MULTI-WORKDAY ERGONOMIC WORKFORCE SCHEDULING WITH DAYS OFF

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) MULTI-WORKDAY ERGONOMIC WORKFORCE SCHEDULING WITH DAYS OFF Tar Raanamanee and Suebsak Nanhavanj School of Managemen Technology Srndhorn Inernaonal Insue of Technology, Thammasa Unversy Pahum Than, 22, THAILAND +662-50-3505, Emal: r.ar@gmal.com; suebsak@s.u.ac.h Absrac Mos ergonomc workforce schedulng problems (WSPs) are concerned wh developng daly work schedules for ndusral workers so as o preven her daly hazard exposures from exceedng a permssble lm. In hs paper, we consder he WSP wh a plannng perod ha covers several workdays. Addonally, allowable days off are ncluded n he work schedules. I s assumed ha all workers workng a he same worksaon (or n he same work area) are exposed o he same hazard level. Daly operaon schedules of worksaon and worker lmaons are also consdered. An neger lnear programmng model s developed o represen he mul-workday ergonomc workforce schedulng problem. Is objecve s o deermne a mnmum number of ulzed workers for he gven plannng perod such ha all workers daly hazard exposures do no exceed he permssble daly lm. An opmzaon sofware ool called ILOG CPLEX s employed o oban he opmal soluon. Keywords: Mul-workday workforce schedulng, Ergonomcs, Hazard exposure, Opmzaon. INTRODUCTION Nowadays, workforce schedulng s an mporan and challengng problem for many organzaons boh n manufacurng and servce ndusres. I has mpac on labor cos, employee morale, and safey. The workforce schedulng problem (WSP) s a combnaoral opmzaon problem ha s nended o assgn a group of workers or employees o work n a se of shfs (e.g. mornng, afernoon, ngh) or o perform a se of asks over a gven me perod. Several problem consrans and resrcons are consdered when a feasble work schedule soluon s developed. The objecve of WSP vares dependng upon he applcaon, work envronmen, and work polcy of he workplace. Is emphass mgh be on he mnmzaon of eher he oal number of workers (Alfares, 2002) or oal cos (Elshafe and Alfares, 2008). WSP has been suded n varous servce sysems, for example, he crew schedulng of he Hong Kong Lgh Ral Trans (Chu and Chan, 998), he schedulng of saff a he Uned Saes Posal Servce (Bard e al. 2003), and he saff schedulng n he healhcare sysem (Brunner and Edenharer, 20). Typcally, WSP has wo dfferen plannng horzons. They are: () mul-perod plannng whn one workday, and (2) mul-workday plannng. The mul-perod WSP focuses on assgnng workers o asks or shfs o dfferen work perods n one workday. 7

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) Ths problem s also known as he job roaon problem n he occupaonal safey and healh feld. Sarbar e al. (2008) suded he mul-perod schedulng of workers for a large assembly lne work sysem. They developed a mahemacal model wh he consderaon of compeences and preference of workers. A work perod was se equal o he lne s prese ask me beween wo produc uns. The objecve was o sasfy personnel requremens a each saon n each perod durng he plannng horzon whle mnmzng he cos and dssasfacon. The mul-workday WSP (MW-WSP) s applcable for varous work envronmens. The problem focuses on assgnng employees o work shfs or asks n several workdays durng a pre-defned plannng perod (e.g., week, monh). For example, Pan e al. (200) suded he manpower schedulng n a manufacurng envronmen. The objecve was o develop mul-workday work schedules ha mnmze he oal paymen on employees. A mxed neger mahemacal model was developed o represen he problem. A wo-sage heursc algorhm was proposed o solve hs problem. Many ndusral workers are frequenly exposed o ergonomcs hazards n her workplaces. Examples of common ergonomcs hazards are ndusral nose, hermal, menal sress, and physcal workload. Excessve hazard exposure can lead o occupaonal njures and llnesses, job dssasfacon, and decreased work effcency and producvy. To avod excessve exposure o ergonomcs hazard, workers mgh be roaed among dfferen asks, worksaons, or work areas whn he same workday. I s necessary o deermne he effecve work schedules ha help o preven workers from beng exposed o any concerned ergonomcs hazard beyond a daly permssble lm. Carnahan e al. (2000) nroduced he schedulng problem by amng a smoohng a Job Severy Index (JSI) ha was used o assess he poenal for back njury. The daly roang work schedules were obaned usng neger programmng and genec algorhm. Tharmmaphornphlas and Norman (2003) developed a mahemacal model o mnmze he maxmum daly nose exposure among workers. Yaoyuenyong and Nanhavanj (2006) proposed a hybrd procedure o deermne an opmal number of workers for job roaon whou beng exposed o excessve nose hazard n he manufacurng envronmen. Job roaon s an admnsrave approach for hazard exposure reducon. In fac, here are oher benefs of job roaon, for examples, prevenng njures, reducng employee boredom, and balancng workloads. Seçkner and Kur (2008) used job roaon schedulng n mul-workng day plannng where each worker wll receve consan number of days-off each week. Ther objecve was o mnmze he workload cos among workers. A job roaon consderng employees boredom was suded n Ayough e al. (202). They red o roae jobs among operaors durng he workday so ha he oal cos ncludng assgnmen and boredom coss was mnmzed. Moreover, a job roaon n an assembly lne employng dsabled workers can be found n Cosa and Mralles (2009). 8

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) As seen above, he mul-workday workforce schedulng problem wh a consderaon of safey or ergonomcs hazard s sll no explored. In hs paper, we nend o deermne a mnmum workforce sze for job roaon durng a mul-workday plannng perod so ha each day he ergonomcs hazard exposure of any worker does no exceed a daly permssble lm. Addonally, days off are allowed when generang he daly roang work schedules. 2. MULTI-WORKDAY ERGONOMIC WORKFORCE SCHEDULING The mul-workday ergonomc workforce schedulng problem (MW-WSP) focuses on developng mul-workday daly roang work schedules for ndusral or servce workers. Accordng o mos safey laws, workers mus no be exposed o a gven occupaonal hazard beyond a daly permssble lm. MW-WSP also consders worker lmaon and worksaon operaon schedule. Specfcally, workers are heerogeneous. The worker can be assgned o specfc jobs or asks accordng o hs/her qualfcaons. The worksaons also have specfc operaon schedules. Ther shudown perods are predeermned for all workdays whn he plannng horzon. The number of workdays for workers are known, ncludng he requred number of days off for ndvdual durng he plannng perod. Each workday can be dvded no mulple work perods. Workers are roaed among dfferen asks or worksaons durng he workday o reduce her hazard exposures. A any worksaon, he hazard exposure s unform. Tha s, all workers performng ndvdual asks a he same worksaon are exposed o he same hazard level. Generally, he larger he number of workers ulzed n job roaon, he lesser he hazard exposure amoun each worker wll receve. Neverheless, ncreasng he number of workers resuls n ncreased oal labor cos. As such, s mporan o deermne he opmal workforce sze for job roaon. In summary, he objecve of MW-WSP s o deermne he mnmum number of ulzed workers and her safe daly roang work schedules wh days off for a mul-workday plannng perod. 3. MATHEMATICAL MODEL MW-WSP can be formulaed as a mxed neger lnear programmng problem (MILP). Is objecve s o deermne a mnmum se of workers for mul-workday job roaon and her daly roang work schedules ha sasfy ergonomcs, worker lmaon, worksaon operaon schedules, and worksaon requremen consrans. The problem mus sasfy he followng condons:. Each worker mus no be exposed o a gven hazard exposure beyond a daly permssble lm. 2. In each work perod, each worker can be assgned o only one ask. 3. When he worksaon s occuped (.e., asks are beng performed), he number of requred workers for he worksaon mus be sasfed. 9

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) 4. Each worker mus be assgned o work for a gven number of workdays durng he plannng perod. 5. Worker lmaon and worksaon operaon consrans mus be sasfed. The formulaon of mahemacal model s based on he followng assumpons:. A workday s dvded no equal work perods. Job roaon occurs only a he end of he work perod. 2. In any gven work perod of he workday, a worksaon may or may no be occuped dependng upon s operaon schedule. 3. The numbers of workers requred a dfferen worksaons do no have o be equal. 4. If a worksaon s scheduled o be occuped, all asks a ha worksaon mus be performed. Smlarly, f he worksaon s shu down, all asks a ha worksaon wll no be performed. 5. The numbers of asks ha he workers can perform are known and do no have o be equal. 6. All workers a he same worksaon receve he same amoun of hazard rrespecve of he asks beng performed. 7. The hazard exposure per perod a each worksaon and he daly permssble lm of hazard exposure are known. Parameers: T number of workdays n a plannng perod; {,, T} K number of work perods per workday; k {,, K} J number of worksaons; j {,, J} I number of avalable workers for job roaon; {,, I} L daly permssble lm of hazard exposure m p jk w j h j a j number of workdays per plannng perod for worker f worksaon j s occuped n work perod k on workday ; 0 oherwse number of workers requred for worksaon j hazard exposure level per work perod a worksaon j f worker can be assgned o a ask a worksaon j; 0 oherwse Varables: n number of ulzed workers for job roaon Decson varables: f worker s assgned o worksaon j n work perod k n workday X = 0 oherwse f worker s assgned o work n workday Y = 0 oherwse f worker s seleced for job roaon e = 0 oherwse 20

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) The mahemacal model can be expressed as follows. subjec o I Mnmze n= e () = J K Xhj L, j= k= J j= (2) X k,, (3) I X = wp j jk,, = T Y = me = jk (4) (5) X p, jk,, (6) jk X a, jk,, (7) j X Y, jk,, (8) Y e, (9) X {0,}, Y {0,}, e {0,}, jk,, (0) 4. NUMERICAL EXAMPLE A hypohecal job shop facly s beng consdered. The facly has hree worksaons (T, T2, and T3) and en avalable workers (W W0). A each worksaon, he ergonomcs hazard s unform. The plannng perod s sx workdays (D D6). All workers mus work fve workdays durng he plannng perod, wh one day off. A workday s dvded no four equal work perods (P P4). For smplcy, s assumed ha he daly permssble hazard exposure lm L s. Table shows he hazard exposure amoun per work perod and number of requred workers a each worksaon. The worksaon operaon schedule s shown n Table 2. Table 3 shows he daa of avalable workers. 2

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) Table : Worksaon daa. Worksaon Hazard Exposure Amoun per Work Perod Number of Requred Workers T 0.448 T2 0.3236 2 T3 0.858 2 Table 2: Worksaon operaon schedule. D D2 D3 P P2 P3 P4 P P2 P3 P4 P P2 P3 P4 T - Y Y Y Y Y Y - Y Y Y - T2 Y - Y Y - Y - Y Y Y Y - T3 - Y Y Y Y Y - Y Y Y Y Y D4 D5 D6 P P2 P3 P4 P P2 P3 P4 P P2 P3 P4 T Y Y Y Y Y Y Y Y - Y Y Y T2 Y Y Y Y Y Y Y - Y - Y Y T3 Y Y Y - Y - Y Y Y Y - Y Noe: Y = occuped; - = shu down Table 3: Worker daa. W W2 W3 W4 W5 W6 W7 W8 W9 W0 T Y Y Y Y Y Y N Y Y N T2 Y Y Y Y Y N Y Y N Y T3 Y Y Y Y Y Y Y N Y Y Noe: Y = he worker can be assgned o he worksaon; N = he worker canno be assgned o he worksaon An opmzaon sofware program called ILOG CPLEX s employed o solve he problem o opmaly. The opmal soluon requres seven workers (from he en avalable workers) o preven any workers daly hazard exposure from exceedng. Daly hazard exposures of he seven workers are shown n Table 4. The mnmum and maxmum daly hazard exposure among workers durng he plannng perod are 0.448 and 0.9992, respecvely. Table 5 shows he daly roang work schedules for he sx-day perod. 22

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) Table 4: Daly hazard exposures of he seven workers. D D2 D3 D4 D5 D6 W 0.952 0.448 0.834 0.952 0.6276 W3 0.952 0.5094 0.7654 0.9992 0.952 W4 0.834 0.833 0.952 0.833 0.6472 W5 0.6472 0.834 0.7654 0.6276 0.6952 W8 0.9708 0.448 0.9708 0.9708 0.7654 W9 0.9992 0.5574 0.834 0.834 0.6276 W0 0.6952 0.6952 0.9708 0.833 0.833 Table 5: The sx-day daly roang work schedules. Ulzed Worker D D2 D3 P P2 P3 P4 P P2 P3 P4 P P2 P3 P4 W T2 - T3 T - T - - T - T3 T3 W3 - T T2 T3 - T3 - T2 T2 T - - W4 - T3 T T3 - T2 T2 T3 W5 - T2 - T2 T3 T3 T - W8 T2 - T2 T2 T - - - T2 T2 T2 - W9 T3 T3 T T3 T3 T3 T3 - W0 - T3 T3 T2 T3 T2 - T3 Ulzed Worker D4 D5 D6 P P2 P3 P4 P P2 P3 P4 P P2 P3 P4 W T - T2 T3 T3 T - - W3 T3 T3 T3 T T3 - T2 T W4 T3 T2 T - T3 T2 T2 - T2 - - T2 W5 - T T2 - - T - T3 T2 T3 - T3 W8 T2 T2 - T2 T2 - T - W9 T T3 T3 - T3 - T3 T - - T T3 W0 T2 - T2 T2 T2 T2 T3 - - T3 T2 T2 Noe: blank cell = day off; - = dle perod 5. CONCLUSION Ths paper nroduces he mul-workday ergonomc workforce schedulng (MW-WSP) wh days off. Is objecve s o develop a mahemacal model o deermne he mnmum number of workers for job roaon and o generae safe daly roang work schedules for workers durng a gven plannng perod for prevenng hem from recevng concerned 23

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) ergonomcs hazard beyond a daly permssble lm. Boh he worker lmaon and worksaon operaon schedule are consdered n hs problem. Workers have lmed ask skll and can be assgned o some asks. Some worksaons do no have o be occuped on a full-day bass. Addonally, some worksaons have several asks o be performed (by several workers). Durng he gven plannng perod, he workers are requred o work for several workdays wh some days off. A mxed neger lnear programmng model s developed o represen MW-WSP. From he gven numercal example, daly roang work schedules are generaed for each workday durng he plannng perod for he seleced workers. The resul also shows ha he daly hazard exposure of each worker does no exceed he daly permssble lm. ACKNOWLEDGMENTS Ths research s suppored by Srndhorn Inernaonal Insue of Technology, Thammasa Unversy, Thaland (va SIIT scholarshp). REFERENCES Alfares, H.K. (2002) Opmum workforce schedulng under he (4, 2) days-off meable, Journal of Appled Mahemacs and Decson Scence, 6(3), 9-99. Ayough, A., Zandeh, M., and Farsjan, H. (202) GA and ICA approaches o job roaon schedulng problem: consderng employee's boredom, Inernaonal Journal of Advanced Manufacurng Technology, 60, 65-666. Bard, J.B., Bnc, C., and deslva, A.H. (2003) Saff schedulng a he Uned Saes posal servce, Compuers & Operaons Research, 30, 745-77. Brunner, J.O. and Edenharer, G.M. (20) Long erm saff schedulng of physcans wh dfferen experence levels n hospals usng column generaon, Healh Care Managemen Scence, 4, 89-202. Carnahan, B.J., Norman, B.A., and Redfern, M.S. (2000) Desgnng safe job roaon schedules usng opmzaon and heursc search, Ergonomcs, 43(4), 543 560. Chu, S.C.K. and Chan, E.C.H. (998) Crew schedulng of lgh ral rans n Hong Kong: from modelng o mplemenaon, Compuers & Operaons Research, 35(), 887-894. Cosa, A.M. and Mralles, C. (2009) Job roaon n assembly lnes employng dsabled workers, Inernaonal Journal of Producon Economcs, 20, 625-632. Elshafe, M. and Alfares, H.K. (2008) A dynamc programmng algorhm for days-off schedulng wh sequence dependen labor coss, Journal of Schedulng,, 85-93. Pan, Q.K., Suganhan, P.N., Chua, T.J., and Ca, T.X. (200) Solvng manpower schedulng problem n manufacurng usng mxed-neger programmng wh a wo-sage heursc algorhm, Inernaonal Journal of Advanced Manufacurng Technology, 46, 229-237. 24

Proceedngs of he 4h Inernaonal Conference on Engneerng, Projec, and Producon Managemen (EPPM 203) Sabar, M., Monreul, B., and Frayre, J.M. (2008) Compeency and preference based personnel schedulng n large assembly lnes, Inernaonal Journal of Compuer Inegraed Manufacurng, 2(4), 468-479. Seçkner, S.U. and Kur, M. (2008) An colony opmzaon for he job roaon schedulng problem, Appled Mahemacs and Compuaon, 20, 49-60. Tharmmaphornphlas, W. and Norman, B.A. (2003) Applyng mahemacal modelng o creae job roaon schedules for mnmzng occupaonal nose exposure, AIHA Journal, 64, 40 405. Yaoyuenyong, S. and Nanhavanj, S. (2006) Hybrd procedure o deermne opmal workforce whou nose hazard exposure, Compuers & Indusral Engneerng, 5, 743-764. 25