Single machine scheduling subject to precedence delays
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE. Single Machine Scheduling Subject to Precedence Delays Lucian FINTA. Zhen LIU. N˚ 2198 Janvier 1994. PROGRAMME 1 Architectures paralle`les, bases de donne´es, re´seaux et syste`mes distribue´s. ISSN 0249-6399. apport de recherche. 1994.
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(141) .ªzù³ ' \s ± +V³ ! Y Y W ² À,N9ghEIWFNdtl ; ² FW ThN\eN9WME7WSJI\jV\JH\F\eUGIgVNf WYEªWFTVNLJIRSTVUXgVN¤f/[hDFUXghGªWFTVNWYUXLMNUg/WYN9DFHJ_ b
(142) ² =
(143) . O³ , ² ; ² 9 # ± rS³ ' ! . . 9.
(144). . . . . 3v N9W ² dN7WFTVN7WSJH\eN9ktNRZ[VWYNfJWAWYUXLMN
(145) ² . OIÀ,[VN7WFEMWYTVN'aJHRZWS\WFT^JW,WKJI\j TJI\AJ \eLJ_X_N9D_Jd^N9_hWFT^Jg WYTVNWSJH\eh\Ug; bIWFT^JWmWSJI\j ² Un\¾gVEHWJA]VDYNf/NRcN\F\jEID EJ__VWFThNWSJI\jV\ E ; btJg^fMWFTJWN N9DFl7WSJI\j Ug ; ² Un\«]VDYNf/NRZN\F\eEHDmEJ__^WFTVNAWKJI\jV\mE; Jg^f¦J_X_WFTVN WSJH\eh\«E ; dtlWYDSJg\eUXWYUXtUXWjlb9WKJI\e ² T^JH\J<\eLJ_X_N9D®_JdN _WYT^JgWSJH\eh\ UXg; ² ± ² ³ LMUg > . 3±*+³K sTt[^\ZbtWFTVN WSJH\eN9k/NRZ[VWFNfJWWYUXLMN
(146) ² .z'U\mJ<]VDFNftNRZN\Y\eEID$EJ_X_^WFTVN WSJH\eh\«Ug ; ² b/\jEWYT^JW N R Jg¦f/N ^gVN
(147) JI\ WFTVNNJDF_UXN\jW WFULMN«£EHDmTVURSTWFTVNLJIRSTVUXgVNmUn\«RcEIgtWFUXgt[VEH[^\e_lN9ktNRZ[VWYUXgVG WFThN']hDFNf/NRZN\F\jEIDK\E$J_X_3WYTVN<WSJH\eh\ÁU g ;² ÂmEIgtWFUg/[VN7WFTVUn\Á]hDFEtRZNft[VDFN7[Vg/WYUX_WFTVN7d^N9GIUgVgVUXghG EWYTVN\YRxThNf/[V_NbVJg^fN7EIdVWKJUXgWYTVN WFULMN N9]^EtRxT^\
(148) '9
(149)
(150) $&$&$
(151) ²
(152)
(153) 5b^\j[^RxT¤WFT^JW£EIDwJ__mO Y D Y qb N9N9DYl WKJI\jME#; C U\]VDYNf/NRcN\F\jEIDEJ__®WFTVN<WKJI\eh\EF; C bVThN9DFN . . 1. . . . . . ; C 9. v3N9W. ?!"',. . . . ² # ± rS³ ' ! ? . . ^d NWYTVN±]^E\Y\eUXdh_Xl RcWFUXWYUXEH[^\x³mWKJI\eN9ktNRZ[hWFNfMJWWFULMN$
(154) C . OHb
(155) Y D Y q À,[VNWFEMWYTVN]VDYNRZNf/N g^RZNDYN9_JWFUEIg^\,d^N9Wj$N9N9gWSJH\eh\,E ; C Jg^f ; C bO Y D Y qb3UXWAUn\ RZ_NJDAWYT^JW Jgtl£NJI\jUXdV_N\FRSTVNft[V_XN7EWKJI\jGIDSJ]VT 7 T^JI\<JW'_NJI\jWA_XN gVGIWYT q W C eK; C eðb ,C. . . . áßéíïî.
(156) O}|.
(157) "!#!%$'&)( " * +," .-/ 0 132. TVN9DYNSeK; C ef/N9gVEHWFN\AWFThNR9JDKf/UXg^J_XUWelE ; C ® rUXgRZN EI]hWFUXLJ_®\YRxThNf/[V_N. C . 9 q W. . eX; C eòbv¾Ã'r¤U\ WFTt[^\AJg . m EIg^\jUf/N DgVE WFThNAGIN9ghN9DSJ_®R9JH\eN TVN9DFNwWSJI\j ]hDFEtRZN\Y\eUgVGWFULMN\JDFN JDFdhUXWFDKJDYl g^JWF[VDKJ_ gt[VL d^N9DK\Z _N¤f/N ^ghNMWFTVN\eN9WK\'EwWSJH\eh\UXg¨J\jUXLMU_JDAJ9lb/UXbj; U\<WFTVN\jN9WEAWKJI\jV\ N9ktNRZ[VWYNfJ£WYN9DWYTVNA_nJI\eW$LJIRSTVUgVNUnf/_XUgVGVbtJgfWKJI\jV\mE ; C b^O Y D Y qbtJDFN RZEIg^\jNRZ[VWYUXN9_l N9ktNRZ[VWYNf3bHJg^fNJHRxTWSJH\eE> ; C3U\]VDFNftNRZN\Y\eEIDmEJ__VWFThN,WKJI\eh\ E> ;*C trUXg^RcN]VDFNRcNf/N9g^RcN f/N9_nJ9lV\ T^J9N [VgVUXWm_N9gVGIWYT®bWFTVN DFNAUn\EHgV_XlEIghN±£]E¢\F\jUXdV_l RcWFUXWYUXEH[^\x³WSJI\j3btf/N gVEIWYNf dtl C b UXgtd^N9WjN9N gMWSJH\eh\E# ; C Jg^fWFTVE¢\eN<E# ; C UXgWFThNv¾Ã<r¦\FRSTVNft[V_XNhv3N9W . . . ). . 9x !" ; .. sTVN9g¿b 9 . ±" ? A " ? C . C. . . W. . . ; C 9. . ³. C. " ? . . . # ,C ' . #
(158) ' . . W . C. . . >. . A ?. !. 9. > . .. W q. e
(159) e =. ±YO³. TVN9DYN 9 > A > U\'WYTVNMWYEIWSJ_]VDFEtRcN\F\jUXgVGWYUXLMN\ E77bmJg^f U\'WYTVNMUg^f/UR JWFEHD £[Vg^RcWFUXEHg® ÂmEIg^\jUf/N DJgJDYdVUXWYDSJDYl\FRSTVNf/[h_XN£EIDI75UWFTLJN\e]Jg "v3N9W
(160) "C ±DYN\e]¿ r@C" ³ d^N WFThNAWFULMN,N ]EtRSTMTVN g¬WYTV N ^DK\eW<±£DFN\j]®/_nJI\eWc³ WKJI\e¦EF ; C \jWSJDFWS\N k/NRc[VWFUEIg[Vg^f/N9D \YRxThNf/[V_N b
(161) Y D Y q¾rUXgRZNN9N DFlWSJH\eE. ; C bO Y D Y qb3U\,]hDFNf/NRZN\F\jEID EÁJ_X_WFTVNWKJI\eh\,E ; C bVN<EIdhWSJUgWFT^JW r@"C .¨z Y
(162) "C v3N9 W ;$C " d^NWFThN\eN W,EmWSJH\eh\ÁTVUnRxT¤\jWSJDYWAN9ktNRZ[VWYUXEHg [Vg^ftN9D ¤f/[VDFUgVGWYUXLMNUg/WYN9DFHJM_ b
(163) "C =r "C c b
(164) Y D Y qVÂm_XNJDF_l*b ; C ;C " b
(165) Y D Y qhÀ,N9gVEHWFN dt l C " WFTVN\jN9W<E<±£gVEIg RZWFUWFUEI[^\S³,WKJI\jV\ATVUnRxT\jWSJDYW<N9k/NRZ[VWFUEIg¤[Vg^f/N9D ¨f/[VDYUXgVGWYUXLMN UXgtWFN DFHJ_± r "C =
(166) "C ³Sb®O Y D Y q^q1WUn\\eULM]V_XN WFTJW . . ). ). ). ). ". . 9 !". . sTVN9DYNZ£EIDYNb. C. . C. . . ±. ? . W q. .. W q. .. 9. åå¬ß9ô ÿ". . . C. . .. 9 ;. C". . ". . C. . . " ? . . . ; .. ; C". . . ³ A. . ". W. . C. . . ? . . ±azù³. ; C 9. W . . !. C. . >. . ?. A >. ? . e! " e =. ±4 ³.
(167) O9|. *!% . TVN9DYNWFTVN ^DK\eWUXgVN [^J_XUXWjlUn\f/[VNWFEWFTVNMaJHRZWS\WFT^JWf/[VDYUXgVGWFULMN Ug/WYN9DFHJ_\ ± r@C" =
(168) "C ³Kb O Y D Y qb3\YRxThNf/[V_N ¥LJlT^J9NUnf/_XUgVG ]^N9DYUXEtfV\<E´_XN9gVGHWFTLMEHDFN7WFT^JgEHD'N ù[^J_ WFE¤z JgfWFT^JWmf/[VDYUXgVGAWYUXLMNUXgtWFN9DYIJ_F\ b
(169) "C =Nr@"C cab
(170) Y D Y qbI\YRxThNf/[V_N LJ9lAT^J9NUnf/_XUgVG]^N9DFUEtfV\Z q gVN [^J_UXWjl± 4 ³WYEIGIN WFTVN9DUWFT¤DFN9_nJWFUEIg^\A±YO³$Jg^f±azù³$UXLMLNf/UnJWFN _ l7UXLM]h_XlWFTJW ). . ". W q. .. e
(171) " e. W q. e
(172) fe9. sTVN9DYNZ£EIDYNbVv¾Ã<r¦T^JI\ J}L¦UXgVUL[VL5LJN\e]Jg®. !. q g R JI\eN¦E ms WKJI\eh\Zb WYTVNMEH]VWFULJ_UXWjlE<v¾Ã<rªDYN9LJUXg^\AWFDY[VNMN9N gªTVN9g¨_XN gVGIWYT^\ Ew]VDYNRZNf/N g^RZN¦f/N9_J9lh\JDYNJ_X_E$NfWYEdN9N DFEUg/d^N9Wj$N9N9gªWKJI\eh\E J\e[VdRST^JUg°EAWYTVN WSJH\eGIDKJ]VT®bU NXb H CKJ 9
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