Reactive Methods to Solve the Berth AllocationProblem with Stochastic Arrival and Handling Times

Transcription

1 Reacve Mehods o Solve he Berh AllocaonProblem wh Sochasc Arrval and Handlng Tmes Nsh Umang* Mchel Berlare* * TRANSP-OR, Ecole Polyechnque Fédérale de Lausanne Frs Workshop on Large Scale Opmzaon November 21-22, 2012, Vevey, Swzerland

2 Conens Movaon Research Objecves Bref Leraure revew Problem Saemen Mehodology Compuaonal Resuls Conclusons and Fuure Work

3 Movaon Hgh level of uncerany n por operaons due o weaher condons, mechancal problems ec. Dsrup he normal funconng of he por Requre quck real me acon. Very few sudes address he problem of real me recovery n por operaons, whle he problem has no been sudedd a all n conex of bulk pors. Our research problem derves from he realsc requremens a he SAQR por, Ras Al Khamah, UAE

4 Research Objecves Develop real me algorhms allocaon problem(bap) for dsrupon recovery n berh For a gven baselne berhng schedule, mnmze he oal realzed coss of he updaed schedule as acual arrval and handlng me daasrevealednrealme.

5 Leraure Revew Very scarce sudes on real me and robus algorhms n conaner ermnals. To he bes of our knowledge, no leraure on bulk pors. OR leraure relaed o BAP under uncerany n conaner ermnals Pro-acve Robusness Sochasc programmng approach usedbyzheneal.(2011), Haneal.(2010) Defne surrogae problems o defne he sochasc naure of he problem: Moorhy and Teo (2006),ZhenandChang(2012),Xueal.(2012)and Hendrkseal.(2010) Reacve approach or dsrupon managemen Zeng e al.(2012) and Du e al. (2010) propose reacve sraeges o mnmze he mpac of dsrupons.

6 Schemac Dagram of a Bulk Termnal YARD SPACE cargo blocks w= 11 ROCK FACTORY CONVEYOR w= 12 OIL TANK TERMINAL PIPELINE w= 2 SILICA SAND w= 4 CLAY w= 6 SODA ASH w= 8 CEMENT w= 10 COAL w= 1 ANIMAL FEED w= 3 GRAIN w= 5 ROCK AGGREGATES w= 7 FELDSPAR w= 9 LIMESTONE secons along he quay k = 1 k = 2 k = 3 k = 4 Vessel berhed a secon k=5 carryng cemen k = 5 k = 6 k = 7 k = 8 QUAY SPACE Vessel 1 Vessel 2 Vessel 3

7 Baselne Schedule Any feasble berhng assgnmen and schedule of vessels along he quay respecng he spaal and emporal consrans on he ndvdual vessels Bes case: Opmal soluon of he deermnsc berh allocaon problem (whou accounng for any uncerany n nformaon)

8 Deermnsc BAP: Problem Defnon Fnd Gven Opmal assgnmen and schedule of vessels along he quay (whou accounng for any uncerany) Expeced arrval mes of vessels Esmaed handlng mes of vessels dependen on cargo ype on he vessel (he relave locaon of he vessel along he quay wh respec o he cargo locaon on he yard) and he number of cranes operang on he vessel Objecve Mnmze oal servce mes (wang me + handlng me) of vessels berhng a he por Resuls Near opmal soluon obaned usng se paronng mehod or heursc based on squeaky wheel opmzaon for nsances conanng up o 40 vessels

9 Real Tme Recovery n Berh Allocaon Problem

10 Problem Defnon: Rea Objecve: For a gven baselne ber realzed coss of he acual berhng n real me Z Z Z Z mn + + = ) ' ( 3 3 = o N w c Z ) ( ) ' ( ( = u N c k b k b c Z ) ) ' ( ' ( 1 + = u N k h a m Z al me recovery n BAP rhng schedule, mnmze he oal g schedule as acual daa s revealed ) ' 2 e e µ Servce cos of unassgned vessels Cos of re-allocaon of unassgned vessels Berhng delays o vessels arrvng on-me

11 Problem Defnon: Real me recovery n BAP Key arrval dsrupon paern n real me For each vessel ϵn, we are gven an expeced arrval me A whch s known n advance. The expeced arrval me of a gven vessel may be updaed F mes durng he plannng horzon of lengh H a me nsans 1, 2 F such ha 0 1 < 2 < 3. (F-1 1) < F < a where a s he acual arrval me of he vessel, and he correspondng arrval me updae a me nsan F s A F for all ϵn. Acual handlng me of a vessel s revealed a he me nsan when he handlng of he vessel s acually fnshed

12 Modelng he Uncerany Uncerany n arrval mes Arrval mes are modeled usng a unform dsrbuon. Acual arrval me a of vessel les n he range [A -V, A +V], where A s he expeced arrval me of vessel a he sar of he plannng horzon. A any gven me nsan n he plannng horzon, he followng 3 cases arse Case I : vessel has arrved and he acual arrval me a s known Case II : he vessel hasn arrved ye bu he expeced arrval me A s known Case III : neher he acual nor he expeced arrval me s known a me nsan, hen he arrval me esmae a a me nsan s such ha a [, A + V ], and s deermned from he followng equaon Pr ob( a a ) = ρ a Snce he arrval me of vessel s assumed o be unformly dsrbued, a = + ρ a ( A A + V )

13 Modelng he Uncerany Uncerany n handlng mes Handlng mes are modeled usng a runcaed exponenal dsrbuon. Handlng me h (k) of vessel berhed a sarng secon k les n he range [H (k), γh (k)], where H (k) s he esmaed (deermnsc) handlng me of vessel berhed a sarng secon k A any gven me nsan n he plannng horzon, he followng 3 cases arse Case I : he handlng of vessel berhed a sarng secon k s fnshed, hen he acual handlng me h (k ) s known Case II : he vessel s beng handled a me nsan, hus he acual berhng poson k of he vessel s known, bu he acual handlng me s unknown. The handlng me esmae a me nsan s gven by Pr ob ( h ( k ' ) h ( k ' )) = Case III : he vessel s no assgned ye, n whch case he handlng me of he vessel a me nsan for any berhng poson k s gven by Pr Snce he handlng mes follow a runcaed exponenally dsrbuon, ob ( h ( k ) h ( k )) = ρ h ρ h h ( k ) = 1 / λ ln( e λ h L ( k ) ρ h ( e λ h L e U ( k ) λ h ( k ) ))

14 Soluon Algorhms Opmzaon Based Recovery Algorhm Re-opmze he berhng schedule of all unassgned vessels usng se-paronng approach every me here s a dsrupon arrval me of any vessel s updaed and devaes from s prevous expeced value. handlng of any vessel s fnshed and devaes from he esmaed value he fuure vessel arrval and handlng mes provded as npu parameers are modeled as dscussed earler he berhng assgnmen of all vessels ha have already been assgned o he quay s consdered frozen and unchangeable Smar Greedy Recovery Algorhm Assgn an ncomng vessel o he quay as arrves as soon as berhng space s avalable, o he secon(s) a whch he oal realzed cos of all he unassgned vessels a ha nsan s mnmzed by modelng he uncerany n fuure vessel arrval and handlng mes of oher vessels Vessel s assgned a or afer he esmaed berhng me of he vessel (as per he baselne schedule) In he deermnaon of he oal realzed cos o assgn a gven vessel a a gven se of secon(s), all oher unassgned vessels are assgned o he esmaed berhng secons as per he baselne schedule

15 Benchmark Soluons Greedy Recovery Algorhm Assgn he vessels as hey arrve as soon as berhng space s avalable. Any gven vessel s assgned a hose se of secons where he realzed cos of assgnng s mnmzed No need o model uncerany n fuure arrval and handlng mes Closely represens he ongong pracce a he por Apror Opmzaon Approach Assume ha all arrval and handlng delay nformaon s avalable a he sar of he plannng horzon Problem of real me recovery reduces o solvng he deermnsc berh allocaon problem wh he objecve funcon o mnmze oal realzed cos of he schedule Provdes a lower bound o he mnmzaon problem of real me recovery beng solved

16 Arrval Dsrupon Scenaro Vessel EAT Vessel 0: 23(21) ATA:26 Vessel 1: 9(2) 14(4) 17(5) ATA:8 Vessel 2: 24(3) 31(7) 15(9) 21(12) 24(13) 16(14) 30(15) 32(16) 21(17) 20(18) 20(19) 21(20) ATA:21 Vessel 3: 22(8) ATA:10 Vessel 4: 16(1) 16(2) ATA:6 Vessel 5: 19(8) 12(10) 15(13) 24(14) 24(15) 18(16) 20(17) 24(18) 22(19) 22(20) ATA:21 Vessel 6: 15(8) ATA:16 Vessel 7: 3(1) 10(6) 13(7) 19(10) 32(11) 23(12) 22(13) 19(14) 26(15) 32(16) 31(17) 31(18) 29(19) 21(20) ATA:21 Vessel 8: 29(1) 20(2) 19(4) 9(5) ATA:7 Vessel 9: 3(2) ATA:20 Vessel 10: 10(1) 15(6) 8(7) 14(8) 13(9) 16(10) ATA:11 Vessel 11: 23(6) 18(7) 15(9) 12(10) 16(11) 20(12) ATA:13 Vessel 12: 29(1) ATA:10 Vessel 13: 5(0) 8(6) ATA:9 Vessel 14: 17(2) 27(4) 13(9) 26(15) 22(16) 27(17) 27(18) 33(19) 25(20) 23(21) 34(22) ATA:23 Vessel 15: 19(2) 12(4) 7(5) 7(6) 29(7) 29(9) 16(10) 20(11) 20(12) 24(13) 28(14) ATA:15 Vessel 16: 15(6) 10(8) 11(9) 28(10) 27(11) 29(12) 16(13) 15(14) ATA:15 Vessel 17: ATA:-12 Vessel 18: 29(8) 13(9) 25(10) 30(12) 34(13) 18(14) 25(15) 20(16) 29(17) 34(18) 34(19) ATA:20 Vessel 19: ATA:-15 Vessel 20: ATA:-1 Vessel 21: 7(6) 20(9) 25(14) 24(19) 22(20) 27(21) 23(22) 26(23) ATA:24 Vessel 22: 12(0) ATA:5 Vessel 23: 21(5) 14(6) 13(7) 10(8) 10(9) 24(13) 19(14) 17(15) 27(16) ATA:17 Vessel 24: ATA:-1

17 Compuaonal Resuls N =10 vessels, M = 10 secons, c 1 = c 3 = 1.0, c 2 = 0.002, U= 4 hours, V= 5, γ= 1.1 Mean Gap wh respec o he apror opmzaon soluon Greedy Approach Opmzaon based Approach Smar Greedy Approach 7.65% 3.16% 7.81%

18 Compuaonal Resuls N =25 vessels, M = 10 secons, c 1 = c 3 = 1.0, c 2 = 0.002, U= 4 hours, V= 5, γ= 1.1 Mean Gap wh respec o he apror opmzaon soluon Greedy Approach Opmzaon based Approach Smar Greedy Approach % % %

19 Compuaonal Resuls N =10 vessels, M = 10 secons, c 1 = c 3 = 1.0, c 2 = 0.002, U= 4 hours, V= 10, γ= 1.1 Mean Gap wh respec o he apror opmzaon soluon Greedy Approach Opmzaon based Approach Smar Greedy Approach % 3.06 % 8.56 %

20 Compuaonal Resuls N =25 vessels, M = 10 secons, c 1 = c 3 = 1.0, c 2 = 0.002, U= 4 hours, V= 10, γ= 1.1 Mean Gap wh respec o he apror opmzaon soluon Greedy Approach Opmzaon based Approach Smar Greedy Approach % % %

21 Compuaonal Resuls N =25 vessels, M = 10 secons, c 1 = c 3 = 1.0, c 2 = 0.002, U= 4 hours, V= 24, γ= 1.2 Mean Gap wh respec o he apror opmzaon soluon Greedy Approach Opmzaon based Approach Smar Greedy Approach % % %

22 Conclusons and Fuure Work Modelng he uncerany n fuure vessel arrval and handlng mes can sgnfcanly reduce he oal realzed coss of he schedule, n comparson o he ongong pracce of re-assgnng vessels a he por. The opmzaon based recovery algorhm ouperforms he heursc based smar greedy recovery algorhm, bu s compuaonally expensve. Lmaon: Modelng of uncerany fals o produce good resuls for larger nsance sze or when he sochascy n arrval mes and/or handlng mes s oo hgh. As par of fuure work, plan o develop a robus formulaon of he berh allocaon problem wh a ceran degree of ancpaon of varably n nformaon.

23 Thank you!

24 Problem Defnon: Real me recovery n BAP Penaly Cos on lae arrvng vessels: Impose a penaly fees on vessels arrvng beyond he rgh end of he arrval wndow, A +U Penaly Cos Arrval TmeWndow = 2U g c 3 g slope = c 3 A -U A A +U a Acual Arrval Tme