Poceedgs of the 2011 Idusta Egeeg Reseach Cofeece T. Dooe ad E. Va Ae, eds. Itegated Wofoce Pag Cosdeg Regua ad Ovetme Decsos Shat Jaugum Depatmet of Egeeg Maagemet & Systems Egeeg Mssou Uvesty of Scece & Techoogy, Roa, MO - 65409, USA Abstact We cosde the tegated wofoce pag ad aocato pobem fo a hgh voume maufactug facty that opeates two o-oveappg shfts of tweve hous each day, wth twety eght shfts fo a two wee pag peod. I such factes, opeatoa wofoce pag s typcay caed out two steps cosstg of the mutshft assgmets ad the sge-shft aocato. The mut-shft decsos baace the egua ad ovetme woe assgmets to dvdua shfts based o capacty pas ad woe avaabty dug the two wee pag peod. The sge-shft decsos esue the woe-mache goup aocatos satsfy the quafcato ad s-eve equemets. I ths pape, we peset a tegated wofoce pag mode that maes these decsos fo a the shfts dug the two wee pag peod. Aayzg the egua ad ovetme aocato epot povdes sghts desgg the coss-tag pogams. Keywods Mut-shft wofoce pag, Sge-shft woe aocato, Ovetme pag, Itegated wofoce pag. 1. Itoducto ad Lteatue Revew Maagg hghy sed wofoce factes that opeate twety-fou hous a day mutpe-shfts ot oy pesets chaeges, but aso oppotutes cost savgs f doe coecty. Wofoce pag decsos fo a two wee pag peod cude the assgmet of egua ad ovetme woes to sevea shfts based o the woe oste, atcpated factoy oadg, factoy ovetme pocy, ad the abo aws specfc to a geogaphc ego. Fo each shft, the umbe of egua woes ca be obtaed fom the woe oste, whe the umbe of equed woes s estmated based o the atcpated factoy oadg detemed by the capacty pas. If thee s a shotage of woes a shft, woes fom othe shfts ae assged as ovetme woes to f the tempoay gap. Whe mag ovetme assgmets the paes shoud esue that the compay ovetme poces ad the egoa abo aws ae stcty adheed to, whch specfy the maxmum umbe of ovetme hous fo a dvdua woe ad the ete factoy. The dvdua ovetme poces ae desged to mata a ght baace betwee the egua ad ovetme assgmets fo a dvdua woe ode to mmze the oss of motvato to wo caused by fatgue. By mtg the tota factoy ovetme, the exta ovetme opeatoa costs ca dastcay be educed. Assgg woes to shfts, becomes esseta ad has bee extesvey used modeg appcato aeas such as use schedug, poce patog, fe fghte schedug ad othe maufactug settgs that opeate 24 hous a day ad 7 days a wee wth mutpe shfts pe day. The paes have the tas of assgg woes to shfts based o the woe equemet ad s sets of the woes whe esug eguatoy costats such as mmum umbe of days off ad maxmum umbe of wo hous pe wee. I the teatue, the vaats of the shft schedug pobems have bee studed ude egua ad compessed wo wee categoy. I [1] ad [2], a optma agothm to sove the mutpe shft wofoce schedug cosdeg a 3-4 day wo wee s peseted. I [3], a thee-step method fo assgg the day wo fo futme empoyees wog o oe shft s descbed. I the fst step, the mma wofoce s cacuated such that the demad s satsfed. I the secod step, the feasbty of tmetabe fo woes s esued by gvg a mmum umbe of days off to each woe. Fay, the thd step, the woes ae aocated to the wo days. I [4], a costat pogammg agothm fo costucto of otatg schedues s peseted. Oce the woes ae assged to a gve shft, the sge-shft decsos cude the aocato of woes to espectve mache goups based o the woe quafcato ad othe factoy costats. The vaous factoy costats fo the sge-shft woe pag cude the aocato of woes to mache goups based o the quafcato, effcecy, ad cetfcato matx. The umbe of woes wth the desed s-eve at a mache goup s detemed by the ma-mache ato ad the s-eve ato. Futhe, the factoy ayout mposes estctos o ceta
Jaugum woe-mache goup aocatos that shoud be cosdeed the mode. Wth the ceased atteto gaed by ceua maufactug ad goup techoogy dug the past decade, thee exsts vast teatue that has focused o woe assgmet pobems. I [5], a IP fomuato of the ceua maufactug woe assgmet pobem cosdeg woe coss-tag, mutpe s eves, ad mutpe tag eves s peseted. The mode cosdes both woe assgmet ad coss tag decsos the sge mode. Othe pactca aspects of coss-tag, such as assocated tag costs ad tme, have bee cuded the mode as costats. Howeve, the authos suggest use of ateatve heustcs fo age data staces. I a eae wo peseted [6], tege pogammg fomuatos ae peseted fo assgg woes to ces ad detemg the tag equemets fo the woes. The woe assgmet to ces aog wth the aggegate tag equemet s haded by the fst mode, whe the secod mode detemes the dvdua tag schedue. Howeve, the authos epot that the age test staces coud ot be soved optmay. I aothe wo, [7] peset a IP to fomuate the og-tem aocato of woes to maches cosdeg fuctuatg demad ad woe abseteesm. I [8], a two-phase heachca methodoogy to fd the optma opeato assgmet to maufactug ces s poposed. A mxed tege pogam was deveoped to geeate ateatve opeato eves ad a IP mode was used to acheve optma opeato assgmet to the ces. I the teatue, the opeatoa wofoce pag modes ae cassfed as mut-shft assgmet modes ad sge-shft aocato modes. I ode to deveop effcet opeatoa wofoce pas cosdeg ovetme decsos, t s esseta to the mut-shft pag modes to the sge-shft aocato modes. I ths pape, we peset a tegated wofoce pag mode that maes both the mut-shft ad the sge-shft decsos smutaeousy fo the two-wee pag hozo. At the stat of each shft, ovetme caddate avaabty ad capacty pas ae updated befoe usg the mode. The woe-shft assgmets fo the fst few mmedate shfts ae foze, so that a fuctuato the updated capacty pa does ot mpact the egua ad ovetme woe assgmets. Based o the egua ad ovetme woe assgmets to shfts ad the woe-mache goup aocatos, effectve coss-tag pogams ca be desged ad mpemeted. Some of the beefts of the tegated pag appoach cude: hgh woe utzato, effcet ovetme assgmets esutg educed opeatoa costs ad woe-shft assgmet cofcts, povsos fo woes to tae paed eaves, ad meetg the poducto tagets fo the pag hozo. The emade of the pape s ogazed as foows: Secto 2 pesets the Pobem Descpto foowed by pobem fomuato of the Itegated Wofoce Pag Mode Secto 3. I Secto 4, we peset the Resuts fom the mpemetatos foowed by the Cocusos ad Futue Wo Secto 5. 2. Pobem Descpto I ths pape, we cosde a Assemby-Test facty of a majo semcoducto maufactue that opeates two ooveappg shfts of tweve hous each day, wth twety eght shfts the two-wee pag peod. These twety eght shfts ae cassfed to fou shft types based o the stat tmes as: Shft Type 1 (Day Shft statg Suday(ST1)), Shft Type 2 (Nght Shft statg Suday(ST2)), Shft Type 3 (Day Shft statg Thusday(ST3)), ad Shft Type 4 (Nght Shft statg Thusday(ST4)). Each woe s assged to oe of these shft types ad s cosdeed as a egua woe fo that patcua shft type. A woe o a aveage wos fo foty-two hous pe wee dug hs/he egua shft, wog ethe thty-sx hous oe wee foowed by foty-eght hous the ext wee (o vce-vesa), tag the day off o ateate Wedesdays as ustated Tabe 1. Tabe 1: Shft Types dug two-wee pag hozo Su Mo Tu We Th F Sa Su Mo Tu We Th F Sa Day Shft ST1 ST1 ST1 ST1 ST3 ST3 ST3 ST1 ST1 ST1 ST3 ST3 ST3 ST3 Nght Shft ST2 ST2 ST2 ST2 ST4 ST4 ST4 ST2 ST2 ST2 ST4 ST4 ST4 ST4
Jaugum Most of the opeatos ths facty ae abo tesve equg woes to maage the capta tesve equpmet. The eve of automato ad eabty s equpmet specfc, thus the umbe of sed woes equed at each mache goup may vay accodgy. Futhe, a mache goup ca be utzed fo poducto f ad oy f the mmum umbes of sed woes ae aocated to opeate t. Hece, the umbe of woes equed evey shft ca be estmated usg the umbe of opeatg mache goups a gve shft. The vaato the woe equemet s caused due to paed ad upaed woe abseteesm o chage the umbe of opeatoa mache goups based o the capacty pas, pevetve mateace schedues, setup opeatos, ad mache faues. Sce, the duato of a shft s tweve hous, geat cae eeds to be tae whe mag the ovetme assgmets to avod poteta cofcts betwee a woe s egua ad ovetme shft assgmets. To avod such cofcts, the ovetme woes fo a gve shft ae seected fom the othe two shft types that do ot opeate dug the same day. Aso, whe mag ovetme aocatos, the paes ae teested esug that a day(o ght) shft s fed usg ovetme woe fom aothe day(o ght) shft, such a aocato s efeed to as pmay ovetme ca. I case, the pmay ovetme ca s ot avaabe, ovetme fo the day(o ght) shft s fed usg the ght(o day) shft that does ot opeate dug the same day, ad s efeed to as secoday ovetme ca. The puts fo mut-shft ad sge-shft pag cude: factoy caeda, estmated weey too-cout, woe oste, equpmet epot, pocess pa, woe cetfcato, hstoca aocatos, ad woe-opeato pefeeces. The factoy caeda gves detas about the opeatoa shfts dug the pag peod, ad the ovetme (OT) caddates fom the pmay OT ca ad the secoday OT ca. The estmated too-cout s based o the oughcut capacty pa that depeds o the factoy oadg. The woe oste gves the detas about the paed ad upaed eaves fo the woe. The equpmet epot gves specfc data about the ma-mache ato ad the seve ato at each mache goup. The pocess pa gves detas about the ctca opeatos. Fay, the woe cetfcato epot gves fomato about the woe quafcato, hstoca aocato gves the hstoy of woemache goup aocatos fom pevous shfts, ad the woe-opeatoa stage pefeece gves the pefeece of a dvdua woe to pefom a gve opeato. Oce the egua ad ovetme woes ae assged to the shfts, the ext tas s to aocate these woes to mache goups fo a the shfts dug the two wee pag hozo. The woe-mache goup aocatos fo a sge-shft ae based o the detaed capacty ad pocess pas. I a facty wth a sees of opeatoa stages, ofte thee exst botteecs that coto the ate of poducto; these opeatoa stages ae efeed to as ctca opeatos. Hece, woe aocato to such opeatoa stages taes poty ove the othe opeatoa stages the facty. Each mache goup, based o ts eabty ad ctcaty, eques a mmum umbe of woes wth specfc s eves. Based o these ues, aog wth the aocato ues, the woe equemet fo a desed s eve ad quafcato at a mache goup s detemed ad s assumed to be costat fo a shft. At a gve opeatoa stage, the woe equemet based o the s-eve vaes based o the eabty of the mache goup. I some ea-wod sceaos, the shft-supevso has to ethe aocate woes to mache goups mauay due to cosdeatos beyod the mathematca modes o eaocate a goup of woes to a set of mache goups due to a uexpected evet, e.g., too faue o uavaabty of WIP. I such cases, t s esseta to aocate the woes to the emag mache goups optmay; we efe to such sceaos as pata aocatos, whch s peseted the ext secto. 3. Itegated Wofoce Pag Mode The tegated wofoce pag mode cosdes both the ovetme pag decsos ad the woe machegoup aocato decsos smutaeousy. Ths mode ca be used at east oce at the begg of evey shft ad case, thee s a chage the capacty pa fo futue shfts the use has the fexbty to eaocate the egua ad ovetme woes to the shfts as equed. Howeve, ths fexbty mght aso cause ast mute chages to the ovetme equests fo the mmedate shfts that foow the pag hozo. Thus to avod such stuatos, the aocato of egua ad ovetme woes to the shfts that mmedatey foow the cuet shft ae foze usg the pata aocato costats. Ths stategy offes the tegated mode both the fexbty ad obustess woe pag dug the two-wee pag hozo. Futhe, the ovetme costat paametes ae adjusted ad automatcay updated evey tme the mode s used.
Jaugum Notato: Set Idces {1,2,...,I} the set of woes; {1,2,...,N} the set of opeatoa stages; {1,2,...,R} the set of mache goups at a opeatoa stage; {1,2,...,L} the set of s eves; {1,2,...,K} the set of shfts; Decso Vaabes X : s the pecetage of the shft duato fo whch a egua woe wth s eve s aocated at mache goup at a opeatoa stage dug shft ; : s the pecetage of the shft duato fo whch a ovetme woe wth s eve s aocated at mache goup at a opeatoa stage dug shft ; { Z 1 f egua woe wth s-eve s assged to the mache goup at opeatoa stage dug shft, = OT 0 othewse; { Y 1 f ovetme woe wth s-eve s assged to the mache goup at opeatoa stage dug shft, = 0 othewse; { U 1 f the woe aocato at a mache goup exceeds the mmum aowabe theshod mt, = 0 othewse; Devatoa Vaabes : s the devatoa vaabe dcatg the excess / shotage of woes wth s eve at a gve mache goup ad opeatoa stage dug shft ; s +/ Paametes c : s the pefeeta cost coeffcet of a egua woe wth s eve to opeate a mache goup at a opeatoa stage dug a gve shft ; co : s the pefeeta cost coeffcet of a ovetme woe wth s eve to opeate a mache goup at a opeatoa stage dug a gve shft ; p +/ : s the cost coeffcet of the devatoa vaabe s +/ ; R : s the woe equemet fo s eve at a mache goup at a opeatoa stage dug a gve shft ; : s the maxmum umbe of opeatos a egua woe ca be assged dug a gve shft ; τ : s the maxmum umbe of opeatos a ovetme woe ca be assged dug a gve shft ; ω : s the mmum amout of tme a woe ca be aocated to a gve opeato dug a gve shft ; ξ : s the maxmum aowabe ovetme hous fo a dvdua woe dug the two wee peod; ξ f actoy : s the maxmum aowabe ovetme hous fo a woes the factoy dug the two wee peod; ϕ : s the pecetage of the shft duato fo whch the woe wth s-eve s patay aocated to mache goup at opeatoa stage dug a gve shft ; M: s a age umbe;
Jaugum Objectve Fucto: Mmze (c.x ) + (co.ot ) + (p +.s+ ) + (p.s ) (1) Subject to: (X + OT) + s s+ = R,,,, (2) Z Y X,, (3) Z τ,, (4) OT,, (5) Y,, (6) X 1,,, (7) OT 1,,, (8) U X.(1/(ω )),,,,, (9) X M.U,,,,, (10) U OT.(1/(ω )),,,,, (11) OT M.U,,,,, (12) OT OT ξ f actoy ξ 1 OT (13) = 1 OT, (14) = ϕ X 1,,,,, (15) ϕ OT 1,,,,, (16) 0 X 1,,,,, (17) 0 OT 1,,,,, (18) s,s+ 0,,,,, (19) Z,Y,U {0,1},,,,, (20) The objectve fucto Equato (1) mmzes the peaty cost of devato the umbe of woes aocated wth a s eve, fom the actua woe equemet at the mache goup at a gve opeatoa stage ; ad the cost of aocato of egua ad ovetme woes to the mache goups fo a the shfts dug the pag hozo. The cost coeffcets of the devatoa vaabes ae assged based o the ctcaty of the opeatoa stage ad the eabty of the mache goup, such that the devato betwee the aocated ad the equed umbe of woes at the ctca opeato s much geate tha those at the o-ctca opeato. Costat set (2) matches the woe equemet fo a mache goups at each opeatoa stage fo evey shft wth the egua ad OT woes. Costat sets (3) ad (4) estct the movemet of the egua woes to a mted umbe of opeatos dug a gve shft. Costat sets (5) ad (6) estct the movemet of the ovetme woes to a mted umbe of opeatos
Jaugum dug a gve shft. Costat set (7) esues that the umbe of hous a egua woe s aocated dug a gve shft s ess tha the shft duato. Costat set (8) esues that the umbe of hous a OT woe s aocated dug a gve shft s ess tha the shft duato. Costat sets (9) ad (10) esue that the aocato of the egua woe to a mache goup dug a gve shft exceeds the mmum theshod aocato duato set by the shft supevso. Costat sets (11) ad (12) esue that the aocato of the ovetme woe to a mache goup dug a gve shft exceeds the mmum theshod aocato duato set by the shft supevso. Costat set (13) esues that the tota umbe ovetme hous fo a woes does ot exceed the factoy ovetme mt. Costat set (14) esues that the tota ovetme assgmet fo each dvdua woe does ot exceed the dvdua ovetme mt. Costat sets (15) ad (16) ae used fo settg the pata aocatos fo the egua ad OT woes espectvey. Costat sets (17) ad (18) mpose the o-egatvty ad the uppe bouds fo the aocatos dug a gve shft fo the egua ad ovetme woes espectvey. Costat set (19) mposes the o-egatvty estctos o the devatoa vaabes. Costat set (20) mposes the bay estctos o the auxay decso vaabes. 4. Resuts I ths secto, we peset the esuts fo a data stace obtaed fom oe of the Assemby-Test facty of a semcoducto maufactug compay. We cosde a sma poto of the facty cosstg of 26 egua woes/shft type, te opeatoa stages ad thee mache goups at each stage. The woe quafcato ad oste, s-eve equemets, dvdua ad factoy ovetme, shft types, ad capacty pas fo each shft dug the pag hozo s peseted [9]. Fo ay gve shft, the woe equemet s fufed usg the egua woes(r), pmay ovetme ca(p), ad secoday ovetme ca(s) based o the avaabty ad quafcato. Woes quafed fo a gve opeatoa stage ae cassfed as S Leve 1 o S Leve 2 woes. Each quafed woe has a pefeece o a scae of 1 3 to wo at a opeatoa stage, whee 1 deotes most pefeed opeatoa stage ad 3 deotes the east pefeed opeatoa stage. Based o the s-eves ad the woe pefeece fo a opeatoa stage, the techoogca cost coeffcets fo the decso vaabes (egua ad ovetme) ae assged. The woe equemet based o the s eves 1 ad 2, at each opeatoa stage fo the pag hozo cosstg of 8 shfts s sted the Tabes 2 ad 3, espectvey. Opeatoa stages 3 ad 5 have bee detfed as ctca opeatos ad the woe aocato at these opeatoa stages caot be voated ude ay ccumstaces. The esuts geeated by the tegated mode detemes the facto of the shft a woe s aocated to a gve mache goup, aog wth ay shotages at a gve opeatoa stage dug the pag hozo. Tabe 4 pesets the umbe of egua woes, pmay OT ca, ad secoday OT ca wth S Leves 1 ad 2 eeded to fuf the woe equemets fo the eght shfts. Tabe 5 pesets a sampe of the detaed woe-opeatoa stage aocato based o the s-eves 1 ad 2 fo the fst shft. The detaed esuts of specfc woe-mache goup aocato fo each of the eght shfts s peseted [9]. Aayzg the esuts Tabes 4 ad 5 the decso maes ca detfy the pospectve set of woes ad set of opeatoa stages fo whch coss-tag mght have a postve mpact. The set of woes wth owe utzato ca be cosdeed as caddates fo the coss-tag pogams. Aso, the set of opeatoa stages that eque fequet aocato of ovetme woes ca be cuded the coss-tag pogams. Hece, ths mode aso heps decso maes to detfy the set of woes ad opeatoa stages to be cuded the coss-tag pogams. Tabe 2: S 1 Woe Requemet Opeatoa Stage Shft 1 2 3 4 5 6 7 8 9 10 Tota Requemet 1 1.50 0.30 1.20 1.60 1.40 2.10 2.40 1.00 0.90 0.80 13.20 2 1.47 0.29 1.18 1.57 1.37 2.06 2.35 0.98 0.88 0.78 12.94 3 1.10 0.22 0.88 1.18 1.03 1.54 1.76 0.74 0.66 0.59 9.70 4 1.67 0.33 1.33 1.78 1.55 2.33 2.66 1.11 1.00 0.89 14.65 5 1.28 0.26 1.02 1.36 1.19 1.79 2.04 0.85 0.77 0.68 11.22 6 0.90 0.18 0.72 0.96 0.84 1.26 1.44 0.60 0.54 0.48 7.92 7 0.98 0.20 0.78 1.04 0.91 1.37 1.56 0.65 0.59 0.52 8.58 8 1.05 0.21 0.84 1.12 0.98 1.47 1.68 0.70 0.63 0.56 9.24
Jaugum Tabe 3: S 2 Woe Requemet Opeatoa Stage Shft 1 2 3 4 5 6 7 8 9 10 Tota Requemet 1 2.00 0.40 1.60 2.13 1.86 2.79 2.19 1.00 0.50 0.30 14.77 2 1.96 0.39 1.56 2.09 1.82 2.74 3.13 1.30 1.17 1.04 17.20 3 1.47 0.29 1.17 1.56 1.37 2.05 2.35 0.98 0.88 0.78 12.90 4 2.21 0.44 1.77 2.36 2.07 3.10 3.54 1.48 1.33 1.18 19.49 5 1.70 0.34 1.36 1.81 1.58 2.37 2.71 1.13 1.02 0.90 14.92 6 1.20 0.24 0.96 1.28 1.12 1.68 1.92 0.80 0.72 0.64 10.53 7 1.30 0.26 1.04 1.38 1.21 1.82 2.07 0.86 0.78 0.69 11.41 8 1.40 0.28 1.12 1.49 1.30 1.96 2.23 0.93 0.84 0.74 12.29 Tabe 4: Regua, Pmay OT, ad Secoday OT Woe Aocato S Leve 1 S Leve 2 Shft Regua Pmay OT Secoday OT Tota Regua Pmay OT Secoday OT Tota 1 9.90 2.00 1.30 13.2 10.68 1.90 2.19 14.77 2 8.50 2.31 2.13 12.94 10.2 4.30 2.70 17.20 3 9.00 0.70 0.00 9.70 10.70 2.20 0.00 12.9 4 9.40 2.15 3.10 14.65 10.30 6.30 2.89 19.49 5 9.65 1.57 0.00 11.22 11.0 2.10 1.82 14.92 3 7.92 0.00 0.00 7.92 10.46 0.00 0.00 10.46 7 8.58 0.00 0.00 8.58 10.50 0.91 0.00 11.41 8 9.24 0.00 0.00 9.24 11.0 1.29 0.00 12.29 Tabe 5: Woe-Mache Goup Aocato fo Shft 1 Opeato S 1 Woe Id. S 2 Woe Id. Requemet [Aocato][Shft] Requemet [Aocato][Shft] 1 1.50 9[1.00][R] 2.00 1[1.00][R] 17[0.50][R] 22[1.00][R] 2 0.30 100[0.30][S] 0.40 8[0.40][R] 3 1.20 5[0.20][R] 1.60 25[1.00][R] 20[1.00][R] 60[0.60][P] 4 1.60 8[0.60][R] 2.13 12[1.00][R] 85[1.00][S] 3[0.13][R] 65[1.00][P] 5 1.40 4[0.40][R] 1.86 23[1.00][R] 56[1.00][P] 3[0.86][R] 6 2.10 7[0.10][R] 2.79 13[1.00][R] 26[1.00][R] 14[1.00][R] 53[1.00][P] 24[0.79][R] 7 2.40 10[1.00][R] 2.19 95[1.00][S] 11[1.00][R] 79[1.00][S] 16[0.40][R] 100[0.19][S] 8 1.00 6[1.00][R] 1.0 2[1.00][R] 9 0.90 7[0.90][R] 0.5 17[0.50][R] 10 0.80 5[0.80][R] 0.3 60[0.30][P]
Jaugum 5. Cocusos ad Futue Wo I ths pape, we peseted a tegated wofoce pag mode that geeates both mut-shft woe-shft assgmets ad sge-shft woe-mache goup aocatos fo a two-wee pag peod based o ovetme, quafcato ad s-eve costats. The mode peseted the pape, heps the decso maes to detfy ad assg ovetme woes to shfts wth woe shotages ad aocate woes to mache goups based o quafcato ad s-eve costats. The output epots hep the decso maes to detfy the set of opeatoa stages ad woes fo desgg effectve coss-tag pogams. These coss-tag pogams ca hep the educto of ovetme aocato ad woe de tme due to ucetates such as: too faue, fuctuatos capacty pas, ad upaed woe abseteesm. Futhe, the mode aso has povsos fo mag pata aocatos fo ay shft dug the pag hozo. The tegated wofoce pag mode peseted ths pape does ot cosde the mpemetato of the coss-tag pogams dug the two-wee pag peod. Mag povsos fo mpemetato of coss-tag pogams s a teestg exteso. Othe teestg extesos cude modeg the oveappg shft stuctue ad the use of cotact woes to meet the tempoay shotage of woes dug the pag hozo. Acowedgemets The autho woud e to tha pesoe fom Ite Copoato fo povdg data ad sghts. Aso, the autho thas the Ite Reseach Couc fo fudg ths poject. Refeeces [1] Hug, R., 1993, A Thee-Day Wowee Mutpe-Shft Schedug Mode," The Joua of the Opeatoa Reseach Socety, 44(2), 141-146. [2] Hug, R., 1994, Mutpe-Shft Wofoce Schedug Ude the 3-4 Wowee wth Dffeet Weeday ad Weeed Labo Requemets," Maagemet Scece, 40(2), 280-284. [3] Azmat, C.S. ad Wdme, M., 2004, A Case Study of Sge Shft Pag ad Schedug Ude Auazed Hous: A Smpe Thee-Step Appoach," Euopea Joua of Opeatoa Reseach, 153(1), 148-175. [4] Lapote, G. ad Pesat, G., 2004, A Geea Mut-Shft Schedug System," The Joua of the Opeatoa Reseach Socety, 55(11), 1208-1217. [5] Noma, B.A. ad Thammaphophas, W. ad Needy, K.L. ad Bdada, B. ad Wae, R.C., 1993, Woe Assgmet Ceua Maufactug Cosdeg Techca ad Huma Ss," Iteatoa Joua of Poducto Reseach, 40(6), 1479-1492. [6] As, R.G. ad Huag, Y., 2001, Fomg Effectve Woe Teams fo Ceua Maufactug," Iteatoa Joua of Poducto Reseach, 39(11), 2431-2451. [7] Bohost, J. ad Somp, J., 2000, Log-Tem Aocato of Opeatos to Maches Maufactug Ces," Goup Techoogy/Ceua Maufactug Wod Symposum, Sa Jua, Pueto Rco. [8] Sue, G.A., 1996, Optma Opeato Assgmet ad Ce Loadg Labo-Itesve Maufactug Ces," 31(2), Poceedgs of the 19th Iteatoa Cofeece o Computes ad Idusta Egeeg. [9] Jaugum, S. ad Gasma, S.E. 2009, Itegated Wofoce Pag Modes fo Semcoducto Maufactugs, Techca Repot, Depatmet of Egeeg Maagemet ad Systems Egeeg, Mssou Uvesty of Scece ad Techoogy, Roa, MO.