Aircraft maintenance workforce scheduling

Transcription

1 78 Aircrft mintennce workforce scheduling A cse study Heshm K. Alfres King Fhd University of Petroleum nd Minerls, Dhhrn, Sudi Arbi Keywords Aircrft industry, Optimiztion, Personnel mngement, Sudi Arbi Abstrct This pper describes n ctul ircrft mintennce lbor scheduling study. The study's objective is to determine the optimum mintennce workforce schedule to stisfy growing lbor requirements with minimum cost. The min recommendtion of the study is to switch from five-dy to seven-dy workweek for ircrft mintennce workers. A new integer progrmming formultion, used to obtin n optimum seven-dy work schedule with no increse in workforce size, is presented. In comprison to the existing five-dy schedule, switching to seven-dy workweek is expected to produce svings of bout 13 per cent, or $100,000 nnully. Journl of Qulity in Mintennce Engineering, Vol. 5 No. 2, 1999, pp # MCB University Press, Introduction During the summer of 1997, study of ircrft mintennce worker schedules ws conducted t the vition deprtment of Sudi Armco in Dhhrn, Sudi Arbi (Alfres, 1997). The objective ws to evlute the current fixed-wing ircrft mintennce worker schedule, nd come up with recommendtions for improvement, if needed. The specific im ws to determine the optimum work schedule tht stisfies incresing mintennce lbor requirements with the minimum cost nd highest efficiency. Sudi Armco is the min oil compny in Sudi Arbi, nd the lrgest oil compny in the world. It is in chrge of ll phses of the oil business, from surveying nd explortion, through producing nd refining, ll the wy to mrketing nd distribution. Becuse oil revenues constitute the mjor prt of the ntionl income, the importnce of the compny to the Sudi industril development cnnot be overemphsized. The vition deprtment is responsible for the ir trnsporttion of the compny's workers nd equipment to remote res, such s oil fields nd explortion sites. The ircrft mintennce division of the deprtment must ensure the sfety nd irworthiness of the compny's lrge privte fleet, which in 1997 included 13 fixed-wing ircrft nd 19 helicopters. The fixed-wing flight line mintennce hd been operting on five-dy (Sturdy-to-Wednesdy) schedule, with two full eight-hour shifts per dy. The line ws experiencing excessive overtime, especilly during the weekends where it hs to support n incresing number of flights. The purchse of three new ircrft, more frequent mintennce checks, nd dditionl flights to new The uthor would like to cknowledge the generous support provided by King Fhd University of Petroleum nd Minerls while crrying out this reserch project.

2 destintions were putting incresing pressures on ircrft mintennce. It ws desired to determine the best schedule of ircrft mintennce to respond to these chllenges. Bsed on the nlysis of lbor demnds, overtime sttistics, current schedule, current workforce size, nd other relevnt sttistics, recommendtion ws mde to switch to seven-dy workweek for the line. Compred to the current five-dy workweek schedule for the flight line, the proposed seven-dy workweek schedule is estimted to sve 13 per cent, or $98,000, of nnul lbor costs. Aircrft mintennce Literture review This literture review will focus, in order, on three subjects relevnt to the study: (1) ircrft mintennce; (2) mintennce stffing; nd (3) personnel scheduling. Strting with ircrft mintennce literture, recent studies emphsize the role of humn fctors nd trining in improving mintennce crew effectiveness. Ivturi et l. (1995) developed frmework to nlyze, identify, nd evlute tem trining strtegies to improve temwork effectiveness in ircrft inspection nd mintennce opertions. Dorn (1996) found humn fctors to hve significnt effect in 101 mintennce-relted ircrft ccidents tht he studied. Shepherd nd Krus (1997) described guidelines for humn fctors trining of mintennce personnel in order to reduce humn error in ircrft mintennce. Mintennce stffing objectives include minimum cost, mximum vilbility, mximum relibility, or combintion of these mesures. Dietz nd Rosenshine (1997) developed method to determine the optiml structure of mintennce workforce, nd used it to mximize militry ircrft sortie genertion subject to limit on mintennce stffing cost. Hecht et l. (1998) presented queueing model to determine verge outge time in US ir trffic control system s function of the number of mintennce technicins ssigned to ech center. Glpin et l. (1993) surveyed opertion nd mintennce stffing prctices in utility plnts nd compred theoreticl nd ctul stffing levels. Al-Zubidi nd Christer (1997) constructed mintennce mnpower simultion model to estimte the costs of different mnpower mngement nd opertionl procedures. Duffu nd Al-Sultn (1997) proposed mthemticl progrmming pproches for plnning nd scheduling mintennce resources, including mnpower, equipment, nd prts. Bker (1974) clssifies lbor scheduling into three types: shift (time-of-dy) scheduling, dys-off (dys-of-week) scheduling, nd tour (time-of-dy nd dys-of-week) scheduling. Since we re concerned with obtining seven-dy coverge per week, our focus is on the dys-off scheduling problem. Nnd nd Browne (1992) provide comprehensive survey of literture on this problem.

3 80 Giving ech worker two consecutive dys off per week, Tiberwl et l. (1972) formulted n integer progrmming model for dys-off scheduling. Alfres (1998) presented two-stge liner progrmming lgorithm for solving the sme problem. 3. Problem nd bckground In July 1997, the vition deprtment of Sudi Armco requested ssistnce in reviewing the existing work schedules nd mnpower distribution for the ircrft mintennce personnel. Avition mngement expressed three concerns to be tken into ccount. (1) The current excessive overtime to cover weekends nd unplnned mintennce. (2) The seven-dy mintennce requirement ssocited with the flight schedule, which is ctive during the weekends. (3) The significnt increse in scheduled mintennce worklod due to chnges in both the mintennce progrm nd the flight schedule. At the time of this study, the fixed-wing ircrft mintennce division, bsed in Dhhrn irport, hd 13 ircrft nd 103 employees. The division consists of six units: (1) plnning/engineering; (2) vionics; (3) line mintennce; (4) specil flights; (5) hngr mintennce; nd (6) shops. According to the division's mngement (Al-Sugir, 1994), ircrft mintennce mnning requirements re ffected by the following fctors:. different types of ircrft;. continuous coverge (seven dys week, 24 hours dy);. trining requirements;. US Federl Avition Administrtion (FAA) Airworthiness Directives (Sudi Armco ircrft hve FAA registrtion);. mnufcturer service bulletins;. ircrft ge nd condition; nd. Sudi Arbi's hrsh environment. Aircrft mintennce requirements cn be brodly clssified s follows:. Scheduled mintennce: including pre-flight, post-flight, dily nd phse checks, clendr time chnges, time limited component chnges, in

4 ddition to A, B, C, nd D checks (periodic ircrft PM/inspection progrms of incresing intensity).. Unscheduled mintennce: to hndle unplnned problems reported by flight or mintennce crews. As rule of thumb, vition deprtment estimtes unscheduled mintennce worklod to be 50 per cent of scheduled mintennce worklod.. Specil mintennce: s required to stisfy specil instructions or directives by the mnufcturer, FAA, or vition mngement. Mintennce worklod is expected to significntly increse due to severl fctors. The first fctor is the purchse of three dditionl ircrft in Second, more frequent inspections due to chnges in the mintennce progrm, i.e. doubling the frequency of B nd C checks. Third, new flights s consequence of strting service to the new Shybh oilfields. Fourth, doubling the number of flights to Northern Are Producing s result of chnging the dys-on/dys-off work schedule from (14/7) to (7/3, 7/4). Currently, line overtime is verging 27 hours per employee per month, but is incresing due to growing mintennce requirements. Chnging the ircrft mintennce lbor schedule ims to reduce excessive overtime, nd llow the workforce to hndle worklod increses indicted in Tble I. This study is concerned with scheduling the line mintennce unit's workforce, which is responsible for mintining ircrft tht re ctively in service. There re two full eight-hour shifts per dy, morning nd fternoon. Two full line mintennce crews, ech with its own foremn, re bi-weekly rotted between the two shifts. Both crews re mde up of one trde, nmely irfrme nd power (A&P) technicins. The worklod of line mintennce workers includes the following duties: pre-flight, through-flight, post-flight checks, clendr nd 50-hour inspections, A checks, time limited component chnges, supporting specil flights, fixing pilot-reported problems nd mintennce discrepncies, nd on the job trining. If we exclude unscheduled mintennce, i.e. fixing pilot-reported problems nd discrepncies found during inspections, the worklod of line mintennce is highly deterministic. Given the weekly flight nd mintennce schedules, we cn ccurtely estimte the time nd number of workers needed for ech scheduled mintennce ctivity. For exmple, tem of two workers will tke one to two hours for preflight check, hlf n hour to n hour for through-flight check, two hours for post flight check, nd 24 hours for n A check. To Aircrft mintennce 81 Worklod indictor % increse Projected mnweeks of ircrft mintennce No. of weekly flights No. of fixed-wing ircrft Tble I. Aircrft mintennce worklod indictors for 1997 nd 1998

5 82 include unscheduled mintennce worklod, we cn dd 50 per cent to lbor requirements, or consider verging ctul pst dt. Whenever the two estimtes differed considerbly, the higher of the two ws used. Informtion on ircrft mintennce processes nd policies ws obtined by interviewing the concerned people, gining insights nd experience-bsed points of view on problems nd possible solutions. For ech shift, dt were collected on the current schedule, current workforce size, nd verge overtime hours per month. Informtion ws lso gthered on ech shift's dily mnpower requirements, reltion to the flight schedule, nd reltion to the other shift. Other relevnt sttistics were lso collected. In ddition to interviews, sources of dt included:. weekly flight schedules;. weekly mintennce plnning schedules;. weekend work schedules;. yerly mintennce projections;. employee time sheets;. mintennce work log books; nd. compny mnul on work schedules (Sudi Armco, 1996). The most importnt step in dt collection ws determining the dily lbor demnds for ech shift for ech dy of the week. This ws ccomplished by considering the projected flight schedule for 1998, with 15 dded flights for new destintions. In ddition, the ctul worklod (from the work logbook) ws considered for smple of severl typicl weeks. The line foremen were sked to estimte the number of workers tht would be needed to stisfy the lbor requirements of both the flight schedule nd ctul work recorded in the logbook. The verge lbor demnds ws determined for ech shift during the workweek re shown in Tble II (plese note tht the weekend in Sudi Arbi is Thursdy nd Fridy). 4. Modeling nd scheduling Since line mintennce crews include only A&P technicins, homogeneous workforce scheduling techniques cn be pplied. The compny policies (Sudi Armco, 1996) specify tht the minimum off period for ny worker during given work stretch must be t lest two dys. Tiberwl et l. (1972) formulted the following single-shift integer progrmming model for scheduling workers Tble II. Dily mintennce lbor demnds for morning nd fternoon shifts Dy-i S-1 Su-2 Mo-3 Tu-4 We-5 Th-6 Fr-7 Morning shift lbor demnd (m i ) Afternoon shift lbor demnd ( i )

6 with two consecutive dys off per week. Minimize Z ˆ X7 iˆ1 x i 1 Aircrft mintennce Subject to jˆ1 xj x i 1 x i r i ; i ˆ 1;... ; 7 2 x i ; r i 0 nd integer; i ˆ 1;... ; where x i =number of workers ssigned to dys-off pttern i, off on dys i nd i 1 r i =minimum number of workers required on dy i. Three lterntive work schedules re vilble for stisfying lbor demnds given in Tble II. The first is to continue with the existing regulr time Sturdy-to-Wednesdy five-dy workweek, scheduling workers for the weekend on n overtime bsis. The second lterntive is to switch to seprte seven-dy workweek schedule for ech shift, in which workers my work on regulr time during the weekends, nd hve two dys off during the weekdys. The third lterntive is similr to the second, but the morning nd fternoon shifts re linked on Fridy. Shift ssignments nd costs of the three lterntives re compred next Alterntive 1: continue with the current five-dy schedule The mximum lbor demnd for weekdys is 11, which occurs on Wednesdy fternoon. Since two work groups lternte between the morning nd fternoon shifts, 11 workers re ssigned to ech shift. These workers re ssigned to weekdys on regulr-time bsis, nd to weekends on voluntry, overtime bsis. The py hours re clculted in Tble III, dding up to 1,012 per week Alterntive 2: switch to seven-dy workweek, seprting the two shifts To stisfy lbor demnds with seven-dy schedule, Tiberwl et l.'s (1972) integer progrmming model ws modified to incorporte two shifts, with the Shift work times Workers W Hours/shift H = 8*dys Hours/week T ˆ W H Py rte (%) R Py hours/week P ˆ T R S-We morning S-We fternoon Th-Fr morning Th fternoon Fr fternoon Tble III. Clcultion of the totl py hours per week for Alterntive 1

7 84 objective of minimizing the totl number of workers. Since lbor demnds for the two shifts re different, r i in constrint (2) is replced by m i for the morning shift, nd by i for the fternoon shift. Moreover, redefining x i s morning shift ssignments nd defining y i s fternoon shift ssignments, x i is replced by y i for the fternoon shift. Tble IV shows the optimum solution of the modified model, which is displyed below. Minimize Z ˆ X7 x iˆ1 i y i 4 Subject to jˆ1 x j x i 1 x i m i ; i ˆ 1;... ; 7 5 jˆ1 y j y i 1 y i i ; i ˆ 1;... ; 7 6 x i ; y i 0 nd integer; i ˆ 1;... ; 7 7 where x i =number of morning shift workers off on dys i nd i 1 y i =number of fternoon shift workers off on dys i nd i 1 Since there is no overlp in the constrints involving the x i 's nd y i 's, we cn solve independently for the two sets of vribles. Alterntively, we cn develop two seprte models for the two shifts, simply by splitting (4) into two objectives of the form (1). Since two full mintennce crews re rotted between the two shifts, the minimum size of ech crew must be 12 workers. Therefore, Alterntive 2 requires 24 workers for the two shifts. Moreover, since ech worker is given two dys off per week, ech worker is pid for five work dys per week, t eight hours per dy, ll regulr time. Therefore, the totl py hours per week re clculted s follows: Alterntive 2 py hours = 2458 = 960 hours/week The bove figure represents significnt sving compred to the 1,012 hours/ week obtined by Alterntive 1. However, this sving is obtined t the expense of incresing the workforce size from 22 to 24 workers. Alterntive 3 utilizes unique pproch to produce even greter svings without ny increse in the workforce size, s discussed next. Tble IV. Morning nd fternoon shift ssignments for Alterntive 2 Shift i Totl Morning workers x i Afternoon workers y i

8 4.3. Alterntive 3: switch to seven-dy workweek, linking the two shifts Although Alterntive 2 reduces py hours compred to Alterntive 1 (current schedule), it requires more workers. This is serious drwbck in developing country like Sudi Arbi, where skilled workers re scrce, prticulrly in highly specilized field such s ircrft mintennce. In order to void the need for more workers while providing seven-dy coverge, the following integer progrmming model ws formulted. This model is similr to the modified two-shift model developed bove, but replcing constrints (5) nd (6) with the following constrints combines Fridy's demnds: x jˆ1 j x i 1 x i m i ; i ˆ 1;... ; 6 8 Aircrft mintennce 85 jˆ1 y j y i 1 y i i ; i ˆ 1;... ; 6 9 jˆ1 x j y j m A unique feture of the bove integer progrmming model is combining Fridy's morning nd fternoon lbor demnds in one constrint (10). The objective is to dd flexibility for minimizing the workforce size. The model does succeed in providing seven-dy coverge with the sme workforce size used to provide only five-dy coverge. The solution specifies tht 11 workers re needed for ech shift, ssigned s shown in Tble V. Assigning 11 workers to ech shift, the totl workforce size is only 22. Moreover, the totl py hours per week re further reduced to: Alterntive 3 py hours = 2258 = 880 hours/week To relize the benefits of this lterntive, certin djustments re needed on Fridys. Tble VI shows the result of the Fridy-combined solution, ssigning four workers to Fridy morning (greter thn the two needed), but only three workers to Fridy fternoon (less thn the five needed). To solve this problem, two workers from the morning shift must join the fternoon shift on Fridys. This mkes the ssignment two workers for the morning nd five for the fternoon on Fridy, stisfying lbor requirements of both shifts. For firness, workers should be rotted periodiclly mong the 22 ssignments, llowing every worker to hve 15 full weekends off in ech 22-week cycle. Obviously the third lterntive, which requires no increse in the number of workers, is the best since it hs the fewest py hours per week. Alterntive 3 Shift i Totl Morning workers x i Afternoon workers y i Tble V. Morning nd fternoon shift ssignments for Alterntive 3

9 86 outperforms Alterntive 2 becuse it stisfies dily lbor demnds with minimum overstffing. Figure 1 compres the dily slck (number of workers ssigned in excess of demnd) for Alterntives 2 nd 3. The totl weekly slck is 18 mndys for Alterntive 2, but only 8 mndys for Alterntive 3. Compred to Alterntive 1 (current schedule), the svings produced by Alterntive 3 re clculted s follows: Sving in py hours per week = 1,012 ± 880 = 132 hours Percentge svings = = per cent Averge lbor py rte (given) = $14.23/hour Annul sving in US dollrs = = $97,675/yer 5. Prcticl considertions Some employees hve expressed degree of reservtion towrds the new seven-dy schedule, becuse they think it would force them to work ll weekends without overtime py. Therefore, implementtion of the seven-dy schedule must be done with creful ttention to employee morle. As emphsized in the literture survey, humn fctors re significnt to the performnce of ircrft mintennce. It is recommended tht the following two points re explined to workers. First, weekend work will be rotted, thus ech worker will hve 15 out of 22 (bout 70 per cent) weekends off. Second, some compenstion will be given for weekend work, possibly in the form of on-cll Morning shifts Afternoon shifts Dy x 1 x 2 x 5 x 6 Totl y 1 y 2 y 3 y 6 Totl Tble VI. Totl morning nd fternoon dily worker ssignments for Alterntive 3 Sturdy Sundy Mondy Tuesdy Wednesdy Thursdy Fridy Note: = offdy Figure 1. Excessive number of workers ssigned on ech weekdy for Alterntives 2 nd SAT SUN MON TUE WED THU FRI Key Alterntive 2 Alterntive 3

10 py. The third nd finl point is tht the nture of the work, i.e. regulrly scheduled weekend flights, imposes requirement for regulrly scheduled weekend work. Mngement must lso highlight the indirect benefits to the workforce. First, more effective lloction of workers should led to improved performnce, nd ultimtely to tngible rewrds such s merit increses. Second, the new schedule is fir, ssigning n equl shre of work, py hours, nd experience mong ll workers. To successfully sell this schedule to ircrft mintennce workforce, mngement itself hs to be totlly comfortble with it. In the finl nlysis, both mngement commitment nd worker understnding nd coopertion will ply vitl role in the success of the proposed work schedule. In the ircrft mintennce cse, it seems tht good mesure of both is vilble in the orgniztion. Aircrft mintennce Conclusions To stisfy mintennce lbor demnds for ech dy of the week, especilly incresing weekend demnds, seven-dy workweek schedule is proposed for both morning nd fternoon shifts. Switching to this schedule would eliminte the need for weekend overtime, yielding n estimted sving of $98,000 per yer. By using unique integer progrmming formultion, no increse is required in the number of workers s result of the proposed schedule. The results of the study were ccepted by the vition deprtment's mngement. However, implementtion of the proposed schedule is plnned to strt when the deprtment moves to the new interntionl irport in Dmmm, s soon s it is officilly opened in My References Alfres, H.K. (1997), ``Mintennce work schedule for Dhhrn fixed-wing ircrft'', Project Report Number 14297, Dhhrn, Sudi Arbi, September. Alfres, H.K. (1998), `Àn efficient two-phse lgorithm for cyclic dys-off scheduling'', Computers & Opertions Reserch, Vol. 25, pp Al-Sugir, A.S. (1994), `Àircrft mintennce division mnpower'', presenttion to the vition deprtment mngement, Sudi Armco, Dhhrn, Sudi Arbis, June. Al-Zubidi, H. nd Christer, A.H. (1997), ``Mintennce mnpower modelling for hospitl building complex'', Europen Journl of Opertionl Reserch, Vol. 99, pp Bker, K.R. (1974), ``Workforce lloction in cyclicl scheduling problems: survey'', Opertionl Reserch Qurterly, Vol. 27, pp Dietz, D.C. nd Rosenshine, M. (1997), `Òptiml speciliztion of mintennce workforce'', IIE Trnsctions, Vol. 29, pp Dorn, M.D. (1996), `Èffects of mintennce humn fctors in mintennce-relted ircrft ccidents'', Trnsporttion Reserch Record, No. 1517, pp Duffu, S.O. nd Al-Sultn, K.S. (1997), ``Mthemticl progrmming pproches for the mngement of mintennce plnning nd scheduling'', Journl of Qulity in Mintennce Engineering, Vol. 3, pp

11 88 Glpin, D.S., Snchez, R.L. nd Dong, C.C. (1993), ``Comprison of combined cycle plnt stffing prctices'', Proceedings of the Joint ASME/IEEE Power Genertion Conference, Knss City, KS, pp Hecht, M., Hndl, J., Czeklski, L. nd Rosin, A. (1998), ``Impct of mintennce stffing on vilbility of the U.S. ir trffic control system'', Proceedings of the Annul Relibility nd Mintinbility Symposium (IEEE), Anheim, CA, pp Ivturi, S., Grmopdhye, A.K., Krus, D. nd Blckmon, R. (1995), ``Tem trining to improve the effectiveness of tems in the ircrft mintennce environment'', Proceedings of the Humn Fctors nd Ergonomics Society, Vol. 2, pp Nnd, R. nd Browne, J. (1992), Introduction to Employee Scheduling, Vn Nostrnd Reinhold, New York, NY. Sudi Armco (1996), Generl Instructions Mnul on Work Schedules, No , revision dte 3/ 30/1996. Shepherd, W.T. nd Krus, D.C. (1997), ``Humn fctors trining in the ircrft mintennce environment'', Proceedings of the Humn Fctors nd Ergonomics Society, Vol. 2, pp Tiberwl, R., Philippe, D. nd Browne, J. (1972), ``Optiml scheduling of two consecutive idle periods'', Mngement Science, Vol. 19 No. 1, pp