An Investgaton of Shared Gate Assgnment Case study n Termnal C of Boston s Logan Internatonal Arport nal Presentaton, 8 December 2009 Gerasmos Skaltsas
An Investgaton of Shared Gate Assgnment Case study n Termnal C of Boston s Logan Internatonal Arport OBJECTIVE: Estmate the mnmum requred number of gates n Termnal C for dfferent scenaros METHODOLOGY: Development of a lnear Integer Program Constructon of nput database Run model under dfferent scenaros (traffc, buffer tmes, maxmum allowed walkng dstance Gerasmos Skaltsas page 1
Termnal C Unted 10 JetBlue 9 Artran 3 Mdwest 1 Cape Ar 1 MASSPORT 4 C14 Jet Blue C 27 Cape Ar Eagl e Termnal B Ar Canada 3 US Arways 18 Amercan 16 Vrgn Am. 1 MASSPORT 1 Termnal E Southwest 2 MASSPORT 11 Termnal A Delta 22 Contnental 7 Gerasmos Skaltsas page 2
ORMULATION O LINEAR INTEGER PROBLEM SETS: G: Set of gates : Set of arcraft K ={1,2,3,4,5,6}: Set of arlnes r PARAMETERS: arr[]: the arrval tme of arcraft dep[]: the departure tme of arcraft gf[]: the AA arcraft group of arcraft group[]: the largest arcraft group that can be assgned to gate dst[,k]: the dstance between gates and k car[,r]: r f arcraft s operated by carrer r, 0 f operated by another carrer DECISION VARIABLES: X[]: 1 f gate s used durng the day, 0 f t remans unused ]: 1 f arcraft s assgned to gate, 0 f t s assgned to another gate OBJECTIVE UNCTION: MINIMIZE Gerasmos Skaltsas page 3
CONSTRAINTS: 1) When arcraft s assgned to gate (]=1) X[] = 1, otherwse X[] = 0 X[ ] ], G, X[ ] ], G n G 2) Every arcraft s assgned to one and only one gate ] 1, n G 3) Each arcraft must be assgned to a gate capable to accommodate the arcraft (AA group) ] gf[] group[], G, 4) No arcraft arrvng earler than the departure of arcraft m + buffer tme can be assgned smultaneously to the same gate wth arcraft m ] m] 1, G,, m m, arr[] dep[m] buffer 5) All flghts of the same carrer must be assgned to gates wthn a specfed dstance range ] Y[k, m] 1, k G, m, r K k, dst[, k] max d, car[,r] car[m, r] 0 Gerasmos Skaltsas page 4
number of movements DATABASE: 1. busest day of the year, rday, 5 October, n total 979 movements, (Columbus day, 8 October) 2. the day that matches to the 15 th percentle of traffc n descendng order, 8 August, n total 909 movements. 3. the medan day, 12 January, n total 855 movements 80 70 60 50 40 30 Average number of movements n Logan (2007) Dataset nput: only flghts assgned to gates between 13:00 and 20:00 Number of constrants decreased (473,746 constrants) Maxmum processng tme 6 hours 20 10 0 Otherwse (all flghts ncluded) processng tme could be > 23 hours or some scenaros ILOG OPL run out of memory (> 1,200,000 constrants) Gerasmos Skaltsas page 5
EXTRACTING THE GATE-IN and GATE-OUT TIMES OR EACH AIRCRAT Scheduled (and actual) gate departure and arrval tmes for all flghts of each day (AA ASPM). All successve flghts wth dentcal arcraft tal numbers are matched Based on specfc crtera : exstence of precedng or followng flght (wth dentcal arcraft tal number) flghts depart from Logan flghts arrves to Logan a set of scheduled (and actual) gate-n and gate-out tmes s computed for each arcraft LIGHTS AIRCRAT AACAR LTNO TAILNO ETMS_EQPT DEP_LOCID ARR_LOCID SCHOUTTM SCHINTM GATE IN GATE OUT GROUP UAL 424 N542UA B752 IAD BOS 12:13 13:45 UAL 181 N542UA B752 BOS SO 14:57 18:23 13:45 14:57 4 UAL 584 N544UA B752 DEN BOS 10:32 16:30 UAL 543 N544UA B752 BOS ORD 17:37 19:03 16:30 17:37 4 UAL 170 N546UA B752 SO BOS 06:25 14:47 UAL 715 N546UA B752 BOS DEN 16:14 18:36 14:47 16:14 4 Procedure appled to: all flghts of Unted, JetBlue, ArTran, Cape Ar and Mdwest any other flght that departed or arrved to Termnal C (based on lghtstat data) Gerasmos Skaltsas page 6
MINIMUM REQUIRED NUMBER O GATES OR EACH SCENARIO B U E R T I M E MAXIMUM WALKING DISTANCE (meters) no constr. 400 300 200 100 no constr. 400 300 200 100 BUSIEST DAY, scheduled tmes (84 arcraft) BUSIEST DAY, actual tmes (81 arcraft) 0 mn 19 19 19 19 20 20 20 20 20 20 10 mn 20 20 20 20 20 21 21 21 21 21 20 mn 23 23 23 23 24 23 23 23 23 25 30 mn 26 26 26 26 28 25 25 25 25 27 40 mn 28 28 28 nfeasble nfeasble 28 28 28 28 nfeasble 50 mn nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble 60 mn nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble nfeasble 15th BUSIEST DAY, scheduled tmes (80 arcraft) 15th BUSIEST DAY, actual tmes (74 arcraft) 0 mn 15 15 15 15 15 17 17 17 17 17 10 mn 17 17 17 17 17 19 19 19 19 19 20 mn 19 19 19 19 20 20 20 20 20 22 30 mn 21 21 21 25 27 21 21 21 24 26 40 mn 23 23 24 25 27 23 23 24 24 27 50 mn 25 25 25 25 28 24 24 26 26 28 60 mn 26 26 27 nfeasble nfeasble 26 26 26 27 nfeasble MEDIAN, scheduled tmes (77 arcraft) MEDIAN, actual tmes (70 arcraft) 0 mn 15 15 15 15 19 18 18 18 18 20 10 mn 17 17 17 17 17 19 19 19 19 20 20 mn 19 19 19 19 20 19 19 19 19 21 30 mn 20 20 20 20 23 22 22 22 23 25 40 mn 23 23 23 23 25 23 23 24 24 27 50 mn 25 25 25 25 nfeasble 24 24 24 25 28 60 mn 26 26 26 27 nfeasble 27 27 27 28 nfeasble Gerasmos Skaltsas page 7
RESULTS: 1. The requred number of gates ncreases by the number of arcrafts 2. The gate assgnment for the actual tmes requres a hgher number of gates compared to the scheduled tmes, even for lower traffc reason: the actual tme that an arcraft occupes a gate, s hgher than the scheduled tme ( 65 mnutes average actual tme, 55 mnutes average scheduled tme) 3. In all cases an ncrease n buffer tmes results n ncreased number of gates 4. or buffer tmes 20 mnutes the optmal solutons s not affected by any dstance constrant 5. When the maxmum allowed dstance s greater than 200 meters the optmal soluton s not affected by the dstance constrant. 6. or buffer tmes 30 mnutes, lmtng the maxmum allowed dstance to less than 100 meters results to a maor ncrease of the optmal soluton (or the problem becomes nfeasble) Gerasmos Skaltsas page 8
CONCLUSIONS: Shared use of gates can result to a sgnfcant decrease n gate demand Accordng to the actual gate assgnment for the three studed days (lghtstat): all 28 gates were used and the walkng dstances between the gates were: 150 meters for Unted Arlnes and 400 meters for Jet Blue or a ratonal buffer tme of 30 mnutes the reducton n requred gates can be: Up to 8 gates n an average day Up to 2 gates even for the busest day of the year Benefts: Reducton n constructon cost (Reducton n operatng cost???) Dsadvantages: Less flexblty for maor carrers (Decentralzaton of operatons???) Gerasmos Skaltsas page 9
QUESTIONS?????? Gerasmos Skaltsas page 10