Optimisation-based scheduling of an avionic system
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(2) >ŝŶŬƂƉŝŶŐ ^ƚƵĚŝĞƐ ŝŶ ^ĐŝĞŶĐĞ ĂŶĚ dĞĐŚŶŽůŽŐLJ >ŝĐĞŶƟĂƚĞ dŚĞƐŝƐ EŽ͘ ϭϴϰϰ. KƉƟŵŝƐĂƟŽŶͲďĂƐĞĚ ƐĐŚĞĚƵůŝŶŐ ŽĨ ĂŶ ĂǀŝŽŶŝĐ ƐLJƐƚĞŵ. ŵŝů <ĂƌůƐƐŽŶ. >ŝŶŬƂƉŝŶŐ hŶŝǀĞƌƐŝƚLJ ĞƉĂƌƚŵĞŶƚ ŽĨ DĂƚŚĞŵĂƟĐƐ ŝǀŝƐŝŽŶ ŽĨ KƉƟŵŝnjĂƟŽŶ ^ Ͳϱϴϭ ϴϯ >ŝŶŬƂƉŝŶŐ͕ ^ǁĞĚĞŶ >ŝŶŬƂƉŝŶŐ ϮϬϭϵ.
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(7) *QMi2Mib a KK M7 iiMBM;. BBB. #bi` +i. Bp. +FMQrH2/;K2Mib. p. *QMi2Mib. pB. GBbi Q7 ##`2p iBQMb. Bt. R AMi`Q/m+iBQM RXR PmiHBM2 Q7 i?2 i?2bBb bmKK `v X X X X X X X X X X X X X X X X X X X X RXk PmiHBM2 Q7 i?2 TT2M/2/ T T2`b X X X X X X X X X X X X X X X X X X X RXj S`2b2Mi iBQMb X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X. R k k 9. k pBQMB+ b+?2/mHBM; kXR h?2 /2p2HQTK2Mi Q7 pBQMB+ `+?Bi2+im`2b X X X X X X X X X X X X X kXk M BMi2;` i2/ KQ/mH ` pBQMB+ b+?2/mHBM; T`Q#H2K X X X X X X X X. 8 e 3. j aBM;H2 K +?BM2 b+?2/mHBM; M/ KBt2/ BMi2;2` T`Q;` KKBM; Rj jXR #`B27 ?BbiQ`B+ H T2`bT2+iBp2 X X X X X X X X X X X X X X X X X X X X X Rj jXk aBM;H2 K +?BM2 b+?2/mHBM; rBi? `2H2 b2 iBK2b M/ /2 /HBM2b X X R9 jXj hBK2@# b2/ 7Q`KmH iBQMb X X X X X X X X X X X X X X X X X X X X X X X R9 jX9 P`/2`@# b2/ 7Q`KmH iBQMb X X X X X X X X X X X X X X X X X X X X X X X RN jX8 SQbBiBQM@# b2/ 7Q`KmH iBQM X X X X X X X X X X X X X X X X X X X X X X ky jXe *QKT `BbQMb Q7 KBt2/ BMi2;2` T`Q;` KKBM; 7Q`KmH iBQMb X X X X kR 9 *QMi`B#miBQMb 9XR H `;2@b+ H2 T`Q#H2K BM pBQMB+ b+?2/mHBM; X X X X X X X X X 9Xk bQHmiBQM TT`Q +? 7Q` pBQMB+ b+?2/mHBM; X X X X X X X X X 9Xj M 2t +i bQHmiBQM TT`Q +? 7Q` bBM;H2 K +?BM2 b+?2/mHBM; 9X9 K i?2m`BbiB+ 7Q` pBQMB+ b+?2/mHBM; X X X X X X X X X X X X X "B#HBQ;` T?v. X X X X. X X X X. X X X X. k8 k8 kd kN jk j8. pB.
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(11)
(12) R AMi`Q/m+iBQM. h?2 Qp2` HH Tm`TQb2 Q7 i?Bb `2b2 `+? T`QD2+i Bb iQ bim/v b+?2/mHBM; M/ `2@ bQm`+2 HHQ+ iBQM T`Q#H2Kb BM `2 H@iBK2 bvbi2KbX h?Bb i?2bBb +QMi`B#mi2b iQ i?Bb `2 #v /2p2HQTBM; bQHmiBQM i2+?MB[m2b # b2/ QM QTiBKBb iBQM 7Q` b+?2/mHBM; T`Q#H2KX h?2 b+?2/mHBM; T`Q#H2K r b T`QTQb2/ #v Qm` BM/mbi`B H T `iM2`- i?2 ar2/Bb? /272M+2 M/ b2+m`Biv +QKT Mv a #- M/ Bi Bb Q7 BMi2`2bi BM i?2 /2@ p2HQTK2Mi Q7 7mim`2 pBQMB+ bvbi2KbX h?Bb i?2bBb +QMbBbib Q7 i?2bBb bmKK `v M/ i?`22 TT2M/2/ T T2`bX q2 bi `i #v BMi`Q/m+BM; i?2 TTHB+ iBQM `2 Q7 i?Bb i?2bBb- r?B+? Bb `2 H@iBK2 bvbi2Kb Q`- KQ`2 bT2+B}+ HHv- pBQMB+ bvbi2KbX JQ/2`M B`+` 7i +QMi BM HQi Q7 2H2+i`QMB+b- bm+? b b2MbQ`b- +im iQ`b#mb2b- M/ +QKTmi2`b- i? i `2bTQM/ iQ- +QMi`QH- M/ K2 bm`2 i?2 bi i2 Q7 i?2 B`+` 7iX h?2 2H2+i`QMB+b Q7 M B`+` 7i Bb + HH2/ pBQMB+b Q` i?2 pBQMB+ bvbi2K Q7 M B`+` 7iX Jm+? Q7 i?2 # bB+ 7mM+iBQM HBiv Q7 i?2 B`+` 7i- bm+? b bi22`@ BM;- M pB; iBQM- M/ +QKKmMB+ iBQM- `2HB2b QM i?2 pBQMB+ bvbi2K #2? pBM; T`QT2`HvX >Qr2p2`- i?2 T`QT2` #2? pBQm` KB;?i #2 /Bz2`2Mi /2T2M/BM; QM i?2 +iBQMb Q7 i?2 TBHQi- i?2 TQbBiBQM Q7 i?2 B`+` 7i- Q` i?2 T?vbB+ H iBK2X avbi2Kb Q7 i?Bb ivT2- r?2`2 i?2 T`QT2` #2? pBQm` /Q2b MQi QMHv /2T2M/ QM i?2 `2bmHib Q7 + H+mH iBQMb- #mi HbQ r?2M i?2v `2 T2`7Q`K2/- `2 2t KTH2b Q7 `2 H@iBK2 bvbi2KbX AM Q`/2` iQ pQB/ K H7mM+iBQM BM `2 H@iBK2 bvbi2K- Bi Bb Q7 pBi H BKTQ`i M+2 iQ K F2 bm`2 i? i i?2 +QKTQM2Mib Q7 i?2 bvbi2K /Q i?2 +Q``2+i i?BM; i i?2 +Q``2+i iBK2 rBi? bm{+B2Mi `2bQm`+2b U+QKTmiBM; iBK2- / i - 2i +2i2` VX _2b2 `+? QM b+?2/mHBM; Q7 `2 H@iBK2 bvbi2Kb K F2b M 2zQ`i iQ M Hvb2 i?2b2. R.
(13) RX. AMi`Q/m+iBQM. bBim iBQMb 7`QK b+?2/mHBM; T2`bT2+iBp2- M/ + M- /2T2M/BM; QM i?2 +QMi2ti#2 TTHB2/ /m`BM; /Bz2`2Mi bi ;2b Q7 i?2 /2p2HQTK2Mi Q7 i?2 bvbi2KX h?2 7QHHQrBM; irQ b2+iBQMb /2b+`B#2 i?2 i?2bBb bmKK `v HQM; rBi? i?2 TT2M/2/ T T2`b M/ i?2B` Tm#HB+ iBQM bi imb- r?BH2 i?2 H bi b2+iBQM HBbib T`2@ b2Mi iBQMb Q7 i?Bb K i2`B H i +QM72`2M+2bX. RXR PmiHBM2 Q7 i?2 i?2bBb bmKK `v h?2 +QMi`B#miBQMb Q7 i?Bb i?2bBb `2 BM irQ `2b2 `+? `2 b, pBQMB+ b+?2/mHBM; M/ b+?2/mHBM; i2+?MB[m2b # b2/ QM QTiBKBb iBQMX h?2 i?2bBb bmKK `v i`2 ib `2H2p Mi bT2+ib 7`QK i?2b2 `2 b BM 7Qm` +? Ti2`bX h?2 Q#D2+iBp2 Q7 i?Bb Bb iQ Tmi i?2 `2b2 `+? Q7 i?2 TT2M/2/ T T2`b BM T2`bT2+iBp2X "2HQr- i?2 7Qm` +? Ti2`b BM i?2 i?2bBb bmKK `v `2 /2b+`B#2/X h?Bb }`bi +? Ti2` ;Bp2b ;2M2` H BMi`Q/m+iBQM M/ /2b+`B#2b i?2 bi`m+im`2 Q7 i?Bb i?2bBbX *? Ti2` k ;Bp2b M BMi`Q/m+iBQM iQ b+?2/mHBM; Q7 pBQMB+ bvbi2KbX h? i +? Ti2` ? b #22M r`Bii2M 7Q` `2 /2` rBi? # +F;`QmM/ BM QTiBKBb iBQM M/ Bi 2M/b rBi? /2b+`BTiBQM Q7 i?2 pBQMB+ b+?2/mHBM; T`Q#H2K i? i Bb i?2 QTiBKBb iBQM T`Q#H2K bim/B2/ BM i?Bb i?2bBbX AM *? Ti2` j- KBt2/ BMi2;2` T`Q;` KKBM; UJASV 7Q`KmH iBQMb 7Q` bBM;H2 K +?BM2 b+?2/mHBM; `2 `2pB2r2/X aBM;H2 K +?BM2 b+?2/mHBM; Bb +Q`2 T`Q#H2K bi`m+im`2 Q7 i?2 pBQMB+ b+?2/mHBM; T`Q#H2K i`2 i2/ BM i?Bb i?2bBbX h?2 H bi +? Ti2` Q7 i?2 i?2bBb bmKK `v- *? Ti2` 9- bmKK `Bb2b i?2 +QMi`B#miBQMb Q7 i?2 TT2M/2/ T T2`bX. RXk PmiHBM2 Q7 i?2 TT2M/2/ T T2`b h?2`2 `2 i?`22 TT2M/2/ T T2`b BM i?Bb i?2bBb- M/ i?2v `2 BM+Hm/2/ BM +?`QMQHQ;B+ H Q`/2`X h?Bb b2+iBQM ;Bp2b b?Q`i /2b+`BTiBQM Q7 2 +? Q7 i?2K HQM; rBi? i?2B` Tm#HB+ iBQM bi imb M/ M mi?Q` bi i2K2MiX. S T2` @ M QTiBKBb iBQM TT`Q +? 7Q` T`2@`mMiBK2 b+?2/mHBM; Q7 i bFb M/ +QKKmMB+ iBQM BM M BMi2;` i2/ KQ/mH ` pBQMB+ bvbi2K S T2` Bb Tm#HBb?2/ BM i?2 DQm`M H PTiBKBx iBQM M/ 1M;BM22`BM;- pQHmK2 RN- Bbbm2 9 BM T ;2b NddĜRyy9- kyR3X mi?Q`b, J i?B b "HBFbi /- hQK b Gƺƺr- 1KBH E `HbbQM M/ 1HBM _ƺMM#2`; #bi` +i, h?2 }`bi T T2` BMi`Q/m+2b M BM/mbi`B HHv `2H2p Mi T`2@`mMiBK2 pBQMB+ b+?2/mHBM; T`Q#H2K HQM; rBi? bmBi #H2 2t +i bQHmiBQM TT`Q +?X h?2 bQHmiBQM TT`Q +? `2HB2b QM +QMbi` BMi ;2M2` iBQMX h?Bb T`Q+2/m`2 Bb BK@. k.
(14) RXkX PmiHBM2 Q7 i?2 TT2M/2/ T T2`b TH2K2Mi2/ BM b+?2/mHBM; iQQH i? i Bb i2bi2/ QM i?`22 BMbi M+2b T`QpB/2/ #v a #X mi?Q` bi i2K2Mi, A ? p2 +QMi`B#mi2/ iQ i?2 KQ/2HHBM;- i?2 JAS 7Q`KmH @ iBQM- i?2 BKTH2K2Mi iBQM- i?2 i2biBM;- M/ iQ r`BiBM; i?2 T T2`X. S T2` " @ 1tTHB+Bi KQ/2HHBM; Q7 KmHiBTH2 BMi2`p Hb BM +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 7Q` KmHiBT`Q+2bbQ` b+?2/mHBM; S T2` " Bb Tm#HBb?2/ BM T ;2b 8edĜ8dk Q7 i?2 T22`@`2pB2r2/ +QM72`2M+2 T`Q@ +22/BM;- PT2` iBQMb _2b2 `+? S`Q+22/BM;b kyRd- #v aT`BM;2` AMi2`M iBQM H Sm#HBb?BM;X 1/BiQ`b, LX EHB2r2`- CX6X 1?KF2- M/ _X "Q`M/ƺ`72`X mi?Q`b, 1KBH E `HbbQM M/ 1HBM _ƺMM#2`; #bi` +i, S T2` " BKT`Qp2b i?2 2t +i +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 T`2b2Mi2/ BM S T2` #v i?2 BMi`Q/m+iBQM Q7 bm#@BMi2`p HbX h?2 bm#@BMi2`p Hb 2M #H2 bi`QM;2` `2H t iBQM BM i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 M/ bKQQi?2` +QMM2+iBQM iQ Qi?2` i2+?MB+ H `2[mB`2K2MibX mi?Q` bi i2K2Mi, A ? p2 #22M `2bTQMbB#H2 7Q` i?2 BKTH2K2Mi iBQM M/ i2biBM; 7Q` i?Bb T T2`X h?2 KQ/2HHBM; M/ r`BiBM; ? p2 #22M /QM2 iQ;2i?2` rBi? i?2 bmT2`pBbQ`X. S T2` * @ K i?2m`BbiB+ TT`Q +? iQ H `;2@b+ H2 pBQMB+ b+?2/mHBM; S T2` * ? b #22M T `iB HHv T`2b2Mi2/ i i?2 +QM72`2M+2 S` +iB+2 M/ h?2@ Q`v Q7 miQK i2/ hBK2i #HBM; kyR3 UShh kyR3V # b2/ QM T22`@`2pB2r2/ 2ti2M/2/ #bi` +iX h?2 7mHH p2`bBQM Q7 S T2` * ? b #22M bm#KBii2/ iQ DQm`@ M H- M/ ? b #22M Tm#HBb?2/ b M JA@`2TQ`i- AaaL yj93@kNey- rBi? MmK#2` GBh>@Jh@_ĜkyRNfykĜa1- kyRNX mi?Q`b, 1KBH E `HbbQM- 1HBM _ƺMM#2`;- M/`2 b ai2M#2`; M/ > MM2b lTTK M #bi` +i, h?2 i?B`/ T T2` 2ti2M/b i?2 2t +i +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 T`2b2Mi2/ BM S T2` BMiQ M K i?2m`BbiB+X AM i?2 K i?2m`BbiB+- i?2 `2H t2/ T`Q#H2K Bb bQHp2/ mbBM; M / TiBp2 H `;2 M2B;?#Qm`?QQ/ b2 `+? UGLaV i? i 2tTHQ`2 M2B;?#Qm`?QQ/b mbBM; JAS bQHp2`X h?Bb rQ`F HbQ T`2b2Mib BKT`Qp2/ JAS 7Q`KmH iBQMb 7Q` KQ/2Hb BM i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2- r?B+? 2z2+i #Qi? i?2 2t +i TT`Q +? M/ i?2 K i?2m`BbiB+X h?2 2t +i TT`Q +? M/ i?2 K i?2m`BbiB+ `2 2p Hm i2/ QM 8 a # BMbi M+2b M/ Rky Tm#HB+ BMbi M+2bX j.
(15) RX. AMi`Q/m+iBQM. h?2 `2bmHib BM/B+ i2 i? i i?2 K i?2m`BbiB+ T2`7Q`Kb #2ii2` i? M i?2 2t +i TT`Q +? QM H `;2 BMbi M+2bX mi?Q` bi i2K2Mi, A ? p2 +QMi`B#mi2/ iQ i?2 KQ/2HHBM;- i?2 JAS 7Q`KmH @ iBQMb M/ i?2 bQHmiBQM TT`Q +?2b Q7 i?Bb T T2`- M/ ? p2- mM/2` bmT2`pBbBQM/QM2 H `;2 T `i Q7 i?2 r`BiBM;X A ? p2 HbQ #22M `2bTQMbB#H2 7Q` +`2 iBM; i?2 Tm#HB+ BMbi M+2b M/ ? p2 #22M BMpQHp2/ BM i?2 BKTH2K2Mi iBQM M/ i2biBM;X. RXj S`2b2Mi iBQMb .m`BM; Kv /Q+iQ` H bim/B2b A ? p2 ii2M/2/ M/ K /2 T`2b2Mi iBQMb i i?2 7QHHQrBM; +QM72`2M+2bX Ç AMi2`M iBQM H *QM72`2M+2 QM PT2` iBQMb _2b2 `+? kyRd UP_kyRdVX h?Bb +QM72`2M+2 iQQF TH +2 BM "2`HBM- :2`K Mv- BM a2Ti2K#2` kyRdX A T`2@ b2Mi2/ i?2 rQ`F Q7 S T2` "X Ç ap2MbF QT2` iBQMb M HvbFQM72`2Mb2M kyRd UaPEkyRdVX h?Bb +QM72`@ 2M+2 iQQF TH +2 BM GBMFƺTBM;- ar2/2M- BM P+iQ#2` kyRdX A T`2b2Mi2/ i?2 rQ`F Q7 S T2` "X. 9.
(16) k pBQMB+ b+?2/mHBM;. h?Bb b2+iBQM ;Bp2b #`B27 BMi`Q/m+iBQM iQ i?2 i2+?MB+ H TTHB+ iBQM `2 Q7 i?Bb i?2bBb- i? i Bb- b+?2/mHBM; Q7 pBQMB+ bvbi2KbX h?2 BMi`Q/m+iBQM Bb BK2/ iQ ;Bp2 T2`bQM rBi? # +F;`QmM/ BM QTiBKBb iBQM bm{+B2Mi BM7Q`K iBQM iQ mM/2`bi M/ i?2 KQiBp iBQM 7Q` i?2 T`Q#H2K bim/B2/ BM i?Bb i?2bBbX *QKTmi2` bvbi2Kb r?2`2 i?2 +Q``2+i #2? pBQm` Bb 7mM+iBQM Q7 iBK2 M/ /Q2b MQi QMHv /2T2M/ QM i?2 `2bmHi Q7 +QKTmi iBQM `2 + HH2/ `2 H@iBK2 +QKTmi2` bvbi2KbX h?2 +QK#BM iBQM Q7 bm+? +QKTmi2` bvbi2K iQ;2i?2` rBi? Bib BMi2` +iBQM- 7Q` 2t KTH2 ?mK M i?`Qm;? F2v#Q `/- Q` ?mK M BMi2`7 +2- Bb + HH2/ `2 H@iBK2 bvbi2KX _2 H@iBK2 +QKTmi2` bvbi2Kb + M #2 +H bbB}2/ BMiQ ? `/ `2 H@iBK2 bvbi2Kb Q` bQ7i `2 H@iBK2 bvbi2KbX ? `/ `2 H@iBK2 bvbi2K Bb bvbi2K r?2`2 bBM;H2 KBbb2/ /2 /HBM2 Ui?2 BMbi Mi `2bmHi Kmbi #2 T`Q/m+2/V +QmH/ ? p2 b2p2`2 +QMb2[m2M+2bX 1t KTH2b Q7 ? `/ `2 H@iBK2 bvbi2Kb `2 +QKTQM2Mib BM i` {+ HB;?ib i M BMi2`b2+iBQM- i?2 bi22`BM; Q7 M B`+` 7i- i?2 #` FBM; bvbi2K BM + `- i?2 +QMi`QH T`Q+2bb Q7 Mm+H2 ` TH Mi- M/ H mM+?BM; `Q+F2i BMiQ bT +2X bQ7i `2 H@iBK2 bvbi2K Bb bvbi2K r?2`2 KBbb2/ /2 /HBM2 /Q2b MQi + mb2 b2p2`2 +QMb2[m2M+2bX 1t KTH2b Q7 bQ7i `2 H@iBK2 bvbi2Kb +QmH/ #2 bi`2 KBM; KQpB2 QM vQm` +QKTmi2` Q` + HHBM; QM +2HH@T?QM2X h?2 rQ`F BM i?Bb i?2bBb Bb +QM+2`M2/ rBi? ? `/ `2 H@iBK2 bvbi2Kb BM B`+` 7iX AM Q`/2` iQ pQB/ KBbb2/ /2 /HBM2 BM ? `/ `2 H@iBK2 bvbi2K- 2 +? i bF Kmbi #2 ;Bp2M 2MQm;? `2bQm`+2b M/ #2 T2`7Q`K2/ i i?2 `B;?i iBK2X h?2 M HvbBb i? i Mbr2` B7 i?Bb Bb TQbbB#H2 Q` MQi Bb Q7i2M + HH2/ b+?2/mH #BHBiv. 8.
(17) kX. pBQMB+ b+?2/mHBM;. M HvbBbX a+?2/mH #BHBiv M HvbBb + M #2 /QM2 BM K Mv /Bz2`2Mi r vb- M/ BM /Bz2`2Mi bi ;2b Q7 i?2 /2p2HQTK2Mi T`Q+2bb Q7 bvbi2KX S`Q#H2Kb bbQ+B i2/ rBi? b+?2/mH #BHBiv M HvbBb i M 2 `Hv bi ;2 Q7 i?2 /2p2HQTK2Mi T`Q+2bb `2 Q7i2M `2H i2/ iQ `2bQm`+2 HHQ+ iBQM- 7Q` 2t KTH2 B7 Bi Bb TQbbB#H2 iQ HHQ+ i2 i bFb iQ KQ/mH2b M/ b iBb7v +2`i BM +QMbi` BMibX >Qr2p2`BM i?2 H i2` bi ;2b Q7 i?2 /2p2HQTK2Mi T`Q+2bb i?2 T`Q#H2Kb `2 Q7i2M `2H i2/ iQ b+?2/mHBM;- 7Q` 2t KTH2 B7 b+?2/mH2 i? i b iBb7v +QMbi` BMib 2tBbib Q` B7 b+?2/mHBM; H;Q`Bi?K rBHH rQ`F mM/2` +2`i BM i bF HQ /bX M BKTQ`i Mi /BbiBM+iBQM 7Q` b+?2/mHBM; T`Q#H2Kb BM `2 H@iBK2 bvbi2Kb `2 r?2i?2` Q` MQi i?2 M HvbBb Bb /QM2 i `mMiBK2 Q` #27Q`2 `mMiBK2 U+ HH2/ T`2@ `mMiBK2VX AM `mMiBK2 b+?2/mHBM; i?2 i bF HQ / Bb ivTB+ HHv MQi FMQrM M/ b+?2/mHBM; H;Q`Bi?K KB;?i ;m ` Mi22 rQ`FBM; bvbi2K mM/2` +2`i BM i bF HQ /bX AM T`2@`mMiBK2 b+?2/mHBM; i?2 2MiB`2 i bF HQ / Bb FMQrM #27Q`2? M/ M/ i?mb b+?2/mHBM; H;Q`Bi?K mbBM; i?Bb Q` b+?2/mH2 i? i b iBb}2b i?2b2 `2[mB`2K2Mib + M #2 T`Q/m+2/X h?2 T`Q#H2K bim/B2/ BM i?Bb i?2bBb #2HQM;b iQ i?2 H i2` bi ;2b Q7 i?2 /2@ p2HQTK2Mi T`Q+2bb M/ Bb #Qmi T`Q/m+BM; T`2@`mMiBK2 b+?2/mH2X h?2 7QH@ HQrBM; b2+iBQMb ;Bp2 /2b+`BTiBQM Q7 i?2 /2p2HQTK2Mi Q7 pBQMB+ `+?Bi2+im`2b M/ i?2 b+?2/mHBM; T`Q#H2K bim/B2/ BM i?Bb i?2bBbX 6Q` 7m`i?2` BM7Q`K iBQM #Qmi b+?2/mHBM; BM `2 H@iBK2 bvbi2Kb M/ pBQMB+ bvbi2Kb- b22 i?2 BMi`Q/m+@ iQ`v T `ib Q7 S?.@i?2b2b (j8) M/ (jj)- `2bT2+iBp2HvX. kXR h?2 /2p2HQTK2Mi Q7 pBQMB+ `+?Bi2+im`2b M B`+` 7i Bb Q7i2M /2p2HQT2/ M/ K BMi BM2/ i?`Qm;? K Mv v2 `b U2p2M /2+ /2bV M/ `2+2Bp2b `2;mH ` mT/ i2b Q7 bQ7ir `2 M/ ? `/r `2 /m`BM; Bib HB72iBK2X AM Q`/2` iQ +`2 i2 b 72 M/ `2HB #H2 B`+` 7i i?2`2 `2 K Mv /Bz2`@ 2Mi `2;mH iBQMb M/ ;mB/2HBM2b `2; `/BM; i?2 +QKTQM2Mib BM M B`+` 7iX 6Q` 2t KTH2- i?2`2 `2 ;mB/2HBM2b 7Q` i?2 bQ7ir `2 /2p2HQTK2Mi M/ p2`B}+ iBQM T`Q+2bb Q7 bQ7ir `2 BM M B`+` 7i- i?2 KQbi `2+2Mi #2BM; .P@Rd3* #v _ /BQ h2+?MB+ H *QKKBbbBQM 7Q` 2`QM miB+b U_h*V- b22 (kN)X aBM+2 M B`+` 7i Bb bmTTQ`i2/ i?`Qm;? K Mv v2 `b- mT/ i2b Q7 bQ7ir `2 M/ ? `/r `2 KB;?i #2 M2+2bb `v /m2 iQ /p M+2b bBM+2 i?2 BMi`Q/m+iBQM Q7 i?2 B`+` 7iX h?mb- M pBQMB+ `+?Bi2+im`2 i? i bmTTQ`i BM+`2K2Mi H /2p2HQTK2Mi M/ p2`B}+ iBQM Q7 bQ7ir `2 M/ ? `/r `2 Bb bQK2i?BM; iQ bi`Bp2 7Q`X ;2M+B2bbm+? b 1m`QT2 M pB iBQM a 72iv ;2M+v U1aV BM 1m`QT2 M/ 62/2` H pB iBQM /KBMBbi` iBQM U6V BM i?2 la- T`QpB/2 ;mB/2HBM2b QM ?Qr iQ 2 b2 BM+`2K2Mi H +2`iB}+ iBQM Q7 M pBQMB+ bvbi2KX q?2M +QKTmi2`b }`bi r2`2 mb2/ BM B`+` 7i- 2 +? pBQMB+ 7mM+iBQM rBi? 2H2+@ i`QMB+ +QKTQM2Mib- bm+? b bi22`BM;- M pB; iBQM- 2i +2i2` - r b BKTH2K2Mi2/ QM /2/B+ i2/ +QKTmi2` +QMM2+i2/ iQ i?2 b2MbQ`b M/ +im iQ`b Bi `2[mB`2/X A7 /Bz2`2Mi pBQMB+ 7mM+iBQMb M22/2/ iQ BMi2` +i rBi? 2 +? Qi?2`- /B`2+i + #H2b. e.
(18) kXRX h?2 /2p2HQTK2Mi Q7 pBQMB+ `+?Bi2+im`2b r2`2 /` rM #2ir22M i?2KX h?Bb FBM/ Q7 pBQMB+ bvbi2K Bb `272``2/ iQ b 72/2` i2/ bvbi2KX h?2 72/2` i2/ bvbi2Kb mM/2`r2Mi b2p2` H i` MbBiBQMbX AM i?2 #2;BMMBM; pBQMB+ bvbi2Kb mb2/ M HQ;m2 +B`+mBibX G i2` /B;Bi H +B`+mBib M/ KQ`2 bQ@ T?BbiB+ i2/ T`Q+2bbQ`b r2`2 BMi`Q/m+2/X b T `i Q7 i?Bb i` MbBiBQM- i?2`2 ? b #22M /Bz2`2Mi K2i?Q/b iQ i` Mb72` / i rBi?BM M pBQMB+ bvbi2KX 6Q` 2t@ KTH2- 2`QM miB+ H _ /BQ- AM+Q`TQ` i2/ U_AL*V 9kN M/ JAG@ah.@R88j Tm#HBb?2/ #v i?2 lMBi2/ ai i2b .2T `iK2Mi Q7 .272Mb2X b i?2 KQmMi Q7 pBQMB+ 7mM+iBQMb i? i r2`2 +QMi`QHH2/ #v bQ7ir `2 ;`2rbQ /B/ i?2 bBx2 M/ r2B;?i Q7 i?2 72/2` i2/ bvbi2KbX "2;BMMBM; BM i?2 H i2 RN3yb M/ 2 `Hv RNNyb- M2r `+?Bi2+im`2 Q7 pBQMB+ bvbi2Kb 2K2`;2/- + HH2/ BMi2;` i2/ KQ/mH ` pBQMB+b UAJV bvbi2KbX AM i?Bb b2iiBM;- KmHiBTH2 pBQMB+ 7mM+iBQMb +QmH/ #2 BKTH2K2Mi2/ QM i?2 b K2 ? `/r `2- miBHBbBM; i?2 +QK@ TmiBM; `2bQm`+2b KQ`2 2{+B2MiHvX u2 `b H i2`- ;mB/2HBM2b QM ?Qr +2`iB7v bm+? KQ/mH2b r2`2 ;`22/ mTQM- b22 .P@kNd #v _h* (jy)X .m`BM; i?2b2 v2 `b/Bz2`2Mi ;mB/2HBM2b M/ 1i?2`M2i M2irQ`Fb r2`2 BMi`Q/m+2/ iQ BKT`Qp2 / i i` Mb72` BM pBQMB+ bvbi2KbX 1t KTH2b Q7 i?2b2 `2 _AL* ee9 1i?2`M2i M2i@ rQ`F- pBQMB+b 6mHH@.mTH2s arBi+?2/ 1i?2`M2i U6.sV /2p2HQT2/ #v B`#mb M/ hBK2@h`B;;2`2/ 1i?2`M2i Uhh1i?2`M2iVX .m`BM; i?2 H bi irQ /2+ /2b- i?2`2 ? b #22M KmHiBTH2 H `;2 `2b2 `+? 2zQ`ib i? i BMp2biB; i2 KQ`2 /p M+2/ pBQMB+ `+?Bi2+im`2bX 1t KTH2b Q7 bm+? `2@ b2 `+? 2zQ`ib `2 i?2 L iBQM H 2`QM miB+b M/ aT +2 /KBMBbi` iBQM ULaV P`BQM aT +2 T`Q;` K BM i?2 la- i? i BMp2biB; i2/ i?2 pBQMB+ `+?Bi2+im`2 7Q` 7mim`2 bT +2 i` p2Hb- M/ i?2 a+ H #H2 `2+QM};m` #G2 2H2+i`QMB+b TH i@ 7Q`Kb M/ iQQHb Ua*_G1hhV T`QD2+i M/ i?2 pBQMB+b bvbi2Kb ?Qbi2/ QM /Bbi`B#mi2/ KQ/mH ` 2H2+i`QMB+b H `;2 b+ H2 /2KQMbi` iQ` 7Q` KmHiBTH2 ivT2b Q7 B`+` 7i Ua>G1uV T`QD2+i BM 1m`QT2- i? i 2t KBM2/ i?2 M2ti ;2M2` iBQM Q7 AJ bvbi2KbX M pBQMB+ `+?Bi2+im`2 i? i r b 7m`i?2` /Bbi`B#mi2/ r b bm;;2bi2/ b T `i Q7 i?Bb `2b2 `+?- 7Q` 2t KTH2 b22 (Rj)X AM bm+? bvbi2K- /Bz2`2Mi AJ mMBib `2 HQ+ i2/ BM i?2 b K2 pBQMB+ bvbi2K- #mi i?2v `2 +QMM2+i2/ i?`Qm;? M 1i?2`M2i M2irQ`FX am+? M `+?Bi2+im`2 rQmH/ ? p2 i?2 /p Mi ;2b Q7 i?2 AJ bvbi2K- bm+? b #2ii2` `2bQm`+2 miBHBb iBQM- r?BH2 HHQrBM; 7Q` T?vbB+ H /BbDQBMi bm#bvbi2KbX E2v +? HH2M;2b 7Q` /Bbi`B#mi2/ AJ bvbi2Kb `2 `2pB2r2/ BM (jd)- r?2`2 bvbi2K b+?2/mH #BHBiv M HvbBb Bb QM2 Q7 i?2 +? HH2M;2bX /Bb /p Mi ;2 Q7 +`2 iBM; +QKTH2t `+?Bi2+im`2 Bb i? i- b i?2 bvbi2K `+?Bi2+im`2 ;`Qrb BM+`2 bBM;Hv +QKTH2t- bQ /Q2b i?2 +? HH2M;2 Q7 M HvbBM; i?2KX q?2M KmHiBTH2 pBQMB+ 7mM+iBQMb `2 BKTH2K2Mi2/ QM i?2 b K2 ? `/@ r `2- vQm M22/ iQ 2Mbm`2 i? i HH bQ7ir `2 TTHB+ iBQMb i? i BKTH2K2Mi i?2 pBQMB+ 7mM+iBQMb ;2i bm{+B2Mi +QKTmiBM; `2bQm`+2b rBi?Qmi z2+iBM; Mv Qi?2` bQ7ir `2 TTHB+ iBQMX h?Bb BM+`2 b2b i?2 +QKTH2tBiv BM /2bB;M M/ p2`@ B}+ iBQM rBi? `2bT2+i iQ i?BM;b bm+? b 7 mHi +QMi BMK2Mi M/ b+?2/mHBM;X _AL* e8j T`QpB/2 M 2t KTH2 Q7 ;mB/2HBM2b QM ?Qr iQ ? M/H2 i?Bb ivT2 Q7 T `iBiBQMBM;X d.
(19) kX. pBQMB+ b+?2/mHBM;. h?Bb i?2bBb 7Q+mb2b QM /2p2HQTBM; bQHmiBQM K2i?Q/b 7Q` b+?2/mHBM; T`Q#@ H2K Q7 BMi2`2bi BM i?2 /2p2HQTK2Mi Q7 7mim`2 AJ bvbi2KbX h?2 Q#D2+iBp2 Q7 i?2 b+?2/mHBM; T`Q#H2K Bb iQ T`Q/m+2 ;HQ# H T`2@`mMiBK2 b+?2/mH2 7Q` #Qi? i?2 T`Q+2bbQ`b M/ i?2 1i?2`M2i M2irQ`F Q7 T `iB+mH ` AJ bvbi2KX .2i BHb Q7 i?Bb T`Q#H2K M/ Bib pBQMB+ bvbi2K Bb 7QmM/ BM a2+iBQM kXkX. kXk M BMi2;` i2/ KQ/mH ` pBQMB+ b+?2/mHBM; T`Q#H2K h?2 7QHHQrBM; b2+iBQM BMi`Q/m+2b i?2 pBQMB+ b+?2/mHBM; T`Q#H2K /2b+`B#2/ BM S T2` *X h?Bb b+?2/mHBM; T`Q#H2K Bb Q7 BMi2`2bi BM i?2 /2p2HQTK2Mi Q7 7mim`2 AJ bvbi2Kb M/ ? b #22M T`QTQb2/ #v Qm` BM/mbi`B H T `iM2` a #X S T2` M/ S T2` " bim/B2/ `2bi`B+iBQM Q7 i?Bb T`Q#H2K r?2`2 bQK2 KQ/2HHBM; bBK@ THB}+ iBQMb r2`2 K /2X h?Bb /Bz2`2M+2 Bb 7m`i?2` /2b+`B#2/ BM a2+iBQM kXkX h?2 T`Q#H2K Bb iQ +QMbi`m+i 72 bB#H2 b+?2/mH2 Q` T`Qp2 i? i MQ b+?2/mH2 2tBbibX AM i?Bb bvbi2K- b+?2/mH2 b? HH #2 T`Q/m+2/ #27Q`2 `mMiBK2 BM b2iiBM; r?2`2 i bFb- rQ`bi + b2 2t2+miBQM iBK2b- M/ `2[mB`2K2Mib Q7 i?2 bvbi2K `2 FMQrM #27Q`2? M/X h?2 bvbi2K Bb T2`BQ/B+ M/ i?2 b+?2/mH2 `2T2 ib QM+2 2p2`v K DQ` T2`BQ/ UK DQ` 7` K2VX hvTB+ HHv- i?2 H2M;i? Q7 K DQ` T2`BQ/ Bb #Qmi QM2 b2+QM/ rBi? iBK2 `2bQHmiBQM BM M MQb2+QM/bX AM i?2 bvbi2K- i?2`2 `2 b2i Q7 MQ/2b +QKT`Bb2/ Q7 /Bz2`2Mi ivT2b Q7 KQ/mH2b UT`Q+2bbQ`bV i? i T2`7Q`Kb i bFbX 1p2`v i bF BM i?2 bvbi2K Kmbi #2 T2`7Q`K2/ QM bT2+B}+ KQ/mH2 M/ Bb MQi HHQr2/ iQ KB;` i2X 1 +? MQ/2 ? b bBM;H2 +QKKmMB+ iBQM KQ/mH2 U*JV M/ QM2 Q` KQ`2 TTHB+ iBQM KQ/mH2b UJbVX h?2 *Jb `2 +QMM2+i2/ iQ bBM;H2 +QKKmMB+ iBQM M2irQ`F U*LV HHQrBM; i?2 MQ/2b iQ +QKKmMB+ i2 rBi? MQi?2` #v b2M/BM; K2bb ;2bX h?2 bvbi2K Bb BHHmbi` i2/ BM 6B;m`2 kXRX h?2 /2+BbBQMb `2[mB`2/ iQ +`2 i2 b+?2/mH2 `2 bbB;MBM; bi `i iBK2b iQ i bFb M/ bbB;MBM; b2M/ iBK2b iQ K2bb ;2b QM i?2 *LX h?2 Tm`TQb2 Q7 i?2 Jb Bb iQ ?Qbi bQ7ir `2 TTHB+ iBQMbX h?2 bQ7ir `2 TTHB+ iBQMb `2 ;`QmT2/ BMiQ T `iBiBQMb #v 2M;BM22`bX h?2 T `iBiBQMb `2 i?2M b+?2/mH2/ QM i?2 Jb b i bFbX PM M J- i?2`2 Bb Q7i2M 72r i bFb rBi? HQM; 2t2+miBQM `2[mB`2K2MibX h?2 *Jb `2 `2bTQMbB#H2 7Q` i?2 +QKKmMB+ iBQM Q7 MQ/2X h?Bb BM+Hm/2b BMi2`M H +QKKmMB+ iBQM #2ir22M i?2 KQ/mH2b M/ 2ti2`M H +QKKmMB+ iBQM i?`Qm;? i?2 *L Q` rBi? Qi?2` 2ti2`M H 2[mBTK2MiX *J Q7i2M BM+Hm/2b K Mv i bFb- rBi? b?Q`i 2t2+miBQM `2[mB`2K2MibX. JQ/mH2 b+?2/mHBM; 1 +? i bF BM i?2 bvbi2K Bb `2T2 i2/ i H2 bi QM+2 2p2`v K DQ` T2`BQ/X h?2 [mQiB2Mi Q7 i?2 K DQ` T2`BQ/ M/ i?2 T2`BQ/ Q7 i bF /2i2`KBM2 i?2 MmK#2` Q7 iBK2b i?Bb i bF Bb T2`7Q`K2/ BM K DQ` T2`BQ/X h?2 T2`BQ/ Q7 i bF Hr vb /BpB/2b i?2 K DQ` T2`BQ/- M/ QM T `iB+mH ` KQ/mH2 i?2 i bF T2`BQ/b `2 HH i?2 b K2X h bFb QM M J `2 T2`7Q`K2/ e9 iBK2b /m`BM; K DQ` T2`BQ/r?BH2 QM i?2 *Jb- i?2v `2 T2`7Q`K2/ QM2 iBK2 /m`BM; K DQ` T2`BQ/X hQ 3.
(20) kXkX M BMi2;` i2/ KQ/mH ` pBQMB+ b+?2/mHBM; T`Q#H2K. *QKKmMB+ iBQM M2irQ`F. LQ/2 1. LQ/2 LQ/2 LQ/2. LQ/2 n. *QKKmMB+ iBQM KQ/mH2. *QKKmMB+ iBQM KQ/mH2. TTHB+ iBQM KQ/mH2b. TTHB+ iBQM KQ/mH2b. AMi2`@MQ/2 +QKKmMB+ iBQM. 1ti2`M H +QKKmMB+ iBQM. AMi` @MQ/2 +QKKmMB+ iBQM. 6B;m`2 kXR, M Qp2`pB2r Q7 bvbi2K i? i +QMbBbi Q7 n MQ/2bX h?2 bi`m+im`2 Q7 i?2 +QMi2Mi Bb i?2 b K2 7Q` HH MQ/2b M/ i?2`27Q`2 QMHv /BbTH v2/ 7Q` MQ/2 R M/ n. mMB[m2Hv B/2MiB7v M Q++m``2M+2 Q7 i bF BM K DQ` T2`BQ/ r2 BMi`Q/m+2 i bF BMbi M+2bX i bF BMbi M+2 Bb imTH2 Q7 M BMi2;2` M/ i bF B/2MiB}2` i? i mMB[m2Hv B/2MiB}2b T `iB+mH ` Q++m``2M+2 Q7 i bF BM K DQ` T2`BQ/X KQ/mH2 + M QMHv T2`7Q`K bBM;H2 i bF i ;Bp2M iBK2- M/ MQ T B` Q7 i bFb QM i?2 b K2 KQ/mH2 `2 HHQr2/ iQ Qp2`H TX h?mb- 2 +? i bF Kmbi #2 ;` Mi2/ MQM@T`22KTi2/ iBK2 bHQi rBi? i?2 /m` iBQM Q7 Bib 2t2+miBQM `2[mB`2@ K2Mi QM Bib KQ/mH2X h?2 2t2+miBQM `2[mB`2K2Mi Q7 i bF +Q``2bTQM/b iQ Bib rQ`bi@+ b2 2t2+miBQM iBK2 Q` Bib rQ`bi@+ b2 /m` iBQMX M //BiBQM H `2[mB`2@ K2Mi Bb i? i i?2 MQM@T`22KTi2/ iBK2 bHQi Q7 2 +? i bF Kmbi #2 rBi?BM QM2 Q7 Bib ;Bp2M bm#@BMi2`p Hb- r?2`2 bm#@BMi2`p H +QMbBbib Q7 `2H2 b2 iBK2 M/ /2 /HBM2 T B`X. S`2+2/2M+2 `2H iBQMb h?2`2 `2 irQ ivT2b Q7 T`2+2/2M+2 `2H iBQM +QMbi` BMib BM i?2 T`Q#H2K- `2@ 72``2/ iQ b /2T2M/2M+B2b M/ +? BMbX h?2 T`2+2/2M+2 +QMbi` BMib 2Mbm`2 i? i / i `2 T`Q+2bb2/ BM i?2 +Q``2+i Q`/2` rBi?BM i?2 bvbi2KX h?2 T`2+2/2M+2 +QMbi` BMib + HH2/ /2T2M/2M+B2b- `2bi`B+i i?2 /m` iBQM #2ir22M T B` Q7 i bFbr?2`2 i?2 i bFb + M #2 QM i?2 b K2 Q` QM /Bz2`2Mi KQ/mH2bX 6Q`K HHv- /2@ T2M/2M+v `2bi`B+ib i?2 /m` iBQM 7`QK i?2 bi `i Q7 i bF BMbi M+2 iQ i?2 bi `i Q7 MQi?2` i bF BMbi M+2 iQ #2 ;`2 i2` i? M Q` 2[m H iQ KBMBKmK H2M;i? M/ bK HH2` i? M Q` 2[m H iQ K tBKmK H2M;i?X. N.
(21) kX. pBQMB+ b+?2/mHBM;. h?2 b2+QM/ ivT2 Q7 T`2+2/2M+2 `2H iBQMb +QMbi` BMib- i?2 +? BMb- `2bi`B+i i?2 /m` iBQM #2ir22M i?2 bi `i M/ 2M/ Q7 b2[m2M+2 Q7 i bFb- r?2`2 i?2 i bFb + M #2 QM i?2 b K2 Q` QM /Bz2`2Mi KQ/mH2bX 6Q`K HHv- +? BM `2bi`B+ib i?2 /m` iBQM 7`QK i?2 bi `i iQ i?2 2M/ Q7 +v+HB+ Q`/2` Q7 i bF BMbi M+2b iQ #2 H2bb i? M K DQ` T2`BQ/X /D +2Mi i bF BMbi M+2b BM +? BM `2 Q7i2M +QMM2+i2/ pB /2T2M/2M+B2bX. *QKKmMB+ iBQM M2irQ`F h?2 `QH2 Q7 i?2 *L Bb iQ b2M/ K2bb ;2b #2ir22M i?2 *Jb BM i?2 bvbi2KX AM i?2 *L- i?2`2 2tBbib b2i Q7 T`2@/2}M2/ bHQib 2p2`v K DQ` T2`BQ/ r?2`2 K2bb ;2b + M #2 b2MiX 1 +? K2bb ;2 QM i?2 *L Bb b2Mi 7`QK bBM;H2 *J iQ b2i Q7 `2+2BpBM; *Jb M/ Kmbi #2 HHQ+ i2/ iQ bHQiX AM Q`/2` iQ b2M/ M/ `2+2Bp2 K2bb ;2- 7Qm` ivT2b Q7 i bFb `2 BMpQHp2/X PM i?2 b2M/BM; *J- i?2`2 `2 irQ i bFb `2bTQMbB#H2 7Q` T`2T `BM; M/ b2M/BM; i?2 K2bb ;2- r?BH2 QM 2 +? `2+2BpBM; *J- i?2`2 `2 irQ i bFb i? i /2[m2m2 i?2 K2bb ;2 M/ `2 / i?2 / i X h?2 7Qm` ivT2b Q7 i bFb BMpQHp2/ BM b2M/BM; M/ `2+2BpBM; K2bb ;2 Kmbi #2 T2`7Q`K2/ BM T `iB+mH ` Q`/2`- r?B+? Bb 2M7Q`+2/ #v /2T2M/2M+B2b M/ +? BMbX 1 +? K2bb ;2 `2[mB`2b +2`i BM # M/rB/i? BM i?2 bHQi Bi Bb b2Mi BMX h?mbi?2 `2[mB`2/ + T +Biv Q7 i?2 K2bb ;2b b2Mi BM bHQi Bb MQi HHQr2/ iQ 2t+22/ i?2 # M/rB/i? Q7 i? i bHQiX hrQ //BiBQM H +QMbi` BMib `2 i? i i bFb Kmbi #2 /2[m2m2/ BM i?2 Q`/2` i? i i?2 K2bb ;2b `2 b2Mi- M/ i? i i?2 i bFb `2bTQMbB#H2 7Q` b2M/BM; M/ /2[m2mBM; i?2 K2bb ;2 Kmbi #2 T2`7Q`K2/ rBi?BM +2`i BM bm#@BMi2`p Hb- r?2`2 i?2 bm#@BMi2`p Hb /2T2M/ QM i?2 bHQi i?2B` K2bb ;2 ? b #22M bbB;M2/ iQX A7 irQ Q` KQ`2 K2bb ;2b `2 b2Mi BM i?2 b K2 bHQi- i?2B` i bFb Q7 i?2 b K2 ivT2 Kmbi #2 T2`7Q`K2/ BM BKK2/B i2 bm++2bbBQM B7 i?2v `2 T2`7Q`K2/ QM i?2 b K2 *JX h?Bb Bb `272``2/ iQ b +Q@ HHQ+ iBQM Q7 K2bb ;2b BM bHQiX #2M2}i Q7 +Q@ HHQ+ iBQM Q7 K2bb ;2b- Bb i? i i?2 i bFb i? i Kmbi #2 T2`7Q`K2/ BM BKK2/B i2 bm++2bbBQM ;2i `2/m+2/ 2t2+miBQM `2[mB`2K2Mib +QKT `2/ iQ B7 i?2v r2`2 T2`7Q`K2/ b2T ` i2HvX AM S T2` M/ S T2` "- MQ +Q@ HHQ+ iBQM Q7 K2bb ;2b BM bHQi Bb HHQr2/X. h2+?MB+ H Q`B2Mi iBQM Q7 i?2 bvbi2K h?Bb b2+iBQM T`QpB/2b bQK2 //BiBQM H +QKK2Mib rBi? `2bT2+i iQ i2+?MB+ H /2@ i BHbX h?2 Tm`TQb2 Q7 i?Bb Bb iQ Tmi i?2 b+?2/mHBM; T`Q#H2K BMiQ T2`bT2+iBp2X h?2 AJ bvbi2K r2 //`2bb Bb bvM+?`QMQmbX h?2 Tm`TQb2 Q7 i?2 T`2@`mMiBK2 b+?2/mHBM; Bb iQ +`2 i2 ;HQ# H bi iB+ b+?2/mH2 7Q` i?Bb bvbi2KX h?2 bvbi2K Bb i?2M `mM #v /BbT i+?2`b ++Q`/BM; iQ i?Bb ;HQ# H bi iB+ b+?2/mH2X h?2 QMHv + b2 Q7 `mMiBK2 b+?2/mHBM; Q7 i?2 bvbi2K Bb /QM2 BMbB/2 i?2 T `iBiBQMb QM i?2 Jb r?2`2 i?2 bQ7ir `2 TTHB+ iBQMb `2 `mM #v ` i2@KQMQiQMB+ b+?2/mH2`X h?2 *L i? i r2 /2b+`B#2 Bb iBK2@/BpBbBQM KmHiBTH2 ++2bb Uh.JV 1i?2`@ Ry.
(22) kXkX M BMi2;` i2/ KQ/mH ` pBQMB+ b+?2/mHBM; T`Q#H2K M2i M2irQ`F i? i bmTTQ`ib KmHiB+ bi- b22 T i2Mi (Ry)X 6Q` 7m`i?2` i2+?MB+ H Q`B2Mi iBQM M/ `2H i2/ `2b2 `+? Q7 i?Bb T`Q#H2K- b22 i?2 BMi`Q/m+iQ`v T `ib Q7 S T2` M/ S T2` *X. RR.
(23)
(24) j aBM;H2 K +?BM2 b+?2/mHBM; M/ KBt2/ BMi2;2` T`Q;` KKBM;. +Q`2 bT2+i Q7 K Mv H `;2@b+ H2 b+?2/mHBM; T`Q#H2Kb Bb iQ +`2 i2 b+?2/mH2 7Q` QM2 K +?BM2X h?2 KQbi 7mM/ K2Mi H Q7 bm+? b+?2/mHBM; T`Q#H2Kb `2 i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2KbX AM bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K b2i Q7 i bFb UDQ#b Q` +iBpBiB2bV b? HH #2 b+?2/mH2/ rBi?Qmi Qp2`H T QM bBM;H2 T`Q+2bbQ` UK +?BM2 Q` `2bQm`+2VX aBM+2 b+?2/mHBM; Q7 K +?BM2b Q7i2M Bb +Q`2 T `i Q7 H `;2` b+?2/mHBM; T`Q#H2K- i?2 T2`7Q`K M+2 Q7 bm+? b+?2/mHBM; Bb +`BiB+ H iQ Q#i BM Qp2` HH +QK@ Tmi iBQM H 2{+B2M+vX b bm+?- bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2Kb ? p2 #22M 2ti2MbBp2Hv bim/B2/X AM i?Bb b2+iBQM- r2 bm`p2v JAS 7Q`KmH iBQMb 7Q` bBM@ ;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2b- r?2`2 i?2 Tm`TQb2 Bb iQ }M/ Qmi B7 72 bB#H2 b+?2/mH2 2tBbib Q` MQiX. jXR #`B27 ?BbiQ`B+ H T2`bT2+iBp2 a?Q`iHv 7i2` i?2 BMi`Q/m+iBQM Q7 JAS #v (R8)- i?`22 JAS TT`Q +?2b iQ bQHp2 b+?2/mHBM; T`Q#H2Kb r2`2 BMi`Q/m+2/X h?2 TT`Q +?2b /Bz2`2/ BM i?2B` +?QB+2 Q7 #BM `v /2+BbBQM p `B #H2X h?2 i?`22 K BM ivT2b Q7 7Q`KmH iBQMb r2`2, BM (3) i?2 p `B #H2 r b iBK2@# b2/ #v bbB;MBM; 2 +? i bF bi `i iBK2- BM (je) i?2 p `B #H2 r b TQbBiBQM@# b2/ #v bbB;MBM; 2 +? i bF TQbBiBQM BM i?2 b+?2/mH2 M/ BM (kj) i?2 p `B #H2 r b Q`/2`@# b2/ #v bbB;MBM; M Q`/2` #2ir22M 2 +? T B` Q7 i bFbX aim/vBM; i?2 TQHv?2/`QM 7Q` M Q`/2`@# b2/ /2+BbBQM p `B #H2- (j) #2; M b2`B2b Q7 TQHv?2/` H `2bmHib Q7 /Bz2`2Mi JAS 7Q`KmH iBQMb 7Q` bBM;H2 K +?BM2 Rj.
(25) jX. aBM;H2 K +?BM2 b+?2/mHBM; M/ KBt2/ BMi2;2` T`Q;` KKBM;. b+?2/mHBM;X h?2 i?`22 K BM + i2;Q`B2b r2`2 bim/B2/ BM /Bz2`2Mi T T2`b rBi? bHB;?iHv /Bz2`2Mi T`Q#H2K 7Q`KmH iBQMb- b22 /2i BHb BM i?2 7QHHQrBM; b2+iBQMbX AM (k3)- i?2b2 `2+2Mi /p M+2b BM TQHv?2/` H `2bmHib 7Q` bBM;H2 K +?BM2 b+?2/mHBM; r2`2 bmKK `Bb2/X .m`BM; i?2 H bi irQ /2+ /2b- i?2`2 ? b #22M bQK2 i?2Q`2iB+ H /p M+2b- T`B@ K `BHv BM i?2 TQbBiBQM@# b2/ TT`Q +?- b22 (ky) M/ (RR)X h?2`2 ? p2 HbQ #22M bQK2 M2r 2ti2MbBQMb rBi? iBK2@# b2/ TT`Q +?- b22 (9) M/ (d)X "mi i?2`2 ? p2 HbQ #22M bQK2 +QKTmi iBQM H +QKT `BbQMb 2p Hm iBM; i?2 T2`7Q`K M+2 QM /Bz2`2Mi 7Q`KmH iBQMb- b22 (9)- (RN)- M/ (k)X. jXk aBM;H2 K +?BM2 b+?2/mHBM; rBi? `2H2 b2 iBK2b M/ /2 /HBM2b AM i?Bb b2+iBQM- r2 BMi`Q/m+2 i?2 i2`KBMQHQ;v M/ MQi iBQM i? i rBHH #2 mb2/ 7Q` MQM@T`22KTiBp2 bBM;H2 K +?BM2 b+?2/mHBM; rBi? `2H2 b2 iBK2b M/ /2 /HBM2b BM i?2 7QHHQrBM; b2+iBQMbX G2i I /2MQi2 b2i Q7 i bFb i? i b? HH #2 b+?2/mH2/ rBi?Qmi T`2@2KTiBQM QM bBM;H2 K +?BM2 i? i + M ? M/H2 i KQbi QM2 i bF i iBK2X bbQ+B i2/ rBi? 2 +? i bF i ∈ I- Bb `2H2 b2 iBK2 ri M/ /2 /HBM2 di - bT2+B7vBM; M BMi2`p H [ri , di ] r?2`2BM i?2 i bF Kmbi #2 T`Q+2bb2/X h?2 T`Q+2bbBM; iBK2 UQ` /m` iBQMV Q7 i bF i ∈ I Bb /2MQi2/ #v pi X h?2 BK Bb iQ 2p Hm i2 B7 i?2`2 2tBbi 72 bB#H2 b+?2/mH2 U M/ B7 QM2 bm+? 2tBbibc ;Bp2 BiV i? i `2bT2+i i?2 `2H2 b2 iBK2 M/ /2 /HBM2 Q7 2 +? i bFX lbBM; i?2 α∣β∣γ +H bbB}+ iBQM b+?2K2 BM (kk)- bHB;?i 2ti2MbBQM Q7 i?2 QM2 Q`B;BM HHv BMi`Q/m+2/ BM (Re)- i?Bb T`Q#H2K + M Bb +H bbB}2/ b 1∣rj , d¯j ∣−X AM (R9)- i?Bb T`Q#H2K r b T`Qp2M iQ #2 LS@+QKTH2i2 7Q` `#Bi` `v `2H2 b2 iBK2b- /2 /HBM2b M/ T`Q+2bbBM; iBK2bX. jXj hBK2@# b2/ 7Q`KmH iBQMb AM i?Bb b2+iBQM- r2 T`2b2Mi /Bz2`2Mi 7Q`KmH iBQMb +2Mi`2/ QM iBK2@# b2/ #BM `v /2+BbBQM p `B #H2bX aBM+2 i?2 MmK#2` Q7 p `B #H2b /2T2M/b QM i?2 b+?2/mHBM; ?Q`BxQM- 7Q` T`Q#H2K rBi? HQM; b+?2/mHBM; ?Q`BxQM i?2 iBK2@BM/2t2/ TT`Q +? Bb MQi T` +iB+ H BM 2p2`v +B`+mKbi M+2X h?2`27Q`2- bQK2 M2r 7Q`KmH iBQMb rBi? i?Bb BM KBM/- bm+? b i?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM M/ i?2 #m+F2i@BM/2t2/ 7Q`KmH iBQM `2 T`2b2Mi2/X. hBK2@BM/2t2/ 7Q`KmH iBQM h?2 iBK2@BM/2t2/ TT`Q +? /BpB/2b i?2 b+?2/mHBM; ?Q`BxQM T = maxi∈I di BMiQ mMBi bBx2 iBK2 T2`BQ/b M/ mb2b #BM `v /2+BbBQM p `B #H2 iQ bi i2 r?2i?2` T `iB+mH ` i bF bi `i i T `iB+mH ` iBK2 T2`BQ/X h?Bb `2[mB`2b i? i HH T`Q+2bbBM; iBK2b Q7 i bFb `2 BMi2;2` UQ` i H2 bi ` iBQM HV- bBM+2 i?2 `2bQHmiBQM rBHH #2 i?2 mMBi bBx2/ iBK2 T2`BQ/X R9.
(26) jXjX hBK2@# b2/ 7Q`KmH iBQMb AMi`Q/m+2 7Q` i bF i ∈ I- M/ iBK2 T2`BQ/ t- t = 0, . . . , T - i?2 #BM `v p `B #H2 ⎧ ⎪ ⎪1, B7 i bF i bi `ib BM iBK2 T2`BQ/ txit = ⎨ ⎪ ⎪ ⎩0, Qi?2`rBb2X "v }M/BM; bQHmiBQM i? i Q#2v T −pi +1. ∑ xit′ = 1,. ∑. t′ =0 t. ∑. i∈I t′ =t−pi +1. xit′ ≤ 1,. ri −1. ∑ xit′ = 0,. t′ =0 T. ∑. t′ =di −pi +1. xit′ = 0,. xit ∈ {0, 1},. i ∈ I,. UjXRV. UjXkV. t = 0, . . . , T,. UjXjV. i ∈ I,. UjX9V. i ∈ I,. t = 0, . . . , T, i ∈ I,. UjX8V UjXeV. r2 ? p2 72 bB#H2 b+?2/mH2 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2bX AM i?2 7Q`KmH iBQM- *QMbi` BMi UjXkV bbB;Mb 2 +? i bF iBK2 T2`BQ/- *QMbi` BMi UjXjV T`2p2Mib 2t2+miBQM Q7 KQ`2 i? M QM2 i bF BM iBK2 T2`BQ/- *QMbi` BMi UjX9V K F2b bm`2 i? i 2 +? i bF `2bT2+i Bib `2H2 b2 / i2- r?BH2 *QMbi` BMi UjX9V K F2b bm`2 i? i 2 +? i bF `2bT2+i Bib /2 /HBM2X P#b2`p2 i? i *QMbi` BMib UjX9VĜUjX8V +QmH/ #2 `2TH +2/ #v b2iiBM; xit = 0 7Q` 2 +? i bF i BM iBK2 T2`BQ/ t ∉ {ri , . . . , di }X h?2 iBK2@BM/2t2/ 7Q`KmH iBQM iQ b+?2/mHBM; T`Q#H2K r b BMi`Q/m+2/ #v (3)- 7Q` r? i r2 iQ/ v rQmH/ + HH K +?BM2 b+?2/mHBM; T`Q#H2KX AM i?Bb BMBiB H 7Q`KmH iBQM i?2 #BM `v p `B #H2 mb2/ r b bHB;?iHv /Bz2`2Mi- BMbi2 / BM/B+ iBM; r?2i?2` Q` MQi i bF b?QmH/ #2 T2`7Q`K2/ i ;Bp2M iBK2X aQK2 v2 `b H i2`(ke) T`2b2Mi2/ p `B iBQM Q7 i?Bb p `B #H2 /2}MBiBQM rBi? #BM `v p `B #H2 i? i BM/B+ i2b B7 i bF }MBb? i +2`i BM iBK2 T2`BQ/X AM i?2 2 `Hv RNNyb i?2Q`2iB@ + H T`QT2`iB2b M/ BM2[m HBiB2b 7Q` i?2 iBK2@BM/2t2/ 7Q`KmH iBQM r2`2 bim/B2/ #v (Rk)X AM (j9)- 7m`i?2` p HB/ BM2[m HBiB2b # b2/ QM FM Tb +F `2H t iBQMb r2`2 T`2b2Mi2/ HQM; rBi? T`Q+2/m`2 iQ Q#i BM bm+? p HB/ BM2[m HBiB2bX h?Bb T`Q+2@ /m`2 r b mb2/ BM +miiBM; TH M2 7` K2rQ`F i? i r b i2bi2/ QM bBM;H2 K +?BM2 b+?2/mHBM; BMbi M+2bX JQ`2 `2bmHib r2`2 Tm#HBb?2/ BM (R)- 2ti2M/BM; i?2 `2bmHib Q7 (Rk)- 7Q+mbBM; QM BM2[m HBiB2b rBi? `B;?i@? M/ bB/2 2[m H iQ 1 M/ 2X. AMi2`p H@BM/2t2/ 7Q`KmH iBQM h?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM r b BMi`Q/m+2/ BM (9)X AM i?Bb 7Q`KmH iBQMi?2 b+?2/mHBM; ?Q`BxQM Bb T `iBiBQM2/ BMiQ BMi2`p HbX G2i Q /2MQi2 i?2 b2i Q7 BMi2`p HbX h?2 H2M;i?b Q7 i?2 BMi2`p Hb `2 `#Bi` `v M/ 7Q` BMi2`p H q ∈ Qi?2 iBK2@TQBMib (taq , taq+1 ] /2}M2 i?2 BMi2`p HX 6Q` 2 +? BMi2`p H q ∈ Q- H2i Iqa R8.
(27) jX. aBM;H2 K +?BM2 b+?2/mHBM; M/ KBt2/ BMi2;2` T`Q;` KKBM;. /2MQi2 i?2 b2i Q7 i bFb rBi? T`Q+2bbBM; iBK2 H2bb i? M Q` 2[m H iQ i?2 H2M;i? Q7 i?2 BMi2`p HX aBKBH `Hv- H2i Iq" /2MQi2 i?2 b2i Q7 i bFb rBi? T`Q+2bbBM; iBK2 H `;2` i? M i?2 H2M;i? Q7 i?2 BMi2`p H q ∈ QX h?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM Bb # b2/ QM irQ /2+BbBQMb, /2i2`KBM2 M BMi2`p H 7Q` 2 +? i bF iQ bi `i BM M/ K2 bm`2 i?2 B/H2 iBK2 7Q` 2 +? BMi2`p HX AM Q`/2` iQ +`2 i2 p HB/ 7Q`KmH iBQM- i?2 mi?Q`b T`Qp2 i? i i?2 i bFb + M Hr vb #2 Q`/2`2/ BM bT2+B}+ r v i? i K F2b i?2 B/H2 iBK2 7Q` M BMi2`p H r2HH /2}M2/X 6Q` 2 +? i bF i ∈ I M/ BMi2`p H q ∈ Q- BMi`Q/m+2 i?2 #BM `v p `B #H2b ⎧ ⎪ ⎪1, a ziq =⎨ ⎪ ⎪ ⎩0,. B7 i bF i bi `ib BM BMi2`p H q Q` 2 `HB2`Qi?2`rBb2-. M/. ⎧ ⎪ ⎪1, B7 i bF i Bb +QKTH2i2/ BM BMi2`p H q Q` 2 `HB2`1 ziq =⎨ ⎪ ⎪ ⎩0, Qi?2`rBb2X HbQ BMi`Q/m+2 7Q` 2 +? BMi2`p H q ∈ Q- i?2 +QMiBMmQmb p `B #H2 = i?2 B/H2 iBK2 Q7 BMi2`p H qX uB/H2 q qBi? i?2b2 p `B #H2b- i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2b + M #2 7Q`KmH i2/ b 1 1 ≤ zi,q+1 , ziq. q ∈ Q, i ∈ I,. UjXdV. a a ziq ≤ zi,q+1 ,. q ∈ Q, i ∈ I,. UjX3V. 1 a ziq ≤ ziq ,. q ∈ Q, i ∈ I,. UjXNV. a 1 ziq ≤ zi,q+1 ,. i ∈ Iqa , q ∈ Q,. UjXRyV. 1 a ziq ≤ zi,q−1 ,. i ∈ Iq" , q ∈ Q,. UjXRRV. 1. q. B/H2. ≤ taq+1 ,. q ∈ Q,. UjXRkV. B/H2. ≥ taq+1 ,. q ∈ Q,. UjXRjV. ∑ pi ziq + ∑ uq 1. i∈I. a. q. ∑ pi ziq + ∑ uq 1. i∈I. a 1 uB/H2 ≤ (taq+1 − t1 q q−1 )(1 − ∑ )(ziq − zi,q+1 ),. q ∈ Q,. UjXR9V. i∈I. a. 1. 1. a. ∑ (ziq − zi,q+1 ) + zi′ ,q+1 − zi′ q ,. i∈Iq". Re. i′ ∈ Iqa , q ∈ Q.. UjXR8V.
(28) jXjX hBK2@# b2/ 7Q`KmH iBQMb *QMbi` BMib UjXdV M/ UjX3V- 2Mbm`2 +QMbBbi2Mi /2}MBiBQM Q7 i?2 #BM `v p `B@ #H2bX *QMbi` BMi UjXNV K F2b bm`2 i? i B7 i bF Bb +QKTH2i2/ BM bQK2 BMi2`@ p H- Bi b?QmH/ #2 bi `i2/ BM i?Bb BMi2`p H Q` 2 `HB2`X *QMbi` BMi UjXRyV 7Q`+2b i?2 7 +i i? i- B7 i bF /Q2b MQi }i BMbB/2 M BMi2`p H- Bi + MMQi bi `i #27Q`2 i?Bb BMi2`p H M/ 2M/ BM M H i2` BMi2`p HX *QMbi` BMi UjXRRV 2Mbm`2b i? i i bFb i? i `2 H `;2` i? M M BMi2`p H + MMQi bi `i M/ 2M/ BM i?2 b K2 BMi2`p HX *QMbi` BMib UjXRkV M/ UjXRjV- 2Mbm`2 i? i i?2 T`Q+2bbBM; iBK2b Q7 i bF b+?2/@ mH2/ mT iQ i?2 bi `i Q7 M BMi2`p H rBi? i?2 B/H2 iBK2 Bb +QMbBbi2Mi rBi? i?2 iBK2 bT2MiX *QMbi` BMi UjXR9V Tmib B/H2 iBK2b iQ x2`Q B7 i bF bi `ib #27Q`2 i?2 BMi2`p H M/ 2M/b 7i2` i?2 BMi2`p HX *QMbi` BMi UjXR8V 2HBKBM i2b Qp2`H T #2ir22M i bF i? i Bb iQQ H `;2 7Q` M BMi2`p H M/ i bF i? i Bb 7mHHv T`Q@ a 1 +2bb2/ rBi?BM i? i BMi2`p HX Smi i?2 +Q``2bTQM/BM; ziq M/ ziq 2[m H iQ x2`Q iQ ++QmMi 7Q` `2H2 b2 iBK2b M/ /2 /HBM2bX 6Q` T`QQ7 i? i i?Bb rBHH vB2H/ 72 bB#H2 b+?2/mH2- b22 (9)X 7Q`KmH iBQM bBKBH ` iQ i?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM Bb mb2/ BM (N)X AM (N)- HQ;B+@# b2/ "2M/2`b /2+QKTQbBiBQM b+?2K2 Bb mb2/ iQ bQHp2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2KX h?2 b+?2K2 Bb iQ- bbB;M M BMi2`p H iQ 2 +? i bF BM `2H t2/ T`Q#H2K M/ 2p Hm i2 M bbB;MK2Mi Q7 BMi2`p Hb iQ i bFb BM bm#T`Q#H2KX h?2 mi?Q`b bQHp2 i?2 `2H t2/ T`Q#H2Kb mbBM; JAS bQHp2` r?BH2 i?2 bm#T`Q#H2Kb `2 bQHp2/ mbBM; +QMbi` BMi T`Q;` KKBM; bQHp2`X h?Bb TT`Q +? Bb TTHB2/ iQ irQ bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2KbX PM2 Bb i?2 T`Q#H2K r2 /2b+`B#2 BM a2+iBQM jXk M/ i?2 Qi?2` Bb bBM;H2 K +?BM2 T`Q#H2K r?2`2 BMi2`p Hb `2 /BbDQBMi- K2 MBM; i? i 2 +? i bF Kmbi #2 7mHHv T2`7Q`K2/ rBi?BM M BMi2`p HX. "m+F2i@BM/2t2/ 7Q`KmH iBQM h?2 #m+F2i@BM/2t2/ 7Q`KmH iBQM r b bm;;2bi2/ #v (d) M/ r b BMbTB`2/ #v bBK@ BH ` TT`Q +?2b mb2/ BM HQi@bBxBM;X AM i?Bb 7Q`KmH iBQM- i?2 b+?2/mHBM; ?Q`BxQM Bb /BpB/2/ BMiQ #m+F2ib Q7 2[m H bBx2X >Qr2p2`- i?2 #m+F2i bBx2 pB Bb b2H2+i2/ iQ #2 H2bb i? M i?2 b?Q`i2bi T`Q+2bbBM; iBK2 Q7 HH i bFb- ?2M+2 pB ≤ mini∈I pi X h?2 `2 bQM 7Q` i?Bb Bb iQ K F2 bm`2 i? i QMHv bBM;H2 i bF + M bi `i BM #m+F2i- M/ 2 +? i bF Kmbi bT M i H2 bi irQ #m+F2ibX h?2 #m+F2i@BM/2t2/ TT`Q +? Bb bBKBH ` iQ i?2 B/2 Q7 i?2 iBK2@BM/2t2/ 7Q`KmH iBQM- r?B+? + M #2 b22M b bT2+B H + b2 Q7 i?2 #m+F2i 7Q`KmH iBQM r?2`2 i?2 #m+F2i bBx2 Bb 2[m H iQ QM2X G2i {1, . . . , B} /2MQi2 i?2 #m+F2ibX 6Q` 2 +? i bF i ∈ I- H2i Bi /2MQi2 i?2 MmK#2` Q7 #m+F2ib Bi Kmbi i H2 bi bT MX 6Q` 2 +? i bF i ∈ I- k ∈ {0, 1}- M/ #m+F2i b ∈ {1, . . . , B}- BMi`Q/m+2 i?2 #BM `v p `B #H2 zibk. ⎧ ⎪ ⎪1, =⎨ ⎪ ⎪ ⎩0,. B7 i bF i bi `ib BM #m+F2i b M/ }MBb?2b BM #m+F2i b + Bi + kQi?2`rBb2X. Rd.
(29) .
(30)
(31) . i I
(32)
(33)
(34) i =
(35) i
(36)
(37) i i I k {0, 1} b {1, . . . , B}
(38)
(39)
(40) uibk.
(41) i
(42) b
(43) i
(44) b = Bi + k .
(45) i
(46) b
(47) i
(48) b = u ibk Bi + k
(49)
(50) . . zibk = 1,. i I,. . zibk 1,. b {1, . . . , B},. !. k{0,1} b{1,...,B}. . . iI k{0,1} b{b Bi k+2,...,b }. zibk 1, uibk + u ibk + iI k{0,1} b{b Bi k+2,...,b 1} . b {1, . . . , B}, ". uibk + u i,b+Bi +k1,k = (2 k i ),. i I, k {0, 1}, b {1, . . . , B},. ((1 k)(1 i ) + 1/pb )zibk uibk ,. i I, k {0, 1}, b {1, . . . , B}, $%. uibk (1 ki )zibk ,. i I, k {0, 1}, b {1, . . . , B},. (1 k)(1 i )zibk u i,b+Bi +k1,k ,. u i,b+Bi +k1,k 1 ki . 1. zibk , pB. i I, k {0, 1}, b {1, . . . , B},. #. $ . $$. i I, k {0, 1}, b {1, . . . , B}. $ . &
(51)
(52) &
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(54)
(55) &
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(59) jX9X P`/2`@# b2/ 7Q`KmH iBQMb p `B #H2 ;2i i?2 +Q``2+i /2}MBiBQMbX _2H2 b2 iBK2b M/ /2 /HBM2b + M #2 KQ/@ 2HH2/ #v `2bi`B+iBM; i?2 T`QT2` zibk - uaibk M/ u1 ibk X h?2 #m+F2i@BM/2t2/ 7Q`KmH iBQM Bb bBKBH ` iQ i?2 iBK2@BM/2t2/ 7Q`KmH iBQM M/ i?2Q`2iB+ HHv i H2 bi b bi`QM; b i?2 iBK2@BM/2t2/ 7Q`KmH iBQMX h?Bb Bb T`Qp2M BM (d)X AM (jR)- #m+F2i@BM/2t2/ TT`Q +? Bb BKTH2K2Mi2/ BM M Bi2` iBp2 7` K2rQ`F- bm++2bbBp2Hv /BpB/BM; i?2 b+?2/mHBM; ?Q`BxQM BMiQ H `;2` TB2+2b- 7Q` `2bQm`+2@+QMbi` BM2/ T`QD2+i b+?2/mHBM; T`Q#H2KX. jX9 P`/2`@# b2/ 7Q`KmH iBQMb h?2 Q`/2`@# b2/ 7Q`KmH iBQMb `2 +2Mi`2/ `QmM/ T B` Q7 i bFb M/ bbm`BM; i? i bm+? T B`b /Q MQi Qp2`H TX q2 rBHH BMi`Q/m+2 irQ 7Q`KmH iBQMb i? i #Qi? mb2 #BM `v /2+BbBQM p `B #H2 i? i BM/B+ i2 BM r?B+? Q`/2` 2 +? T B` Q7 i bFb Q++m`- M/ +QMiBMmQmb p `B #H2 `2T`2b2MiBM; i?2 bi `iBM; iBK2 Q7 2 +? i bFX "v +QMM2+iBM; i?2 Q`/2`@p `B #H2 7Q` 2 +? T B` Q7 i bFb iQ i?2B` bi `i iBK2 p `B #H2b pB +QMbi` BMib- 2 +? T B` Q7 i bFb + M #2 2Mbm`2/ MQi iQ Qp2`H TX >Qr i?Bb Bb /QM2 Bb i?2 K BM /Bz2`2M+2 #2ir22M i?2 irQ 7Q`KmH iBQMbX AMi`Q/m+2- 7Q` 2 +? T B` Q7 i bFb i ∈ I- j ∈ I- j ≠ i- i?2 #BM `v p `B #H2 ⎧ ⎪ ⎪1, yij = ⎨ ⎪ ⎪ ⎩0,. B7 i bF i 2t2+mi2 #27Q`2 i bF jQi?2`rBb2X. UjXk9V. 6Q` 2 +? i bF i- i ∈ I- BMi`Q/m+2 i?2 +QMiBMmQmb p `B #H2 si = bi `i iBK2 Q7 i bF iX. UjXk8V. .BbDmM+iBp2 7Q`KmH iBQM h?2 /BbDmM+iBp2 7Q`KmH iBQM mb2b i?2 T`2pBQmbHv /2}M2/ p `B #H2b iQ +`2 i2 +QKTH2i2 b+?2/mH2 7Q` bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2bX h?2 7Q`KmH iBQM Bb sj ≥ si + pi − M (1 − yij ), yij + yji = 1,. i ∈ I, j ∈ I, i ≠ j,. i ∈ I, j ∈ I, i < j,. r i ≤ s i ≤ d i − pi ,. i ∈ I,. UjXkeV UjXkdV UjXk3V. r?2`2 *QMbi` BMib UjXkeVĜUjXkdV bbm`2 i? i MQ irQ i bFb Qp2`H T- M/ *QM@ bi` BMi UjXk3V K F2b 2 +? i bF `2bT2+i Bib `2H2 b2 iBK2 M/ /2 /HBM2X LQi2 i? i *QMbi` BMi UjXkeV Bb Q7 #B;@J ivT2 M/ rBHH vB2H/ r2 F GS@`2H t iBQMX h?2 }`bi `iB+H2 iQ BMi`Q/m+2 M Q`/2`@# b2/ /2+BbBQM p `B #H2 7Q` b+?2/mH@ BM; T`Q#H2K r b (kj) BM i?2 +QMi2ti Q7 DQ#@b?QT b+?2/mHBM;X AM i?2 b K2 v2 ` p `B Mi Q7 /2}MBM; M Q`/2`@# b2/ p `B #H2 r b HbQ bim/B2/ BM (k9) 7Q` i?2 i` p2HHBM; b H2bK M T`Q#H2KX AM i?Bb b2iiBM;- i?2 #BM `v /2+BbBQM p `B #H2 /2@ MQi2/ B7 i bF r b i?2 BKK2/B i2 T`2/2+2bbQ` iQ MQi?2` i bF BM b+?2/mH2 Q` MQiX RN.
(60) jX. aBM;H2 K +?BM2 b+?2/mHBM; M/ KBt2/ BMi2;2` T`Q;` KKBM;. h?2 TQHv?2/` H bim/B2b Q7 /BbDmM+iBp2 7Q`KmH iBQM 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K r b bi `i2/ #v (j)- r?Q bim/B2/ i?2 TQHv?2/` BM i?2 +QM@ i2ti Q7 DQ# b?QT b+?2/mHBM; 7Q` rB/2 ` M;2 Q7 +QMbi` BMibX M 2ti2M/2/ /2b+`BTiBQM Q7 i?2 TQHv?2/` Q7 i?2 /BbDmM+iBp2 7Q`KmH iBQM r b ;Bp2M 72r v2 `b H i2` BM (kd)- r?Q miBHBb2/ i?2 `2bmHib BM +miiBM; TH M2 T`Q+2/m`2X. GBM2 `@Q`/2`BM; 7Q`KmH iBQM h?2 HBM2 `@Q`/2`BM; 7Q`KmH iBQM Bb p `B iBQM Q7 i?2 /BbDmM+iBp2 7Q`KmH iBQM r?2`2 i?2 Q`/2`@# b2/ /2+BbBQM p `B #H2b `2 +QMM2+i2/ rBi? i?2 i`B M;H2 BM@ 2[m HBiv BMbi2 / Q7 #B;@J +QMbi` BMibX AM Q`/2` iQ ;2i r2HH@/2}M2/ b+?2/mH2 M Q#D2+iBp2 7mM+iBQM iQ KBMBKBb2 i?2 bmK Q7 i?2 bi `iBM; iBK2b Bb mb2/X h?2 7Q`KmH iBQM bbmK2b i? i I Bb Q`/2`2/ rBi? `2bT2+i iQ b+2M/BM; `2H2 b2 iBK2b M/ bQHpBM; min ∑ si , UjXkNV i∈I. bm#D2+i iQ yij + yji = 1, yij + yjk + yki ≤ 2,. i ∈ I, j ∈ I, i < j,. UjXjyV. i ∈ I, j ∈ I, k ∈ I, i ≠ j ≠ k,. sj ≥ ri yij + ∑ pk (yik + ykj − 1) + ∑ pk ykj , k∈I, k<i,k≠j. i ∈ I, j ∈ I,. UjXjRV UjXjkV. k∈I, k≥i,k≠j. s i ≤ d i − pi ,. i ∈ I,. UjXjjV. rBHH +`2 i2 72 bB#H2 b+?2/mH2 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2bX AM i?2 7Q`KmH iBQM- *QMbi` BMib UjXjyVĜUjXjRV bbm`2 p HB/ b2[m2M+2- *QMbi` BMi UjXjkV 7Q`+2b 2 +? i bF `2bT2+i Bib `2H2 b2 iBK2- r?BH2 K FBM; bm`2 i? i i bFb /Q2b MQi bi `i #27Q`2 T`2+2/BM; i bFb `2 }MBb?2/X *QMbi` BMi UjXjjV 7Q`+2b 2 +? i bF iQ }MBb? #27Q`2 Bib /2 /HBM2X LQi2 i? i Mv 72 bB#H2 Q`/2` ;Bp2M #v i?2 #BM `v /2+BbBQMb yij rBHH ? p2 i H2 bi QM2 +Q``2bTQM/BM; 72 bB#H2 b+?2/mH2c i?2 QM2 r?2`2 HH i bFb `2 b+?2/mH2/ b 2 `Hv b TQbbB#H2 rBi? `2bT2+i iQ i?2B` Q`/2`X AM (Rk)- *QMbi` BMi UjXjRV r b }`bi mb2/ b M 2ti2MbBQM iQ i?2 /BbDmM+iBp2 7Q`KmH iBQM r?2M bim/vBM; i?2Q`2iB+ H T`QT2`iB2b Q7 7Q`KmH iBQMbX "mi i?2 HBM2 ` Q`/2`BM; 7Q`KmH iBQM- b b?QrM #Qp2- r b BMi`Q/m+2/ BM (k8)- HQM; rBi? bQK2 p HB/ BM2[m HBiB2bX. jX8 SQbBiBQM@# b2/ 7Q`KmH iBQM h?2 TQbBiBQM@# b2/ 7Q`KmH iBQM Bb Q`; MBb2/ `QmM/ i?2 MQiBQM i? i b+?2/@ mH2 + M #2 `2T`2b2Mi2/ #v i?2 TQbBiBQM 2 +? i bF Q++mTB2bX h?2 7Q`KmH iBQM BM+Hm/2b #BM `v /2+BbBQM p `B #H2 i? i bT2+B7v B7 i bF Bb T2`7Q`K2/ i bT2+B}+ TQbBiBQM- M/ +QMiBMmQmb p `B #H2 7Q` i?2 bi `iBM; iBK2 Q7 i?2 i bF T`Q+2bb2/ i 2 +? TQbBiBQMX ky.
(61) jXeX *QKT `BbQMb Q7 KBt2/ BMi2;2` T`Q;` KKBM; 7Q`KmH iBQMb G2i i?2 Q`/2`2/ b2i P +QMi BM TQbBiBQM 7Q` 2 +? i bF i? i b? HH #2 b+?2/@ mH2/X 6Q` i bF i ∈ I- M/ TQbBiBQM p ∈ P- BMi`Q/m+2 i?2 #BM `v p `B #H2 ⎧ ⎪ ⎪1, zip = ⎨ ⎪ ⎪ ⎩0,. B7 i bF i Bb T2`7Q`K2/ BM TQbBiBQM pQi?2`rBb2X. UjXj9V. 6Q` TQbBiBQM p ∈ P- BMi`Q/m+2 i?2 +QMiBMmQmb p `B #H2 μp = bi `i iBK2 Q7 i?2 i bF i? i 2t2+mi2 BM TQbBiBQM pX. UjXj8V. bQHmiBQM iQ ∑ zip = 1,. i ∈ I,. UjXjeV. p ∈ P,. UjXjdV. p∈P. ∑ zip = 1, i∈I. μp + ∑ zip pi ≤ μp+1 ,. p ∈ P, p < ∣P∣,. UjXj3V. i∈I. ∑ zip ri ≤ μp ≤ ∑ zip (di − pi ), i∈I. p ∈ P,. UjXjNV. i∈I. rBHH #2 72 bB#H2 b+?2/mH2 iQ i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2bX AM i?2 7Q`KmH iBQM- *QMbi` BMi UjXjeV bbB;Mb 2 +? i bF TQbBiBQM- *QMbi` BMi UjXjdV bbB;Mb 2 +? TQbBiBQM i bF- *QM@ bi` BMi UjXj3V 2Mbm`2b i? i irQ i bFb i /D +2Mi TQbBiBQMb /Q MQi Qp2`H T- M/ *QMbi` BMi UjXjNV K F2b i?2 bi `i iBK2 Q7 i?2 i bF i 2 +? TQbBiBQM `2bT2+i Bib `2H2 b2 iBK2 M/ /2 /HBM2X aBM+2 i?2`2 Bb MQ 2tTHB+Bi +QMM2+iBQM #2ir22M i bF M/ Bib bi `iBM; iBK2- i?Bb 7Q`KmH iBQM Bb HBiiH2 H2bb ~2tB#H2 /2 HBM; rBi? iBK2@`2H i2/ +QMbi` BMib- bm+? b KmHiBTH2 iBK2 rBM/Qrb Q` KBMBK HfK tBK H iBK2 H ;b- rBi?Qmi BMi`Q/m+BM; +QMbi`m+iBQMb HBF2 #B;@J +QMbi` BMibX h?2 MQiBQM Q7 mbBM; TQbBiBQM@# b2/ p `B #H2 BM Q`/2` iQ 7Q`KmH i2 M JAS 7Q` b+?2/mHBM; T`Q#H2K r b }`bi BMi`Q/m+2/ #v (je) BM +QMi2ti Q7 K +?BM2 b+?2/mHBM;X AM (kR)- i?2 TQHv?2/` Q7 i?2 TQbBiBQM@# b2/ 7Q`KmH iBQM r b bim/@ B2/X AM `2+2Mi v2 `b- i?2 mi?Q`b Q7 (ky) BMi`Q/m+2/ //BiBQM H BM2[m HBiB2b 7Q` i?2 TQbBiBQM@# b2/ 7Q`KmH iBQM # b2/ QM i?2 b?Q`i T`Q+2bbBM; iBK2@`mH2X AM i?2 b K2 v2 `- (RR) mb2/ i?2 TQbBiBQM@# b2/ 7Q`KmH iBQM rBi? bQK2 BM2[m HBiB2b iQ 2tTHQ`2 M2B;?#Qm`?QQ/b BM K i?2m`BbiB+X. jXe *QKT `BbQMb Q7 KBt2/ BMi2;2` T`Q;` KKBM; 7Q`KmH iBQMb h?2 JAS 7Q`KmH iBQMb BMi`Q/m+2/ BM i?2 T`2pBQmb b2+iBQMb ? p2 #22M +QK@ T `2/ BM /Bz2`2Mi b2iiBM;b BM i?2 HBi2` im`2X h?2`2 ? p2 #22M 72r i?2Q`2iB+ H +QKT `BbQMb M/ T`BK `BHv +QKTmi iBQM H +QKT `BbQMbX h?Bb b2+iBQM ii2KTib iQ bmKK `Bb2 i?2b2 `2bmHibX kR.
(62) jX. aBM;H2 K +?BM2 b+?2/mHBM; M/ KBt2/ BMi2;2` T`Q;` KKBM;. AM (Rk)- i?2 mi?Q`b bim/B2/ b2`B2b Q7 HBM2 ` T`Q;` KKBM; `2H t iBQMb Q`B;BM iBM; 7`QK i?2 /BbDmM+iBp2 M/ iBK2@# b2/ 7Q`KmH iBQMbX h?2 mi?Q`b b?Qr2/ i? i i?2 HBM2 ` T`Q;` KKBM; `2H t iBQM Q7 i?2 iBK2@# b2/ 7Q`KmH iBQM /QKBM i2b i?2 HBM2 ` T`Q;` KKBM; `2H t iBQM Q7 i?2 /BbDmM+iBp2 7Q`KmH iBQM 7Q` i?2 T`Q#H2K Q7 KBMBKBbBM; i?2 r2B;?i2/ bmK Q7 bi `i iBK2b 7Q` bBM;H2 K @ +?BM2 T`Q#H2K rBi? `2H2 b2 iBK2b U1∣rj ∣ ∑ wj Sj VX bBKBH ` T`QT2`iv Bb b?QrM BM (d)- r?2`2 i?2 HBM2 ` T`Q;` KKBM; `2H t iBQM Q7 i?2 #m+F2i@BM/2t2/ 7Q`Km@ H iBQM Bb b?QrM iQ #2 i H2 bi b bi`QM; b i?2 iBK2@BM/2t2/ 7Q`KmH iBQMX 6Qm` JAS 7Q`KmH iBQMb- i?2 /BbDmM+iBp2- i?2 iBK2@BM/2t2/- i?2 HBM2 ` Q`@ /2`BM;- M/ i?2 TQbBiBQM@# b2/ 7Q`KmH iBQMb r2`2 +QKT `2/ BM (RN)X h2bi r2`2 +QM/m+i2/ 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K r?2M KBMBKBbBM; i?2 r2B;?i2/ +QKTH2iBQM iBK2- i?2 K tBKmK H i2M2bb- i?2 MmK#2` Q7 i `/v DQ#b M/ i?2 iQi H r2B;?i2/ i `/BM2bbX h?2b2 +QKT `BbQMb r2`2 K /2 #Qi? rBi? M/ rBi?Qmi `2H2 b2 iBK2b- ?2M+2 bQK2 Q7 i?2 T`Q#H2Kb r2`2 LS@+QKTH2i2 M/ bQK2 + M #2 bQHp2/ BM TQHvMQKB H iBK2X h?2B` `2bmHib BM/B+ i2/ i? i i?2 GS@ `2H t iBQM Q7 i?2 /BbDmM+iBp2 7Q`KmH iBQM M/ i?2 TQbBiBQM@# b2/ 7Q`KmH iBQM r2`2 2 bB2` iQ bQHp2 i?2M i?2 iBK2@BM/2t2/ 7Q`KmH iBQM M/ i?2 HBM2 ` Q`/2`BM; 7Q`KmH iBQM- #mi i?2v +?B2p2/ r2 F2` #QmM/bX h?2 TQbBiBQM@# b2/ M/ i?2 /BbDmM+iBp2 7Q`KmH iBQMb +?B2p2/ 72 bB#H2 bQHmiBQM i?2 7 bi2bi 2p2M i?Qm;? i?2 +?B2p2/ bQHmiBQM r b MQi Hr vb QTiBK HX v2 ` H i2`- +QKTmi iBQM H +QKT `BbQMb #2ir22M bBt JAS 7Q`KmH iBQMb r2`2 T2`7Q`K2/ BM (k)X h?2 bBt 7Q`KmH iBQMb r2`2 i?2 /BbDmM+iBp2- i?2 iBK2@ BM/2t2/- i?2 TQbBiBQM@# b2/- i?2 HBM2 `@Q`/2`BM; M/ irQ //BiBQM H 7Q`Km@ H iBQMbX h?2 irQ //BiBQM H 7Q`KmH iBQMb r2`2 ?v#`B/ Q7 /BbDmM+iBp2 M/ TQbBiBQM@# b2/ 7Q`KmH iBQMb- M/ i` p2HHBM; b H2bK M T`Q#H2K BMbTB`2/ 7Q`@ KmH iBQMX h?2 +QKT `BbQM r b K /2 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#@ H2K rBi?Qmi `2H2 b2 iBK2b r?BH2 ii2KTiBM; iQ KBMBKBb2 iQi H i `/BM2bbX h?2B` `2bmHib BM/B+ i2/ i? i i?2 TQbBiBQM@# b2/ 7Q`KmH iBQMb T2`7Q`K2/ #2bi BM `2@ /m+BM; i?2 iQi H i `/BM2bb- M/ i?2 ?v#`B/ p2`bBQM M/ i?2 h` p2HHBM; a H2bK M S`Q#H2K UhaSV p2`bBQM T2`7Q`K2/ rQ`biX q?2M BMi`Q/m+BM; i?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM BM (9)- i?2 mi?Q`b K /2 +QKTmi iBQM H +QKT `BbQMX 6Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#@ H2K rBi? ;2M2`B+ Q#D2+iBp2 7mM+iBQM M/ `2H2 b2 iBK2b U1∣rj ∣ ∑ αj Ej + βj Tj Vi?2 mi?Q`b +QKT `2/ i?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM rBi? i?2 /BbDmM+iBp2 7Q`KmH iBQM- M/ i?2 iBK2@BM/2t2/ 7Q`KmH iBQMX AM i?Bb +QKT `BbQM- i?2 iBK2@ BM/2t2/ bQHp2/ KQbi BMbi M+2b iQ QTiBK HBiv 7QHHQr2/ #v i?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM- M/ H bi r b i?2 /BbDmM+iBp2 7Q`KmH iBQMX qQ`i? iQ MQi2 Bb i? i i?2 /BbDmM+iBp2 7Q`KmH iBQM T`Q+2bb2/ MQ/2b BM i?2 JAS bQHp2` Km+? 7 bi2` i? M i?2 iBK2@BM/2t2/ 7Q`KmH iBQM QM i?2b2 BMbi M+2bX h?2 mi?Q`b HbQ K /2 +QKT `BbQM QM T`Q#H2K rBi?Qmi `2H2 b2 iBK2b U1∣−∣ ∑ wj Tj VX AM i?Bb b2iiBM;i?2v +QKT `2/ i?2 BMi2`p H@BM/2t2/ 7Q`KmH iBQM rBi? i?2 iBK2@# b2/ 7Q`KmH @ iBQM M/ i?2 HBM2 `@Q`/2` 7Q`KmH iBQMX AM i?Bb +QKT `BbQM- i?2 BMi2`p H@BM/2t2/ TT`Q +? T2`7Q`K2/ #2bi rBi? `2bT2+i iQ i?2 `2H iBp2 JAS@; T- #mi r?2M +QK@. kk.
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(64)
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(67) 9XkX bQHmiBQM TT`Q +? 7Q` pBQMB+ b+?2/mHBM; i i?2 +Q`2 Q7 i?2 K2i?Q/ BKTH2K2Mi2/ BM i?Bb b+?2/mHBM; iQQH Bb +QM@ bi` BMi ;2M2` iBQM T`Q+2/m`2X S `i Q7 i?Bb T`Q+2/m`2 Bb iQ `2KQp2 +QMbi` BMib M/ QMHv // i?2K B7 Bi Bb M2+2bb `vX b `2bmHi Q7 i?Bb- 2 +? bi2T Q7 i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 BMpQHp2b bQHpBM; `2H t iBQM Q7 i?2 Q`B;BM H T`Q#H2KX A7 i?Bb `2H t iBQM Bb BM72 bB#H2 BM Mv bi2T- r2 ? p2 T`Qp2/ i? i i?2 Q`B;BM H T`Q#H2K Bb BM72 bB#H2X //BiBQM HHv- r2 ? p2 T`2@T`Q+2bbBM; +QKTQ@ M2Mib i? i + M /Bb+Qp2` BM72 bB#BHBiv rBi? `2bT2+i /2T2M/2M+B2b M/ }t2/ i bFbX h?2b2 T`2@T`Q+2bbBM; +QKTQM2Mib `2 7m`i?2` /2b+`B#2/ BM S T2` X aBM+2 M pBQMB+ bvbi2K Bb /2p2HQT2/ Bi2` iBp2Hv- Bi Bb mb27mH iQ K F2 mb2 Q7 b+?2/mH2b Q` BM7Q`K iBQM 7`QK bBKBH ` BMbi M+2bX h?2 +?QB+2 Q7 mbBM; +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 ? b #22M /QM2 rBi? i?Bb BM KBM/X aBM+2 i?Bb T`Q+2/m`2 ;2M2` i2b +QMbi` BMib- i?2 +QMbi` BMib ;2M2` i2/ 7Q` M BMbi M+2 KB;?i #2 mb27mH 7Q` MQi?2` BMbi M+2 B7 i?2`2 `2 KBMQ` /Bz2`2M+2b #2ir22M i?2KX. 9Xk bQHmiBQM TT`Q +? 7Q` pBQMB+ b+?2/mHBM; h?2 pBQMB+ b+?2/mHBM; T`Q#H2K T`QTQb2/ #v a # Bb +? HH2M;BM;X AM i?2 #2@ ;BMMBM; Q7 i?2 T`QD2+i r2 /2p2HQT2/ bi M/ `/ JAS KQ/2H bmBi2/ 7Q` i?Bb ivT2 Q7 b+?2/mHBM; T`Q#H2KX q?2M r2 i`B2/ iQ bQHp2 i?Bb JAS KQ/2H 7Q` i?2 bK HH2bi BMbi M+2 T`QpB/2/ #v a #- r2 7 BH2/ iQ +?B2p2 72 bB#H2 bQHmiBQM rBi?BM r22F Q7 `mMiBK2X h?Bb bK HH2bi BMbi M+2 ? / #Qmi e 8yy i bFb M/ r2 FM2r i? i i?2 H `;2bi BMbi M+2b T`QpB/2/ #v a # rQmH/ ? p2 KQ`2 i? M 9y yyy i bFbX h?mb- bQK2i?BM; M22/2/ iQ #2 /QM2X h?Bb b2+iBQM T`2b2Mib i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 r?B+? Bb i?2 +Q`2 Q7 i?2 K2i?Q/ i? i r2 ? p2 /2p2HQT2/ iQ bQHp2 bm+? T`Q#H2KbX. +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 h?2 b+?2/mHBM; T`Q#H2K +QMbBbib Q7 7Qm` + i2;Q`B2b Q7 +QMbi` BMib, *J b+?2/mH@ BM;- J b+?2/mHBM;- *L b+?2/mHBM; M/ S`2+2/2M+2 `2H iBQMb +QMbi` BMibX h?2 KQbi +? HH2M;BM; Q7 i?2b2 Bb i?2 *J b+?2/mHBM;X h?Bb Bb T`BK `BHv /m2 iQ i?2 K Mv i bFb QM i?2 *JbX >Qr2p2`- r2 ? p2 H2 `M2/ i? i i?2 BMbi M+2b T`Q@ pB/2/ #v a # ? p2 bQK2 +? ` +i2`BbiB+b i? i r2 + M i F2 /p Mi ;2 Q7X h?2 KQbi BKTQ`i Mi Q7 i?2b2 `2, Ç h?2`2 2tBbi }t2/ i bFb QM *Jb Ç J Mv `2[mB`2K2Mib Q7 i?2 T`Q#H2K `2 MQi /B{+mHi iQ 7mH}H BM BbQH iBQM h?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 i? i Bb /2b+`B#2/ Bb bmBi #H2 7Q` i?2b2 +? ` +i2`BbiB+bX h?2 B/2 #2?BM/ i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 Bb iQ K F2 `2H t2/ b+?2/mHBM; /2+BbBQM- r?BH2 `2bT2+iBM; i?2 Qi?2` +QMbi` BMib Q7 i?2 T`Q#H2KX h?2 `2H t2/ b+?2/mHBM; /2+BbBQM Bb i?2M i?2 2p Hm i2/ BM bm#T`Q#H2KX h?Bb bm#T`Q#H2K ? b #22M /2bB;M2/ bQ i? i B7 bQHmiBQM iQ i?2 kd.
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(69) 9XjX M 2t +i bQHmiBQM TT`Q +? 7Q` bBM;H2 K +?BM2 b+?2/mHBM; `2bi`B+iBQM Bb `2KQp2/- M/ +Q@ HHQ+ iBQM Q7 K2bb ;2b Bb HHQr2/- # b2/ mTQM i?2 B/2 b BM (jk)X MQi?2` /Bz2`2M+2 #2ir22M i?2 T T2`b ? b #22M i?2 `2H t iBQM mb2/ BM i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2X AM S T2` - 2 +? *J@i bF Bb bbB;M2/ iQ #2 BM QM2 Q7 i?2 T `ib Q7 i?2 K DQ` T2`BQ/ MQi Q++mTB2/ #v }t2/ i bFbX 1 +? bm+? T `i r b `272``2/ iQ b b2+iBQMX h?Bb r b +? M;2/ BM S T2` "r?2`2 i?2 +QM+2Ti Q7 bm#@BMi2`p Hb r b BMi`Q/m+2/X qBi? i?2 BMi`Q/m+iBQM Q7 bm#@BMi2`p Hb- bm#@BMi2`p H r b bbB;M2/ iQ 2 +? i bF BMbi2 / Q7 bbB;MBM; b2+iBQM iQ 2 +? i bFX bbB;MBM; bm#@BMi2`p Hb iQ i bFb K /2 i?2 `2H t2/ T`Q#H2K bi`QM;2` #mi ;Bp2b H2bb ~2tB#BHBiv BM i?2 bm#T`Q#H2K +QKT `2/ iQ bbB;MBM; b2+iBQMb iQ i bFbX >Qr2p2`- M /p Mi ;2 Q7 bbB;MBM; bm#@BMi2`p Hb iQ i bFb Bb i?2 bi`QM; +QMM2+iBQM iQ i?2 `2[mB`2K2Mib Q7 *L i bF iBK2bX 1bT2+B HHv 7Q` i?2 i bFb i? i `2 `2bTQMbB#H2 7Q` b2M/BM; K2bb ;2 BM *L bHQiX b `2bmHi Q7 i?Bbi?2 bbB;MK2Mi Q7 bm#@BMi2`p Hb ;Bp2b +QKTH2i2 *L b+?2/mH2X AM S T2` " M/ S T2` *- i?Bb K2 Mb i? i 7Q` 2 +? bm#T`Q#H2K- i?2 *L b+?2/mH2 ? b H`2 /v #22M /2i2`KBM2/ #v i?2 bQHmiBQM 7`QK i?2 T`2+2/BM; `2H t2/ T`Q#H2KX h?2 JAS 7Q`KmH iBQMb 7Q` i?2 `2H t2/ T`Q#H2K M/ i?2 bm#T`Q#H2K `2 7m`i?2` BKT`Qp2/ BM S T2` *X AM S T2` *- i?2 +QM+2Ti Q7 bm#@BMi2`p H bbB;M@ K2Mi Bb +QK#BM2/ rBi? i?2 *L K2bb ;2 +Q@ HHQ+ iBQM- b22 (jk)- QM2 Q7 i?2 b2[m2M+BM; 7Q`KmH iBQMb i2bi2/ BM i?2 " +?2HQ` i?2bBb (e)- iQ;2i?2` rBi? bQK2 7m`i?2` BKT`Qp2K2MibX. 9Xj M 2t +i bQHmiBQM TT`Q +? 7Q` bBM;H2 K +?BM2 b+?2/mHBM; h?Bb b2+iBQM BKb i /2b+`B#BM; i?2 +QMM2+iBQM #2ir22M i?2 +QMbi` BMi ;2M@ 2` iBQM T`Q+2/m`2 mb2/ BM i?2 TT2M/2/ T T2`b M/ JAS 7Q`KmH iBQMb 7Q` b+?2/mHBM;X h?2`27Q`2- i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2 Bb T`2b2Mi2/ 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; T`Q#H2K rBi? `2H2 b2 iBK2b M/ /2 /HBM2b- HBF2 i?2 JAS 7Q`KmH iBQMb r2`2 BM *? Ti2` jX. LQi iBQM G2i I /2MQi2 i?2 b2i Q7 i bFb iQ #2 b+?2/mH2/X 6Q` 2 +? i bF i ∈ I- H2i Qi /2MQi2 Bib b2i Q7 bm#@BMi2`p Hb M/ pi Bib /m` iBQMX 6Q` 2 +? bm#@BMi2`p H q ∈ Qi / Q7 i bF i- H2i t`iq M/ tiq /2MQi2 Bib bi `i M/ 2M/- `2bT2+iBp2HvX G2i S /2MQi2 i?2 b2i Q7 b2[m2M+2b Ub2i Q7 i bFb rBi? Qp2`H TTBM; bm#@BMi2`p HbV M/ S ;2M i?2 b2i Q7 b2[m2M+2b ;2M2` i2/ #v i?2 bm#T`Q#H2KX 6Q` b2[m2M+2 s ∈ S- H2i IsP /2MQi2 Bib b2i Q7 i bFbX HbQ- H2i R /2MQi2 i?2 b2i Q7 b2;K2MibX h?2 b2;K2Mib `2 i?2 b2i Q7 T `iBiBQMb Q7 i?2 b+?2/mHBM; ?Q`BxQM Q#i BM2/ #v {(t`iq , t/i′ q′ ) ∶ t`iq < t/i′ q′ , q ′ ∈ Qi′ , q ∈ Qi , i′ ∈ I, i ∈ I}X 6Q` ;Bp2M b2;K2Mi r ∈ R- H2i Qir. kN.
(70) 9X. *QMi`B#miBQMb. /2MQi2 i?2 b2i Q7 bm#@BMi2`p Hb Q7 i bF i i? i Bb +QKTH2i2Hv +QMi BM2/ rBi?BM b2;K2Mi rX. o `B #H2b h?Bb b2+iBQM BMi`Q/m+2b i?2 p `B #H2b mb2/ 7Q` i?2 `2H t2/ T`Q#H2K M/ i?2 bm#@ T`Q#H2K i? i Bb /2b+`B#2/ BM i?2 7QHHQrBM; b2+iBQMbX 6Q` i bF i ∈ I- BMi`Q/m+2 i?2 +QMiBMmQmb p `B #H2 xi = bi `i iBK2 Q7 i bF iX 6Q` i bF i ∈ I M/ bm#@BMi2`p H q ∈ Qi - BMi`Q/m+2 i?2 #BM `v p `B #H2 ⎧ ⎪ ⎪1, αiq = ⎨ ⎪ ⎪ ⎩0,. B7 i bF i Bb bbB;M2/ iQ bm#@BMi2`p H qQi?2`rBb2X. 6Q` i ∈ I- i′ ∈ I- i ≠ i′ - BMi`Q/m+2 i?2 #BM `v p `B #H2 ⎧ ⎪ ⎪1, yii′ = ⎨ ⎪ ⎪ ⎩0,. B7 i bF i bi `ib #27Q`2 i bF i′ B7 i bF i′ bi `ib #27Q`2 i bF iX. 6Q` 2 +? b2[m2M+2 s ∈ S ∪ S ;2M - BMi`Q/m+2 i?2 #BM `v p `B #H2 ⎧ ⎪ ⎪1, βs = ⎨ ⎪ ⎪ ⎩0,. B7 i?2`2 Bb MQ Qp2`H T #2ir22M i bFb BM b2[m2M+2 sQi?2`rBb2X. _2H t2/ T`Q#H2K h?2 Tm`TQb2 Q7 i?2 `2H t2/ T`Q#H2K Bb iQ +`2 i2 M bbB;MK2Mi Q7 bm#@BMi2`p Hb iQ i bFbX .Bz2`2Mi Q#D2+iBp2 7mM+iBQMb + M #2 mb2/ iQ ;mB/2 i?Bb b2 `+?- M/ BM Qm` rQ`F- i?2 +?QB+2 Q7 Q#D2+iBp2 7mM+iBQM ? b ? / ;`2 i BKT +i QM i?2 +QKTmi iBQM H 2{+B2M+v Q7 i?2 +QMbi` BMi ;2M2` iBQM T`Q+2/m`2X 6Q` Q#D2+@ iBp2 7mM+iBQMb i? i r2`2 mb2/ iQ ;mB/2 i?2 b2 `+? 7Q` Qm` pBQMB+ b+?2/mHBM; T`Q#H2K- b22 S T2` M/ S T2` *X h?2 `2H t2/ T`Q#H2K 7Q` i?2 bBM;H2 K +?BM2 b+?2/mHBM; rBi? `2H2 b2 iBK2b M/ /2 /HBM2b Bb 7Q`KmH i2/ b ∑ αiq = 1,. i ∈ I,. U9XRV. q∈Qi ` / ∑ tiq αiq ≤ xi ≤ ∑ tiq αiq − pi ,. q∈Qi. i ∈ I,. / ` ∑ ∑ pi αiq ≤ max max tiq − min min tiq ,. i∈I q∈Qir. jy. U9XkV. q∈Qi. i∈I q∈Qir. i∈I q∈Qir. r ∈ R,. U9XjV.
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