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1. Analityczny Proces Hierarchiczny
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Rysunek 1. Struktura hierarchiczna
ħUyGáRRSUDFRZDQLHZáDVQHQDSRGVWDZLHàXF]DN:\VRFNLV :QDVWĊSQ\PHWDSLHLVWRWQąUROĊRGJU\ZDMąHNVSHUFLRUD]LFKLQG\ZLGXDOQHSUHIHUHQFMH :PHWRG]LH$+3SUHIHUHQFMHGHF\GHQWDRNUHĞODQHVąSU]\SRPRF\Z]JOĊGQ\FKRFHQZDĪQRĞFL NU\WHULyZLZDULDQWyZ2GE\ZDVLĊWRQD]DVDG]LHSRUyZQDQLDSDUDPLF]\QQLNyZ]WHJRVDPHJR SR]LRPXZ]JOĊGHPNU\WHULXPNWyUH]QDMGXMHVLĊEH]SRĞUHGQLRZ\ĪHM2WU]\PDQHZWHQVSRVyE Z\QLNLSRUyZQDĔSDUDPLPRĪQD]DSLVDüZPDFLHU]\SUHIHUHQFML7ZyUFDPHWRG\]DSURSRQRZDá ZFHOXZ\UDĪHQLDRFHQG]LHZLĊFLRVWRSQLRZąVNDOĊ%RGLQ*DVVV-HVWWRNOXF]RZ\ PRPHQWNWyU\SR]ZDODZVSRVyELORĞFLRZ\GRNRQDüW\FKSRUyZQDĔ.DĪGHPXVWRSQLRZLZVND OL]RVWDáRSU]\SLVDQH]QDF]HQLHVáRZQHFREDUG]RXáDWZLDSRVWĊSRZDQLHSRGF]DVGRNRQ\ZDQLD RFHQHNVSHUWPRĪHQDMSLHUZGRNRQDüSRUyZQDQLDZHUEDOQLHSyĨQLHMGRSLHURSU]\SLVDüRGSR ZLHGQLąZDUWRĞüOLF]ERZą
Tabela 1. 6NDOD6DDW\CHJR Skala 2EMDĞQLHQLH EUDNPRĪOLZRĞFLZ\UyĪQLHQLDHOHPHQWXGRPLQXMąFHJR MHGHQ]HOHPHQWyZPDQLH]QDF]QLHZLĊNV]H]QDF]HQLH Z\UDĨQDSU]HZDJDMHGQHJR]HOHPHQWyZQDGGUXJLP EDUG]R]QDF]ąFDSU]HZDJDMHGQHJR]HOHPHQWyZQDGGUXJLP DEVROXWQDSU]HZDJDMHGQHJR]HOHPHQWyZQDGGUXJLP ZDUWRĞFLSRĞUHGQLHVWRVXMHVLĊJG\Z\VWĊSXMHSUREOHP]MHGQR]QDF]Q\PXĪ\FLHPNWyUHJRĞ ]HOHPHQWyZVNDOLSRZ\ĪHM 2GZURWQRĞFL GODSRUyZQDĔZSU]HFLZQąVWURQĊ ħUyGáRRSUDFRZDQLHZáDVQHQDSRGVWDZLH6DDW\V .ROHMQ\PNURNLHPZSURFHGXU]HMHVWZ\]QDF]HQLHSULRU\WHWyZJOREDOQ\FKLORNDOQ\FKGOD SRV]F]HJyOQ\FKHOHPHQWyZVWUXNWXU\-HGQDNDE\MHREOLF]\üQDOHĪ\QDMSLHUZ]QDOHĨüZHNWRU\ ZáDVQHRUD]ZDUWRĞFLZáDVQHPDFLHU]\SRUyZQDĔZ\NRU]\VWXMąF]DJDGQLHQLD]DOJHEU\OLQLRZHM 6DDW\]DSURSRQRZDáNLONDLQQ\FKPHWRGNWyUHZVSRVyEPQLHMVNRPSOLNRZDQ\GDMąSU]\EOLĪRQH Z\QLNL-HGQD]QLFKSROHJDQDSU]HPQRĪHQLXSU]H]VLHELHZV]\VWNLFKHOHPHQWyZ]NDĪGHJR ]ZLHUV]\RGG]LHOQLHRUD]Z\FLąJQLĊFLHGODNDĪGHJRLORF]\QXSLHUZLDVWNDNWyUHJRVWRSLHĔMHVW UyZQ\OLF]ELHW\FKHOHPHQWyZDFR]DW\PLG]LH±WDNĪHVWRSQLRZLPDFLHU]\]HZ]JOĊGXQDWR ĪHZV]\VWNLHDQDOL]RZDQHPDFLHU]HPXV]ąE\üV\PHWU\F]QH:NROHMQ\PNURNXX]\VNDQHZ\ QLNLQRUPDOL]XMHVLĊGRMHGQRĞFLSRSU]H]SRG]LHOHQLHLFKSU]H]VXPĊZV]\VWNLFKSLHUZLDVWNyZ RWU]\PDQ\FKZF]HĞQLHM7DNRWU]\PDQH]QRUPDOL]RZDQHZ\QLNLVąSU]\EOLĪRQ\PLZHNWRUDPL ZáDVQ\PLPDFLHU]\6DDW\.HDUQVV±:OLWHUDWXU]HPHWRGDWDQD]\ZDQDMHVWPH WRGąORJDU\WPLF]Q\FKQDMPQLHMV]\FKNZDGUDWyZOXEĞUHGQLHMJHRPHWU\F]QHM=QDQHVąMHGQDN UyZQLHĪLQQHSRGHMĞFLDPLQPHWRGDQDMPQLHMV]\FKNZDGUDWyZVXPNROXPQRZ\FKPHWRG\ ZDĪRQHXNáDG\UyZQDĔOLQLRZ\FKRSDUWHQDPLQLPDOL]DFMLRGOHJáRĞFL=DNDULD'DKODQ+XVVLQ V 2EOLF]RQHZNWyU\Ğ]Z\ĪHMZ\PLHQLRQ\FKVSRVREyZZHNWRU\ZáDVQHVąW]ZSULRU\WHWDPL ORNDOQ\PL1DQDMZ\ĪV]\PSR]LRPLHVWUXNWXU\F]\OLSR]LRPLHSRUyZQDĔNU\WHULyZZ]JOĊGHP FHOXJáyZQHJRSULRU\WHW\ORNDOQHVąMHGQRF]HĞQLHJOREDOQ\PLLZ\UDĪDMąWRNWyUH]Z\PLHQLR Q\FKNU\WHULyZPDQDMZLĊNV]H]QDF]HQLHZNRQWHNĞFLHVIRUPXáRZDQHJRFHOX1DQDMQLĪV]\P SR]LRPLH JG]LH XPLHMVFRZLRQH Vą ZDULDQW\ GHF\]\MQH SRVWĊSXMH VLĊ SRGREQLH :LHONRĞFL Vą EDUG]RZDĪQHJG\ĪáąF]ąRQH]HVREąHOHPHQW]QDMZ\ĪV]HJRSR]LRPX]HOHPHQWDPLSR]LRPX QDMQLĪV]HJRFRVSUDZLDĪHFDáDVWUXNWXUDMHVWVSyMQąFDáRĞFLą3ULRU\WHW]QDMZ\ĪV]ąZDUWRĞFLą X]QDMHVLĊ]DQDMNRU]\VWQLHMV]\$GDPXVàDVDNV±
.ROHMQ\PLZDUWRĞFLDPLX]\VNLZDQ\PL]G]LDáDĔSU]HSURZDG]DQ\FKQDPDFLHU]DFKSRUyZ QDĔVąȜmax , indeks C.I. (Consistency IndexRUD]ZVSyáF]\QQLNC.R. (Consistency Ratio1DM
ZLĊNV]DZDUWRĞüZáDVQDPDFLHU]\F]\OLȜmax = max{Ȝ1, Ȝ2, Ȝ3, ..., Ȝn`JG]LHn – liczba pierwiast
NyZZLHORPLDQXFKDUDNWHU\VW\F]QHJRRNUHĞODVWRSLHĔ]JRGQRĞFLSRUyZQDĔSDUDPLF]\OLWRF]\ VąRQHNRQVHNZHQWQHLQLHZ\NOXF]DMąVLHELHQDZ]DMHP:OLWHUDWXU]H]DOHFDVLĊDE\Ȝmax = n
ZDUWRĞüZáDVQDPDFLHU]\MHVWUyZQDU]ĊGRZLPDFLHU]\SRQLHZDĪZyZF]DVZ\VWĊSXMHFDáNRZL WD]JRGQRĞüRFHQ6DDW\2]GHPLUV
Na podstawie ȜmaxREOLF]DVLĊLQGHNVQLH]JRGQRĞFLF]\OLSR]LRPRGFK\OHQLDRGSRĪąGDQHM
VSyMQRĞFL:\UDĪDVLĊJRZ]RUHP CI = (Ȝmax – n) n – 1 1DSRGVWDZLHWHJRLQGHNVXEXGXMHVLĊZVSyáF]\QQLNC.R.NWyU\MHVWáDWZLHMV]\ZLQWHUSUHWDFML JG\ĪZSURFHQWDFKZ\UDĪDZMDNLPVWRSQLXSRUyZQDQLDHOHPHQWyZGDQHJRSR]LRPXVWUXNWXU\ VąQLH]JRGQHZ]JOĊGHPVLHELHEUDNNRQVHNZHQFMLZLFKDQDOL]LH2EOLF]DVLĊJR]HZ]RUX C.R. î C.I. R.I. JG]LH]DR.I.DQJRandom IndexSU]\MPXMHVLĊW]ZORVRZ\LQGHNVQLH]JRGQRĞFL-HVWRQRE OLF]DQ\]SUyE\QDNWyUąVNáDGDMąVLĊORVRZRZ\EUDQHPDFLHU]H$GDPXVàDVDNV Tabela 2. :DUWRĞFLZVSyáF]\QQLND5,GODSUyE\ n 5, ħUyGáRRSUDFRZDQLHZáDVQHQDSRGVWDZLH6DDW\2]GHPLUV =DOHFDVLĊDE\ZDUWRĞüZVSyáF]\QQLNDQLH]JRGQRĞFLGODPDFLHU]\RZ\PLDUDFKZLĊNV]\FK QLĪîQLHE\áDZLĊNV]DQLĪGODPDFLHU]\î±QDWRPLDVWGODPDFLHU]\î± 3U]HNURF]HQLHW\FKSURJyZZVND]XMHQDWRĪHRFHQ\QLHVąNRQVHNZHQWQHLSRZLQQ\E\üSRZWy U]RQH3DUOLĔVNDV=GUXJLHMVWURQ\MHGQDNQDOHĪ\]DXZDĪ\üĪHZSUDNW\FHV\WXDFMD JG\C.R. F]\OLV\WXDFMDEUDNXMDNLHMNROZLHNQLH]JRGQRĞFLUyZQLHĪMHVWQLHNRU]\VWQDJG\Ī ZUHDOQ\PSUREOHPLHGHF\]\MQ\PGHF\GHQFLFLąJOH]GRE\ZDMąQRZąZLHG]ĊLQDE\ZDMąQRZH XPLHMĊWQRĞFLFRPRĪHVNXWNRZDü]PLDQąRSLQLLQDGDQ\WHPDW$GDPXVàDVDNV
2. Przykład symulacji
:OLWHUDWXU]H]RVWDáMXĪXNV]WDáWRZDQ\SHZLHQVWDQEDGDĔZ]DNUHVLHVWRVRZDQLD0&'$ ZHNRQRPLLHNVSHU\PHQWDOQHM3U]\NáDGRZR/¡NHQ]DSRPRFąHNVSHU\PHQWXSRUyZQ\ZDá]D VWRVRZDQLHGZyFKPHWRG0&'$GRSURMHNWRZDQLDV\VWHPXHQHUJHW\F]QHJRXZ]JOĊGQLDMąFHJR SUHIHUHQFMHNRQVXPHQWyZ8PRĪOLZLáRWRZ\V]F]HJyOQLHQLHLFK]DOHW3U]HSURZDG]RQHHNVSHU\ PHQW\Z\ND]Dá\ĪHUyĪQHPHWRG\Z\V]F]HJyOQLRQHZUDPDFKJUXS\0&'$QLHPXV]ąSURZD G]LüGRWDNLFKVDP\FKZ\QLNyZ5yĪQLFHWHPRJąE\üVSRZRGRZDQHPLQUyĪQ\PVSRVREHP ]DGDZDQLD S\WDĔ VWRSQLHP WUXGQRĞFL GDQHM SURFHGXU\ F]\ WHĪ UyĪQ\P VSRVREHP Z\UDĪDQLD SUHIHUHQFML-HGQDNĪHPHWRGD$+3RND]DáDVLĊQDMHIHNW\ZQLHMV]DJáyZQLH]HZ]JOĊGXQDPDáR VNRPSOLNRZDQąSURFHGXUĊ/¡NHQV±3RQLĪHM]DSUH]HQWRZDQRLQQ\SURVW\SU]\NáDG ]DVWRVRZDQLDWHMPHWRG\1DU\VXQNXSU]HGVWDZLRQRVWUXNWXUĊGODSUREOHPXZ\ERUXVDPRFKRGXSU]\MPXMąFF]WHU\ NU\WHULD5R]SRF]\QDMąFSU]HGPLRWRZąDQDOL]ĊRNUHĞORQRQDVWĊSXMąFHNU\WHULDZ\ERUX &HQDĺ 6SDODQLHĺ .RPIRUWĺ 'HVLJQĺ Rysunek 2. 6WUXNWXUDKLHUDUFKLF]QDGODSU]\NáDGRZHJRSUREOHPXGHF\]\MQHJR ħUyGáRRSUDFRZDQLHZáDVQH 7\PVDP\PQDGDMHVLĊLPZDJĊZDUWRĞüZQDZLDVDFKNWyUDE\áDJáyZQąGHWHUPLQDQWą : W\P SU]\NáDG]LH ]DáRĪRQR ĪH E\áD WR FHQD VDPRFKRGX ZDUWRĞü SRF]ąWNRZD NXSRZDQHJR VDPRFKRGX]JRGQLH]XVWDZąRUDFKXQNRZRĞFL:DUWRĞüWHJRNU\WHULXPZ\QLRVáD1DWR PLDVWQDMPQLHMLVWRWQ\PF]\QQLNLHPLMHGQRF]HĞQLHQDMEDUG]LHMVXELHNW\ZQ\PE\áGHVLJQ %LRUąFSRGXZDJĊIDNWĪHNU\WHULXPFHQ\LVSDODQLDVWDQRZLá\ZDJLSXQNWRZHMPRGHOHP VDPRFKRGXNWyU\ZW\FKNDWHJRULDFKRND]DáVLĊQDMEDUG]LHMHNRQRPLF]Q\E\áUHQDXOWFOLR7RWH GZDF]\QQLNLZ]GHF\GRZDQHMPLHU]HZSá\QĊá\QDUDQNLQJ .ROHMQ\PDVSHNWHPREOLF]HĔSU]\]DVWRVRZDQLXPHWRG\$+3MHVWIDNWĪHVDPRFKRG\VNR GDIDELDLYRONVZDJHQJROIEĊGąFHW\PLVDP\PLVDPRFKRGDPLZVZRMHMNODVLHG]LDáDMąFHZUD PDFKMHGQHMJUXS\SURGXFHQFNLHMX]\VNDá\QLHPDOĪHWDNLHVDPHZ\QLNL'RSLHURF]ZDUWHPLHM VFHSRSU]HFLQNXZ\ND]DáRUyĪQLFHSXQNWRZHVNRGDIDELD±LYRONVZDJHQJROI± 2VWDWQLPDQDOL]RZDQ\PVDPRFKRGHPE\áPHUFHGHVVFODVV0HUFHGHVX]\VNDáQDMZ\ĪV]H ZVSyáF]\QQLNLNRPIRUWXLGHVLJQXDOHLFKZDJLSU]\Z\ERU]HQDMOHSV]HJRVDPRFKR GXZRVWDWHF]Q\PUDQNLQJXZVWRVXQNXGRGZyFKSR]RVWDá\FKNU\WHULyZE\á\PDáR]QDF]ąFH
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Podsumowanie
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Literatura
$GDPXV:àDVDN3=DVWRVRZDQLHPHWRG\$+3GRZ\ERUXXPLHMVFRZLHQLDQDG]RUXQDGU\QNLHPILQDQ sowym. Bank i Kredyt, 41±%RGLQ/*DVV6,2QWHDFKLQJWKHDQDO\WLFKLHUDUFK\SURFHVV Computers & Operations Research, 30±
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of Operational Research, 109±
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Rural Development, 4± 2PNDUSUDVDG696XVKLO.$QDO\WLFKLHUDUFK\SURFHVV$QRYHUYLHZRIDSSOLFDWLRQVEuropean Journal of Operational Research, 169± 3DUOLĔVND05RODLQIRUPDFMLZJRVSRGDUFHU\QNRZHMQDSRGVWDZLHZ\EUDQ\FKUROQ\FKU\QNyZKXUWRZ\FK. :DUV]DZD:\GDZQLFWZR6**: 3RVNURENR71RZHNRQFHSFMHLWHRULHUR]ZRMXZHNRQRPLL:6&]DMD$%HFOD73RVNURENR-:áRGDUF]\N :\]ZDQLDZVSyáF]HVQHMHNRQRPLL'LILQ:DUV]DZD
6DDW\7/.HDUQV.3Analytical planning. The Organization of Systems3LWWVERXUJK5:63XEOLFDWLRQV 6DDW\7/'HFLVLRQPDNLQJZLWKWKHDQDO\WLFKLHUDUFK\SURFHVVInternational Journal of Services Sciences,
6DDW\7/2]GHPLU0:K\WKHPDJLFQXPEHUVHYHQSOXVRUPLQXVWZRMathematical and Computer
Model-ling, 38±
6PLWK9(FRQRPLFVLQWKHODERUDWRU\Journal of Economic Perspectives, 8±
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