtis of watr vapor and many othr gass. http://wbbook.nist.gov/chmistry/fluid/
More informationDENTAL CAD MADE IN GERMANY MODULAR ARCHITECTURE BACKWARD PLANNING CUTBACK FUNCTION BIOARTICULATOR INTUITIVE USAGE OPEN INTERFACE. www.smartoptics.
DENTAL CAD MADE IN GERMANY MODULAR ARCHITECTURE BACKWARD PLANNING CUTBACK FUNCTION BIOARTICULATOR INTUITIVE USAGE OPEN INTERFACE www.smartoptics.d dntprogrss an b rsion c v o m d ss.d! A fr ntprog.d w
More informationPoisson Distribution. Poisson Distribution Example
Poisson Distribution Can b usd to valuat th probability of an isolatd vnt occurring a spcific numbr of tims in a givn tim intrval,.g. # of faults, # of lightning stroks tim intrval Rquirmnts: Evnts must
More informationGovernment Spending or Tax Cuts for Education in Taylor County, Texas
Govrnmnt Spnding or Tax Cuts for Education in Taylor County, Txas Ian Shphrd Abiln Christian Univrsity D Ann Shphrd Abiln Christian Univrsity On Fbruary 17, 2009, Prsidnt Barack Obama signd into law th
More informationCHAPTER 88 THE BINOMIAL AND POISSON DISTRIBUTIONS
CHAPTER 88 THE BINOMIAL AND POISSON DISTRIBUTIONS EXERCISE Pag 97 1. Concrt blocks ar tstd and it is found that on avrag 7% fail to mt th rquird spcification. For a batch of nin blocks dtrmin th probabilitis
More informationSolutions to Homework 8 chem 344 Sp 2014
1. Solutions to Homwork 8 chm 44 Sp 14 .. 4. All diffrnt orbitals mans thy could all b paralll spins 5. Sinc lctrons ar in diffrnt orbitals any combination is possibl paird or unpaird spins 6. Equivalnt
More information