Improving Airline Network Robustness and Operational Reliability by Sequential Optimisation Algorithms

Transcription

1 Netw Spat Econ (2006) 6: DOI.07/s y Improvng Arlne Network Robustness and Operatonal Relablty by Sequental Optmsaton Algorthms Cheng-Lung Wu # Sprnger Scence + Busness Meda, LLC 2006 Abstract A sequental optmsaton algorthm s developed to mprove the operatonal relablty of arlne schedules. Smulaton results show that departure delays are reduced by 30% after optmsaton by usng extra 260 mn buffer tmes n the schedule. Ths also ncreases the network-wde schedule relablty from 37 to 52% and an estmated delay cost savng of $20 mllon dollars per annum for a small arlne network. The advantage of sequental optmsaton s that t consders the delay/punctualty propagaton n arlne networks, so to prevent arlnes from plannng excessve buffer tmes to ndvdual flghts by consderng arcraft rotaton as a whole process. Keywords Arlne schedule robustness. Arlne schedule relablty. Sequental optmsaton. Arcraft routng. Delay propagaton 1 Arlne Schedule Plannng and Operatons Arlne schedule plannng typcally nvolves four steps from schedule desgn, fleet assgnment, arcraft routng to crew parng/rosterng. At the stage of arcraft routng, schedule plannng nvolves the optmsaton of arcraft routng by formulatng arcraft routng as nteger programmng problems such as the work by Arguello et al. (1998), Barnhart et al. (1998), Luo and Yu (1997), Rexng et al. (2000), Teodorovc and Stojkovc (1995) and Yan and Young (1996). Sophstcated optmsaton algorthms have been developed to solve complex nteger programmng problems and satsfactory results can be acheved wthn reasonable computng tmes and resources nowadays. In the real practce, arcraft routng problems are hardly solved by a sngle step. Instead, the routng optmsaton and problem solvng process may nvolve nterventon from experenced arlne schedulers, e.g., manually adjustng routng C.-L. Wu (*) Department of Avaton, Unversty of New South Wales, Sydney NSW 2052, Australa e-mal: C.L.Wu@unsw.edu.au

2 236 C.-L. Wu plans to reflect some operatng constrants such as arcraft turnaround tmes at specfc arports and flght punctualty targets of key feeder flghts. Ths Ffne-tunng_ procedure s wdely used by arlnes because the current approach n arcraft routng optmsaton, e.g., nteger programmng s not an operaton-orented approach, but more optmsaton focused. The lack of consderaton n arcraft routng optmsaton to reflect real operatonal ssues may result n lower schedule robustness and relablty n daly operatons (Mederer and Frank, 2002). The observable consequences of lower schedule relablty are flght delays and potental delay propagaton n an arlne_s network. Typcal arcraft routng optmsaton s amed at searchng for the optmal soluton of an nteger program wth sde constrants wthout explct consderaton of some ssues n arlne operatons such as turnaround effcency at arports, the allocaton of buffer tmes n schedules and the relablty/robustness of schedule operatons. In day-to-day arlne operatons, we can observe that some flghts tend to arrve late and need to be turned around wthn a shorter tme and consequently result n departure delays and delay propagaton n the network (Mukherjee et al., 2004; Watterson and De Proost, 1999). Gven the current arcraft routng optmsaton approach, the robustness and relablty of arlne schedules s not well consdered aganst stochastc dsruptons n operatons. Therefore, experenced arlne schedulers may manually adjust the prelmnary results of arcraft routng to acheve hgher schedule relablty and/or hgher punctualty. In addton, ths task s usually conducted under certan operatonal constrants, e.g., lmted use of buffer tmes, arport slot avalablty, achevng punctualty targets and reducng delay propagaton n the network. Regardng the algorthms to optmally adjust arlne schedules at ths stage of plannng, most schedulers rely heavly on ndvdual experence rather than on sound theoretcal backgrounds and algorthms. The delay propagaton n arlne schedules s well known to arlnes and has been studed recently (Beatty et al., 1998; Mederer and Frank, 2002; Wu, 2005). To mtgate the mpact of delay propagaton and to mprove on-tme performance, arlnes embed buffer tmes n schedules (n turnaround tmes or block tmes), so to absorb accumulated and unexpected delays n arcraft rotaton. Ths measure may mprove on-tme performance, but the drawback s to consume longer arcraft turn tmes and possbly longer block tmes for flghts (Howarth and O_Tool, 2005; Sunday Tmes, 2000). Delays may propagate n a network va arcraft rotaton, passenger transfer and crew rosterng, f embedded buffer tmes are not enough to absorb delays. By the same token, flght punctualty also propagates and ths s the case whch one can observe n a normal day of arlne operatons. In order to mprove the robustness of schedules and reduce the lkelhood of delay propagaton, arlne schedulers may manually adjust the optmsed arcraft routng results. However, two problems are often encountered n ths Ffne-tune_ process ncludng: (1) determnng the optmal usage of expensve arcraft tmes as buffer tmes; and (2) establshng the punctualty benchmark wth whch new schedules are desgned and compared. To solve these two problems n the schedule fne-tune process, sequental optmsaton algorthms are proposed n ths paper. Algorthms are developed to apply sequental optmsaton n fne-tunng arcraft routng plans based on the prelmnary results of arcraft routng plannng. To evaluate the effectveness of embedded buffer tmes n draft arlne schedules, a smulaton model s used to generate the benchmark requred to effectvely allocate scarce arcraft tmes. In the followng parts of the

3 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental paper, t starts wth the arlne schedule smulaton model, followed by the ntroducton of schedule relablty ndces developed to evaluate the operatonal relablty of arlne schedules. Sequental optmsaton algorthms are developed to fne-tune arcraft routng schedules under certan constrants. Developed algorthms are then appled n a case study to demonstrate the effectveness of the proposed sequental optmsaton algorthm n more detal. 2 Schedule Smulaton and Schedule Relablty Index 2.1 Schedule Smulaton Two ssues are often encountered by schedulers durng the process of arcraft routng optmsaton ncludng: a) how to determne the optmal use of schedule buffer tmes and, and b) how effectvely schedule buffer tmes can mprove operatonal relablty and save delays. Snce an arcraft s assgned to carry out a few flghts n a flght cycle (beng one day for domestc operatons and one week for nternatonal operatons), these two ssues may become extremely complcated and hard to solve n a bg arlne network, f the only evaluaton tool for schedulers s ther experence n schedulng. In order to evaluate the punctualty/delay status of a flght schedule at plannng stages, a smulaton model developed earler s used to provde the estmated delays of draft schedules n varous plannng scenaros (Wu, 2005). An arlne schedule s composed of a number of flght sectors to be carred out by arlne fleets. A flght sector s defned to start from the on-block of an arcraft at the orgn arport gate untl the on-block of the arcraft at the destnaton arport gate. Hence, a flght sector comprses turnaround operatons at the orgn arport and arborne flght operatons n the ar space between the orgn and destnaton arport. Consequently n the smulaton model, a flght sector s modelled by two components, namely the turnaround module and the enroute module. Indvdual flght sectors are then nter-connected n the schedule smulaton model accordng to the gven arcraft routng schedules. The smulaton of schedule operaton s carred out by Monte Carlo technques to consder stochastc dsruptons n arlne operatons and the stochastc nature of operatonal actvtes n arlne operatons. In a smulaton run, each flght of the schedule s smulated by randomly selected samples from stochastc functons derved from hstorcal arlne data. The schedule s then smulated for 1,000 tmes (wth 1,000 samples for each flght of the schedule) so to control the smulaton nose level. The turnaround module comprses a number of parallel workflows, whch are conducted smultaneously and parallelaly on the arport ramps to turn around an arcraft for a followng flght. Major workflows nclude passenger de-boardng/ boardng (also ncludes crewng and cabn cleanng), cargo and baggage unloadng/ loadng, caterng unloadng/loadng and other ndependent work such as arcraft engneerng check and fuellng. Certan procedures must be followed for actvtes n the same workflow and delays to an actvty may delay followng actvtes n the workflow and possbly the departure tme. For nstance, cabn cleanng does not start untl all passengers have left the arcraft and passengers wll not start boardng untl cabn cleanng s fnshed. Gven the sequental nature of actvtes n work-

4 238 C.-L. Wu flows and stochastc dsruptons wthn workflows, Sem-Markov Chans are used to model these workflows. Snce the operatng tmes of actvtes n workflows vary accordng to a few factors such as avalable human resources and work loadng, the use of Markov Chans also reflects the stochastc aspects of arcraft turnaround operatons. Dsruptng events n workflows, e.g., mssng check-n passengers or late baggage loadng, are modelled as Fdsruptng states_ n the Markov model wth proper transton probablty lnkng to normal operatons (normal Fstates_) Turnaround Module Let t ATD be the actual tme of departure of flght (O Z N, the set of all flghts n a study schedule), whch forms a probablty densty functon (PDF) of flght and s denoted by f ATD ðþ. t S D denotes the gven scheduled departure tme of flght, and departure delays are defned by Eq. (1) as follows: D D ¼ t ATD S D ð1þ where D D denotes the departure delay of flght from Arports I to J (OI m J ). t ATD s a dependent varable nfluenced by two other varables, called: the actual tme of arrval of the prevous flght m (m m and Om Z N), denoted by tm ATA, and the stochastc turnaround operaton tme of flght, denotedbyt OP. T OP s the (longest) tme requred to fnsh all turnaround actvtes ncludng two major turnaround processes (passenger processng and cargo/baggage processng), delays from dsruptons, and other arcraft servce actvtes as descrbed n Eq. (2). t ATD ¼ t ATA m þ T OP ¼ t ATA m þ max T cargo ; T pax ; T events For nstance, T cargo s the tme requred to fnsh cargo and baggage processng for flght. A total of 4 actvtes need to be carred out n ths process and each actvty k (k Z 4) has a stochastc operatng tme and an expected operatng tme, e k as gven n Eq. (3). ð2þ T cargo ¼ XW k¼1 e k ð3þ Actvty k s modelled as a Markovan state, whch transts to any state at any tme t wth a state transent probablty functon, A k (t) as shown by Eq. (4). By the same token, the tme requred to fnsh passenger processng,.e., T pax s also modelled as a Markov Chan. X W Z e k ¼ XW ðe k ½Š t Þ ¼ XW 1 ta k ðþdt t ð4þ k¼1 k¼1 Dscrete events, whch operate ndependently from the above mentoned workflows mght delay arcraft departure only f the fnsh tme of an event exceeds the scheduled departure tme. Dscrete events are modelled as stochastc varables n Eq. (5) wth a PDF denoted by F e q t n Eq. (5) denotes the expected k¼1 0 ðþ. ee q

5 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental dsrupton tme of event q (q Z Q, the set of all potental events) and P e q denotes the occurrence probablty of such an event. T events h h ¼ max e e q ¼ max P e q E q½š t ¼ max P e q Z 1 0 tf e q ðþdt t ð5þ Enroute Module The enroute module descrbes the arborne flght operatons between arports. It s a complex procedure for flght operatons from pushng back at the gate, taxng, takng off, arborne operatons and landng at the destnaton arport. To smplfy the smulaton model and focus on arlne operatons on the ground, the enroute module aggregately descrbes the arborne flght operatons by stochastc functons. Hence, consderatons n arport layouts, runway congeston, queues on taxways and enroute ar traffc control delays are modelled aggregately by stochastc functons wth model parameters calculated from hstorcal block tmes between arports. Although ths module s not as sophstcated as the turnaround module, t closely reflects the overall flght operaton patterns n arcraft rotaton, subject to current capacty constrants n the arport and ar traffc control systems. Further more, arlnes around the world hardly have any nfluence on arport and ar traffc control procedures, except changng the hubbng patterns of flghts at some hub arports at whch the arlne s the domnant hubbng carrer. The enroute module s descrbed by Eqs. (6) and (7). t ATA s the actual tme of arrval of flght at the destnaton Arport J, whch forms a PDF, denoted by f ATA ðþ. t t ATA s nfluenced by the other two stochastc varables: the actual tme of departure of flght at Arport I,.e., t ATD and the expected en-route flght tme between Arports I and J, denoted by e ER n Eq. (6). e ER s derved from the PDF functon of en-route flght tme of flght, denoted by f ER ðþ. t Hence, the arrval delay of flght s modelled by D A n Eq. (7), where S A denotes the gven scheduled arrval tme at the destnaton Arport J. t ATA ¼ t ATD þ e ER ¼ t ATD þ Z 1 0 tf ER ðþdt t ð6þ D A ¼ t ATA S A ð7þ Delays due to constrans of arport capacty and arspace congeston are modelled aggregately by the stochastc functon of enroute operaton tmes (t ER from f ER ðþ) t n Eq. (6), whch counts from the tme an arcraft s pushed back at a gate untl the tme an arcraft s on chock at the destnaton arport. Accordngly, the actual turnaround tme of an arcraft s the tme between on and off chock at a gate. The departure/arrval delay,.e., D D and D A n Eqs. (1) and (7) could sometmes be negatve values due to early departure/arrval of flghts. Gven the current capacty constrants at major arports and the pressure to reduce the scheduled turnaround tmes for most arlnes, early departure/arrval operatons are lmted. Turnaround operatons may

6 240 C.-L. Wu start early or fnsh early, but ths also puts pressure on ground resources allocaton as well because early starts also dsrupt resource allocaton. Hstorcal punctualty data s obtaned from an arlne to calculate those parameters requred to calbrate and run the schedule smulaton model. The most sgnfcant advantage of such a smulaton model s that we are able to probe the Bexpected status of a draft schedule plan before operaton. It s well known that buffer tmes are usually embedded n arlne schedules, so to provde arlnes wth some protecton aganst the stochastcty n operatons. Gven desgned buffer tmes, delays stll exst n arlne operatons and the resultng delays are the complex nteracton among three key factors: turnaround operatons, schedules and stochastc dsruptons n operatons. Among three factors, the arlne schedule s a fxed tmetable, whle the other two factors are stochastc n nature. Wth embedded buffer tmes, arlnes expect those buffer tmes to take effect and absorb some delays n operatons. Snce arcraft tmes have hgh opportunty costs (as revenue-makng tmes), t s hardly seen that an arlne would buffer ts schedule to reduce delays to nearly the zero-delay level (called the Perfect Case) as llustrated n Fg. 1 (Wu, 2005). Instead, arlnes tend to use lmted buffer tmes scatterng among flght sectors, hopng that these buffer tmes wll control delay propagaton n the network to a satsfactory extent. By usng the smulaton model together wth approprate parameters (usually by usng the standard operatng procedure data n arcraft operatons), we are able to probe the Bexpected delays (on-tme performance) before schedule operatons, whch closely reflect schedule plannng phlo- Realty Case Plannng factors 1. System constrants (arspace & arports) 2. Stochastc delays delays network Commercal requrements Schedule plans schedule ops delays Dream Case Resources (a/c, crew) Ground operaton effcency (labour & arports) network Perfect Case Ops factors delays network Schedule Plannng Schedule Operatons Results Fg. 1 Inherent delays of arlne operatons (source: Wu, 2005)

7 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental sophy, schedulng constrants and trade-offs. The expected delays (called nherent delays) of such an optmsed schedule wth lmted buffer (called the Dream Case) are usually hgher than the Perfect Case, because arlne operatons are always subject to dsruptons from varous sources, e.g., passengers and arport ground congeston. Very often t s found by arlnes that the real delays after schedule operatons (called the Realty Case) are hgher than the delay level of the Dream Case, mostly due to nadequate schedule buffer tmes (or the reluctance to desgn more buffer tmes due to trade offs) and stochastc dsruptons n arlne operatons. Fgure 1 below llustrates the relatonshp among three possble stuatons n schedule operatons. A comprehensve model calbraton process s conducted earler to adjust parameters used n the smulaton model, so to mmc the current flght operatons n the real envronment (Wu, 2005). A set of parameters s obtaned from an arlne to generate the nherent delays of the Dream Case. The same set of parameters s then further calbrated to generate smulaton results, whch are close to current results. When the flght schedule s changed, correspondng model parameters are modfed and fed nto the smulaton model to generate smulated schedule operaton results ncludng mean delays and on-tme performance (OTP) fgures. Flght schedules are run by the smulaton model for 1,000 tmes (representng 1,000 days operaton), so to reduce the nfluence of smulaton noses on results. 2.2 Schedule Relablty Index At the stage of arcraft routng optmsaton, arlnes always encounter the trade off between lmtng the use of expensve buffer tmes n schedules and reducng delays (or mprovng on-tme performance) by usng more buffer tmes. In order to mnmse the use of expensve buffer tmes n a schedule, a benchmark s requred to mantan the balance of the trade off between the use of buffer tmes and flght delays. A set of schedule relablty ndces s proposed to serve as benchmarks n schedule plannng. The schedule relablty of flght s defned by comparng the nherent delays generated from the Dream Case wth the real delays from the Realty Case as formulated by Eq. (8) below. R D ¼ EDD D D R A ¼ EDA D A R ¼ EDD þ ED A D D þ D A ð8þ where R D R A denotes the departure/arrval relablty of flght, respectvely; ED D ED A represents the nherent departure/arrval delay of flght, whle D D and D A the actual departure and arrval delay of flght. Hence, R s used to evaluate the overall operatonal relablty of flght. The concept behnd ths schedule relablty ndex s to benchmark real schedule delays aganst the nherent delays so arlnes can evaluate how close the schedule operaton s to the expected delay levels n schedule plannng. By ths ndex, the schedule relablty reflects both the schedule plannng phlosophy, e.g., the wllngness to buffer schedule, and the stuaton n whch real operatons are conducted by the arlne. For nstance, f R D has a value larger than 0%, t means

8 242 C.-L. Wu that the real departure delays of flght D D s less than the nherent delays ED D. It mples that the real operaton outperforms the expectaton and the scheduled ground tmes may be shortened so to save arcraft tmes, f needed. However, qute often we see R D less than 0%, meanng that the real delay level s hgher than the expected one. Ths may result from nadequate buffer tmes for turnarounds, delay propagaton n arcraft rotatons, less robust turnaround operatons, or excessve dsruptons occurred n turnarounds. 3 Sequental Optmsaton and Algorthms The bggest challenge to mprove the robustness of arcraft routng s not about the optmsaton technques one can employ when solvng nteger programmng problems. Rather, t s more about how an arlne can mprove the robustness of schedule operatons. Currently, the nteger programmng approach s wdely used by arlnes to solve arcraft routng problems. However, gven the nature of nteger programmng, optmsaton tends to produce tght schedules under cost mnmsaton objectves wthout thorough consderaton of delay propagaton effects n networks. Very often t s seen from arlne operatons at arports that some partcular flghts need more turnaround tmes than other flghts due to the effcency of turnaround at certan arports, connectng passengers nbound/outbound the flghts, work loadng of ground staff at certan tmes and so forth. The nteger-programmng approach to optmse arcraft routng may also cause some problems n real-world operatons such as delay propagaton, frequent delays to specfc flghts and tght turnarounds, f further manual schedule fne-tune s not conducted thoroughly. Gven the current arcraft routng optmsaton and schedule adjustment procedures, sequental optmsaton algorthms are proposed n ths paper to mprove the effcency and effectveness of the manual schedule tunng process and to supplement exstng nteger programmng algorthms. The goal of sequental optmsaton s to mprove the schedule robustness and relablty n daly arlne operatons and mnmse delays. After ntal arcraft routng, a routng plan s generated whch conssts M rotaton patterns to cover N flghts n a network. A rotaton pattern j (also called a route) conssts of a number of flght sectors for an arcraft to conduct n a rotaton cycle. Flght n rotaton j (denoted by flght (,j)) s defned to start from the onblock tme of the arcraft at the orgn arport gate untl the on-block tme of the same arcraft at the destnaton arport gate, namely the actual tme of arrval, tj ATA. The actual tme of departure of flght (,j) s defned as the off-block tme of the arcraft at the orgn arport gate and s denoted by tj ATD. The scheduled tmes of departure and arrval for flght (,j) are denoted by S D j and S A j, respectvely. Hence, the departure delay of flght (,j) sðtj ATD S D j Þ and denoted by DD j ; the arrval delay of flght (,j) sðtj ATA S A j Þ and denoted by DA j. Based on Fschedule relablty_ defned earler, the goal to mprove the relablty of flght (,j) s to control the real delay levels as close as possble to the benchmark standard,.e., the nherent delays. Hence, to optmse the operatonal relablty of a schedule, the gven arcraft routng patterns are further relaxed by allocatng extra buffer tmes. Snce buffer tmes are expensve costs to arlnes, the use of buffer

9 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental tmes n the relaxaton process s lmted to acheve a chosen performance target, whch s measured by delays n ths model. A relablty target, denoted by R TAR, can be chosen arbtrarly by an arlne as the schedule operaton target. Accordng to the defnton of the relablty ndex gven earler by Eq. (8), the resultng target departure delays for flght (,j) s: D TAR j ¼ EDD j R TAR ð9þ Accordngly, the schedule adjustment for flght (,j), SA D j s expressed by Eq. () below, where D R j s the estmated delays of flght (,j) from smulaton. It s noted that f SA D j s larger than zero, t mples that the current delay level of flght (,j) s hgher than the target level and vce versa. Ths also mples that an arlne can save excessve arcraft tmes from those flghts whch have SA D j less than zero and use the saved arcraft tmes on those flghts whch have SA D j larger than zero. SA D j ¼ D R j DTAR j ðþ Therefore, the total avalable schedule adjustment tmes for rotaton j (denoted by SA D j ) can be expressed by Eq. (11), where K s the number of flghts n rotaton j. SA D j ¼ XK SA D j ¼1 ð11þ Snce delays and punctualty propagate along arcraft rotatons n a network, the relaxaton of ground tmes of earler flghts n rotaton j wll reduce the delays of followng flghts n the same rotaton. Accordngly, the fnal schedule adjustment tmes for flght (,j) (denoted by F SA D j ) wll be less than or equal to the avalable schedule adjustment tme estmates,.e., SA D j as shown by Eq. (12). Hence, the fnal total schedule adjustment tmes for rotaton j (denoted by F SA D j ) wll be less than or equal to the ntal schedule adjustment tme estmates,.e., SA D j n Eq. (13). FSA D j SA D j 8 1 K and 8j 1 j M ð12þ FSA D j SA D j 8j 1 j M ð13þ Gven the unque delay/punctualty propagaton effect, the optmsaton of arcraft routng schedule s conducted sequentally wthn each rotaton. The objectve functon of sequental optmsaton can be expressed by Eq. (14) as follows: To mnmse: X M X K D R j j¼1 ¼1 ð14þ

10 244 C.-L. Wu Subject to: FSA D j SA D j 8j 1 j M ð15þ n o D R j 15 mns or n o D R j D TAR j ð16þ where Eq. (15) constrans the usage of total adjustment tmes of rotaton j less than or equal to the frst estmaton,.e., SA D j ; M stands for the total number of rotatons of the study schedule, whch s equal to the fleet sze. Equaton (16) lmts the estmated delay tmes of flght (, j) after schedule adjustment under 15 mn (whch s the ndustry delay threshold) or under the chosen target delay level ðd TAR j Þ, whchever requres less buffer tmes. To conduct the optmsaton, an algorthm s developed as follows: Step 1: For rotaton j of the schedule, 1 e j e M: Step 2: Run the smulaton model and generate the nherent delay estmates,.e., ED D j =ED A j for each flght (, j) n rotaton j. Calculate current schedule relablty,.e., R D j =R A j for each flght (, j) n rotaton j and compare these wth the chosen target schedule relablty ndex, R TAR. Step 3: Calculate the ntal estmate of schedule adjustment, SA D j by ðsa D j ¼ D R j DTAR j Þ and calculate the total avalable schedule adjustment for rotaton j, SA D j by ðsa D j ¼ P K ¼1 SAD j Þ: Step 4: For flght (,j) (1e e K ) n rotaton j: If SA D j > 0 and D R j > 15, add SA D j mnutes (n the multple of 5 mn) to the ground tme of flght (,j). If SA D j < 0, deduct SA D j mnutes (n the multple of 5 mn) from the ground tme of flght (,j). Repeat Steps 2 and 3 for all flghts n rotaton j. Step 5: Repeat Steps 1 4 for all rotatons. The optmsaton algorthm above mproves schedule relablty of each flght n a rotaton sequentally accordng to the chosen relablty target, the hstorcal operatng delays, the total avalable schedule adjustment tmes and the mpact of delay/ punctualty propagaton n the rotaton. The sequental nature of the optmsaton algorthm fully utlses the concept of Fpunctualty/delay propagaton,_ so to avod excessve use of arcraft tmes n optmsaton. 4 Applcaton n Schedule Plannng 4.1 Research Data and Case Study Network To demonstrate the effectveness of the proposed sequental optmsaton algorthm on schedule plannng, a case study s conducted by usng schedule nformaton and

11 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental punctualty data of an anonymous arlne, denoted by FArlne X._ A selected fleet wth 17 narrow-body arcraft flyng to 20 destnatons s used n the followng case study. Schedules and operatonal data,.e., the standard operatng tmes of actvtes n arcraft turnaround processes adopted by the carrer, are used n the schedule smulaton model to estmate the level of nherent delays of the study schedule (the Dream Case). Ths result s used together wth hstorcal operatng delays to calculate the current operatonal relablty of each flghts/rotatons n the schedule. The smulaton model s then calbrated based on exstng model parameters of the Dream Case and real operatng statstcs n the prevous years. Calbraton results are summarsed by Fg. 2 below. Parameters used n the turnaround module and the enroute module of the smulaton model are calbrated to reflect the current operatng delay levels. Dsruptng events n arcraft turnarounds, e.g., mssng passengers and late baggage loadng are smulated by the real occurrence probablty derved from hstorcal IATA delay codes recorded by the arlne. The average duratons of dsruptng events are calbrated accordngly to reduce the gap between smulaton results and the Realty Case. It s seen from Fg. 2 that calbraton results are close to real delay levels. Calbraton errors between two cases are kept under 5% durng the calbraton exercse. The calbrated smulaton model s then employed to conduct schedule smulaton based on gven draft schedules and generate smulated delays after correspondng schedule changes. 4.2 Sequental Optmsaton Results The chosen relablty target of schedule optmsaton n the followng case study s to meet ether one of the followng two crtera: (1) 70% ndvdual relablty for Dept Delays (Realty) Dept Delays (Calbrated) Arcraft Number Fg. 2 Comparson between calbraton results and real delays

12 246 C.-L. Wu each flght n the network; or (2) less than 15 mn mean delays, whchever requres the least buffer tmes. Schedule adjustments n optmsaton are only made to the scheduled ground tmes of flghts. In other words, extra buffer tmes are embedded n the ground tmes (turnaround tmes) of flghts, so to control departure delays. When schedule adjustments are requred for a flght, a unt of schedule adjustment s 5 mn. Ths prevents the fnal schedule from havng unrealstc departure tmes, e.g., 9:13 departure. Ths practce also comples wth the current polcy of arport slot allocaton and coordnaton at those slot-constraned arports (IATA, 2004). The developed sequental optmsaton algorthm s appled to Arlne X_s network and the summary results are shown n Fg. 3. The usage of buffer tmes for each rotaton (operated ndvdually by one arcraft) s compared wth the estmated savng of delay tmes after sequental optmsaton. Addtonal 260 mn are used to relax arcraft routng plans accordng to optmsaton crtera gven above, and ths also generates an estmated savng of 540 mn delay network-wde. Delays of some flghts n some rotatons are sgnfcantly reduced after optmsaton such as arcraft 2, 3 and 6, whle the mpact of mnor schedule changes on some rotatons such as arcraft 8 and 11 s less than others. The sgnfcant delay reducton effect (beng the surrogate of punctualty mprovement) after sequental optmsaton also reveals the extent to whch delay propagaton may mpact arlne operatons. A rough estmate of the mpact scale of delay propagaton from results above s 1-mn delay mght result n 2-mn delay network-wde for Arlne X. If we assume that the monetary cost of one unt buffer tme and delay tme s $200 per mnute, then the estmated mpact of the sequental optmsaton on the new schedule s equvalent to an extra expendture for Arlne X by $19 mllon dollars per annum (calculated from $200/mn@260 mn/day@365 days/year) but a delay cost savng by $39 mllon dollars per annum (calculated from $200/ mn@540 mn/day@365 days/year), resultng n $20 mllon dollars net savng on operatng costs per annum. Ths estmated cost savng could be sgnfcant enough for the study regonal fleet and could have a postve mpact on the proftablty of an arlne Schedule tme added Delay tme saved Arcraft Number Fg. 3 Schedule adjustment and the mpact on network-wde delay tme savng

13 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental Fg. 4 Delay reducton by the optmsed schedule Dream Case Optmsed Schedule Realty Case Arcraft number The optmsed schedule s tested by the schedule smulator to evaluate how the optmsed schedule may react to current operatng envronment faced by Arlne X. Smulaton results of the optmsed schedule are compared wth the nherent delays of the Dream Case and the current delays of the Realty Case n Fg. 4 below. Although the delay level of the optmsed schedule s only as good as 70% of the expected level,.e., nherent delays, the optmsed schedule effectvely controls the overall delays across the network to the requred target level. Total departure delays of the orgnal schedule are 1,816 mn, whch s reduced to 1,278 mn after optmsaton. Ths result also reflects on the ncrease of average network-wde schedule relablty from 37 to 52% after optmsaton. To demonstrate the mpact of sequental optmsaton on mprovng schedule relablty and reducng delays, the optmsaton results of Arcraft 1 are gven n Fg. 5 comparng the relablty ndex before and after optmsaton. It_s seen that the orgnal relablty of the rotaton decreases from 70% at the start of the cycle to 25% at the end of the cycle. It mples that the real delay level of ths rotaton s hgher than the nherent delay level expected from Arlne X_s schedule. Ether the Fg. 5 Relablty of rotaton by Arcraft 1 (before/after optmsaton) 80% 70% 60% 50% 40% 30% 20% % 0% Relablty (before) Relablty (after) Flght No

14 248 C.-L. Wu nherent delay level s too low because Arlne X s too optmstc to the operaton of these flghts n the rotaton, or the nherent delay level s close enough but the operatons of these flghts are not relable enough. When delays before optmsaton are compared wth those after optmsaton for ths rotaton n Fg. 6, t can be seen that delays after optmsaton are better controlled below mn. Schedule adjustments to ths rotaton cycle nclude: 5 mn to Flght 3, 15 mn to Flght 4 and 5 mn to Flght 5, totallng extra buffer tmes of 25 mn for Arcraft 1. The usage of buffer tmes n optmsaton reflects closely the current operatng status as shown n Fg. 6, so more buffer tmes are deployed for those flghts that suffer from hgher delays than others. Gven the cost of deployng more buffer tmes, the estmated average delay tme savng after optmsaton s 54 mn for ths rotaton. The major advantage of the proposed sequental optmsaton algorthm s to utlse the delay/punctualty propagaton n a close network so to utlse lmted schedule tmes and prevent from usng excessve buffer tmes durng the optmsaton process. To demonstrate how punctualty propagaton can help sequental optmsaton and to llustrate the convergence of the proposed optmsaton algorthm, nterm results of the optmsaton of Arcraft 1 are extracted and shown n Fg. 7. Current operatng delays n ths rotaton hke sgnfcantly startng from Flght 4, so subsequent flghts n the rotaton suffer from severe delay propagaton. The Ftarget delay level_ s calculated based on the target relablty (70%) and the nherent delays of ths rotaton, whch are strongly nfluenced by current ground operatons and schedulng polcy of Arlne X. The optmsaton process starts from Flght 1. The ntal estmate of the total schedule adjustment tmes for all flghts n ths rotaton s calculated by (11) as 66 mn. The optmsaton procedure frst makes 5-mn change to Flght 3. From Fg. 7 we can see the smulated delay of the rotaton after the frst schedule change s reduced from the current level and consequently the re-calculated total schedule adjustment for followng flghts drops to 50 mn, thanks for punctualty propagaton Delays (before) Delays (after) Flght No Fg. 6 Delays before/after optmsaton for Arcraft 1

15 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental Target Delay Level (R=70%) Operatng Delays SA (+5, 3) SA (+15, 4) SA (+5, 5) Flght No Fg. 7 Comparson of nterm results of sequental optmsaton for Arcraft 1 After addng 15 mn to Flght 4, the delay level of the rotaton drops further to a lower level, causng the requred total schedule adjustment tmes for followng flghts by only 17 mn. The mpact of punctualty propagaton n ths rotaton s best seen by Flght 4, and we can also observe how sgnfcantly delays of the followng flghts after 4 are reduced. The optmsaton process stops after addng 5 mn to Flght 5. At the end, the used schedule tmes n the optmsaton s 25 mn, whch s sgnfcantly lower than the frst estmaton n the begnnng of optmsaton,.e., 66 mn. Wthout the sequental optmsaton algorthm, the applcaton of 66 mn to the rotaton wll mprove the relablty of each flghts much more sgnfcantly, but wll result n spendng extra 41 mn when compared wth results of sequental optmsaton. By ths optmsaton algorthm, arlnes can optmally utlse valuable arcraft tmes on crtcal flghts n the network to effectvely acheve the target schedule relablty. 4.3 Implcatons and Lmtatons In practce, the mmedate challenge before fnalsng arcraft routng plans s to match scheduled departure/arrval tmes of flghts wth arport slots avalable to an arlne. For flghts departng/arrvng at those arports frequently served by an arlne, the arport slot avalablty ssue s a relatvely mnor concern as the arlne can always swap slots among ts own flghts. Snce the magntude of flght tme adjustment n the above optmsaton s generally below 15 mn, ths change would not mpose too much pressure on arport slot avalablty, even though an arlne does not enjoy a domnant poston at some arports. The further mplcaton of arport slots s the Fsaleablty_ of flghts to passengers. Snce the sequental optmsaton or any manual changes durng arcraft routng plannng always nvolves alterng the schedule, the optmsed schedule tmes are not necessarly the most saleable tmes for potental passengers. There s a

16 250 C.-L. Wu possblty that marketng/sales decsons may overturn some results of arcraft routng wth specfed departure/arrval tme requests for certan flghts. Ths practce s seen qute often n the arlne ndustry especally for arlnes operatng hubbng schedules due to the need to consder connectng tmes and connectng opportuntes for passengers at hub arports. The present sequental optmsaton algorthm has not yet fully consdered the constrants arlnes may face when dealng wth hubbng and schedule synchronsaton across the network. Due to ths lmt, the applcablty of the current algorthm seems more benefcal to those arlnes, whch do not operate hghly synchronsed hubbng schedules. However, the proposed algorthm can be generalsed to consder hubbng schedules n future work as sde constrants, f needed. Consderng the operaton of strong hubbng actvtes, there has been growng concerns over the economc benefts/costs for strong hubbng schedules and the congeston costs mposed on arports and ar passengers (Goolsbee, 2005). The depeakng of hubbng schedules recently by Amercan Arlnes at Chcago O_Hare and Dallas-Fort Worth (DFW), by Lufthansa at Frankfurt, and by Delta Ar Lnes at Atlanta, demonstrate the vulnerablty of heavy hubbng operatons n terms of operatonal relablty of arlne schedules and the hdden costs to operate such schedules (Feld, 2005; Goedekng and Sala, 2003). The trend n arlne schedulng has gradually shfted from maxmsng connectng opportuntes and network traffc n the past to maxmsng the operatonal relablty of arlne schedules under the nfluence of dsruptons (Kang, 2004). Hence, arlnes are nowadays more wllng to trade off hubbng and arcraft utlsaton wth relable and robust Bweak-hubbng or more pont-to-pont schedule operatons (Mederer and Frank, 2002; Wu, 2005). Gven ths trend, the proposed sequental algorthm wll gradually see ts beneft n arlne schedule plannng n the future. An essental advantage of the proposed sequental optmsaton s to combne schedule smulaton models wth schedule optmsaton algorthms. The advantage s to provde arlne schedulers wth mmedate feedback durng schedule plannng. However, the argument on smulaton applcatons often roots n the valdty of the smulaton model n representng the real-world operatons. The smulaton model used here s developed from the perspectve of arlne operatons and hghly focuses on arcraft turnaround operatons and the network effects of stochastc dsrupton n arlne operatons. Snce arlne operatons are fully bounded and strongly nfluenced by arport operatons and ar traffc control, an alternatve approach s to smulate the arport system by network queung models such as the MEANS model (MIT, 2005). 5 Conclusons A schedule optmsaton algorthm s proposed and tested n ths paper by usng sequental optmsaton technques. The objectve of the sequental optmsaton s to optmally deploy lmted and valuable arcraft tmes as buffer n a network and acheve a target schedule relablty of 70% or a mean departure delay of 15 mn, whchever requres the least extra buffer tmes. Smulaton results of the optmsed schedule show that the total estmated departure delays of the optmsed schedule are 1,278 mn, whch s reduced from 1,816 mn before optmsaton. Ths reflects

17 Improvng Arlne Network Robustness and Operatonal Relablty by Sequental on the ncrease of network-wde schedule relablty from 37 to 52% after optmsaton. Results also show that the optmal use of schedule buffer tmes by 260 mn can save up to 540 mn delay. In monetary terms, t sums up to a net estmated savng of $20 mllon dollars per annum by a unt delay cost of $200 per mnute for a small-sze network. The proposed optmsaton algorthm can be used by arlnes durng arcraft routng plannng, especally n the schedule fne-tune process. The use of schedule smulaton models n schedule plannng provdes arlnes wth mmedate feedback upon schedule alternatons and the vsualsaton of possble results of schedule operatons. The major advantage of sequental optmsaton s that t consders operatonal characterstcs of arcraft rotaton,.e., the mostly noted delay/punctualty propagaton phenomenon n a network. Ths unque attrbute dstngushes the proposed optmsaton algorthm from other schedule optmsaton technques such as nteger programmng, whch hardly consders stochastc operatonal factors n arlne operatons. Consequently, sequental optmsaton prevents arlnes from allocatng excessve buffer tmes to ndvdual flghts, and meanwhle mantan the requred schedule relablty targets. Therefore, expensve arcraft tmes are only used for crtcal flghts, allowng punctualty to propagate before plannng more buffer tmes for later flghts n the same rotaton. References Arguello M, Bard J, Yu G (1998) Models and methods for managng arlne rregular operatons. In: G Yu (eds) Operatons research n the arlne ndustry. Kluwer Academc: Boston Barnhart C, Boland N, Clarke L, Johnson E, Nemhauser G, Sheno R (1998) Flght strng models for arcraft fleetng and routng. Transp Sc 32(3): Beatty R, Hsu R, Berry L, Rome J (1998) Prelmnary evaluaton of flght delay propagaton through an arlne schedule. 2nd USA/Europe Ar Traffc Management R&D Semnar, Orlando Feld D (2005) Hubs attract low-cost trade. Arlne Busness, March ssue, 15 Goedekng P, Sala S (2003) Breakng the bank. Arlne Busness, September ssue, Goolsbee A (2005) Tragedy of the arport. Howarth G, O_Tool K (2005) Expect delays. Arlne Busness, July ssue, Internatonal Ar Transportaton Assocaton (IATA) (2004) Worldwde schedulng gudelne Kang L (2004) Degradable arlne schedulng: an approach to mprove operatonal robustness and dfferentate servce qualty. PhD thess, Massachusetts Insttute of Technology Luo S, Yu G (1997) On the arlne schedule perturbaton problem caused by the ground delay program. Transp Sc 31(4): Mederer M, Frank M (2002). Increasng robustness of flght schedules through stochastc modelng of plannng parameters. AGIFORS Arlne Operatons Conference (Downloadable from webste: MIT (2005) MIT extensble ar network smulaton. Mukherjee A, Lovell D, Ball M, Odon A, Zerbb G (2004) Modelng delays and cancellaton probabltes to support strategc smulatons. NEXTOR (Downloadable from webste: Rexng B, Barnhart C, Knker T, Jarrah A, Krshnamurthy N (2000) Arlne fleet assgnment wth tme wndows. Transp Sc 34(1):1 20 Sunday Tmes (2000, August 13) Arlne extend flght tmes to conceal growng delays Teodorovc D, Stojkovc G (1995) Model to reduce arlne schedule dsturbances. J Transp Eng 121: Watterson A, De Proost D (1999) On-tme performance: operatonal challenges for arlnes. Mercer on Transport (Downloadable from webste: Wu C-L (2005) Inherent delays and operatonal relablty of arlne schedules. J Ar Transp Manag 11: Yan S, Young H-F (1996) A decson support framework for mult-fleet routng and mult-stop flght schedulng. Transp Res 30A: