The Coastal Seaspace Sector Design and Allocation Problem
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1 The Catal Seapace Sect Degn and Allcatn Pblem Ban J. Lunday 1 Hanf D. Sheal 2 Ken E. Lunday 3 1 Depatment f Mathematcal Scence Unted State Mltay Academy 2 Gad Depatment f Indutal and Sytem Engneeng gna Tech 3 Headquate U.S. Cat Guad* embe *The ew expeed heen ae the f the auth and d nt epeent the ew f the Cmmandant n any unt f the U.S. Cat Guad.
2 Pblem Statement Gen: A et f matme eel f patllng a catal eapace A egn f eapace wthn 200 nm f the a catlne A dcetzatn f the eapace nt aea A et f htcal demand f each aea A numbe f aea n t be agned t each eel Fnd: A mdel that agn n aea t a ect f each eel uch that 1. The aea fm cntguu ect 2. We mnmze a cnex cmbnatn f the: Maxmum deatn f eel agned htcal demand fm t pptnally expected demand Maxmum tme fm a eel hme pt t the fathet aea n t ect Maxmum tme-baed pan f the eel ect (Sme elated* pblem: plce ect degn ale tety degn chl dtctng pltcal dtctng nw emal ect degn 2
3 What de th pblem l le? The Seapace (Stat f Flda 7520 nm 2 The eel Hme Pt Cung Speed (nt Rel. Cap.* 1-2 Ft Pece FL Dana Beach FL Mam FL Key Wet FL Ft Mye Beach FL San Juan PR Mam FL San Juan PR Key Wet FL Mam FL 21 3 * Detemned a AHP Dcetze the eapace f agnment (Saaty 1990; Yuef and Dnhue
4 Ou mdelng appach: Cntuct a pannng abecence Ceate atfcal nde: t nde f each eel Decn aable: 1f aea agned 1f t eel 0 /w ac ( n the abecence cntucted f eel 0 /w A 4
5 Pgammng Fmulatn t Cntuct a Spannng Abecence (becte functn elated calculatn (enfce cntguty (becte functn mn ( A A n t Cnnect the t nde t nly ne aea n t tee Indegee=1 f aea agned t eel Ac eque bth nde t be agned t Agn n aea t eel Agn each aea t ne-and-nly-ne eel The tcy pat! S hw hall we enfce cntguty Wlad pan dtance Bnay etctn
6 Cntguty Cntant en #1 Subtu Elmnatn Cntant A( S S S S 2 S n The numbe f ac n a ubet 1 The numbe f aea wthn a ubet n a eel tee (f at leat ne aea agn d t eel F eey ubet f aea that culd be n a eel tee F eey eel S (Lucena and Reende
7 Cntguty Cntant en #2 (a & b STP-RLT ew decn aable: Cntant: u u 1 u 0 u n.f nde u 1 n ac. n dected path fm t t nde A Fx the ac cunt f the t nde f the abecence Bund the ac cunt Incement cunt baed n cntucted ac Pptn. Tanfmatn a Refmulatn Lneazatn Technque (RLT yeld tw altenate equalent lnea epeentatn. (Haua et al. 2010; Mlle et al. 1960; Sheal and Adam 1990 and 1994; Sheal and Dcll
8 Cntguty Cntant en #3 Multcmmdty Flw A ( aea that eache cmmdty f flw n ac ( ew decn aable: Cntant:. ( 0 \ 0 ( 0 ( ( ( A A Outflw f ne unt fm t nde Inflw f ne unt nt nde Cneatn f flw at all the nde Outflw fm nde 0 Flw can nly be nnze f ac ( n the abecence f 8 (Haua et al. 2010
9 Mdelng Enhancement Symmety Defeatng Cntant 1A Smallet ndexed agned nde a the tual t nde 1B Weae but me cmpact en f 1A 2 Defeat the ymmety amng the le eel wth ame ptage Obecte Functn Petubatn n-peemptely weght the ymmety defeatng cntant( 9 : 1 n : mn 1 : W w w (Ghnem and Sheal 2011; Sheal and Syte 1983
10 Cmpaate Tetng 4 altenate fmulatn 3 altenate f lutn enhancement technque Dect CPLEX applcatn (.e. nne CPLEX ymmety beang technque n-heachcal becte petubatn 6 cmbnatn f 3 ymmety defeatng cntant 2 methd egadng the aea nde cnnected t t nde 1 methd egadng le-eel ymmety Implementatn Ennment C++ nng CPLEX 12.1 Intel Mdel T7100 Pce wth 4GB RAM 10
11 Cmpaate Tetng Reult (1 f 3 Mdelng Statege (6 h CPU tme =5% Stategy Feable Slutn -ptmal Slutn Bet Slutn Subtu Elmnatn 100% 82.4% 5.9% STP-RLT #1 100% 82.4% 47.1% STP-RLT #2 100% 82.4% 41.1% Multcmmdty Flw* 31.3% 6.0% 5.9% MC Flw efmulatn nly tactable when: Inng ymmety defeatng cntant( n-peemptely petubng the becte functn Obecte functn petubatn (6 h CPU tme =5% Technque Feable Slutn -ptmal Slutn Bet Slutn ne; CPLEX default ettng 75% 70.8% 10% n-peempte 100% 45.0% 60% CPLEX ymmety beang ptn 75% 70.8% 30% 11
12 Cmpaate Tetng Reult (2 f 3 Symmety Defeatng Cntant (6 h CPU tme =5% Mdelng Feable Slutn -ptmal Slutn Bet Slutn Rt de #1 83.3%* 83.3% 8.3% Rt de #2 83.3%* 58.3% 33.3% Le eel 83.3%* 33.3% 33.3% Rt de #1 & Le eel Rt de #2 & Le eel 83.3%* 75.0% 8.3% 83.3%* 58.3% 0% * MC Flw efmulatn nly tactable when nn-peemptely petubng the becte functn Same pefmance tend cnfmed e aant f the ntance baed n alteng The elate ptmalty gap Tme cmputatnal tme lmt The eel et (hghe demand lad pe eel The htcal demand et (a dtbuted e the eapace 12
13 Cmpaate Tetng Reult (3 f 3 A cle l at the tp fu cmbnatn (24 h CPU tme =1% Cntguty Mdelng Symmety Defeat Mech. Ob. Pet CPU Tme (h Aued Opt Gap STP-RLT #1 Rt de #2 n-pe %* STP-RLT #2 Rt de #2 n-pe %* STP-RLT #2 Rt de #2 & Le eel n-pe % Subtu Elmn. ne n/a % * Wthn % f ptmal baed n aued ptmalty gap f fnal lutn Same pefmance tend cnfmed e aant f the ntance baed n alteng The eel et (hghe demand lad pe eel The htcal demand et (a dtbuted e the eapace 13
14 Cnclun & Futue Reeach Cnclun STP-RLT efmulatn f mplementatn t btan a nea-ptmal lutn STP-RLT efmulatn cmbned wth ymmety defeat cntant and becte petubatn ae pmng a heutc Futue Reeach Lage ntance (and/ tghte dcetzatn Altenate methd t dcetze the eapace Mdfcatn f AHP eel atng t defeat ymmety Allw f altenate ptage f eel 14
15 Quetn 15
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