scheduling and project planning - tu...

19
1/1 §19 (#4) 2013-01-23 16:25:31

Upload: others

Post on 03-Nov-2019

2 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

1/1 §19 (#4)2013-01-23 16:25:31

- 19.1 -
Page 2: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

<i3a.. 9 i e.. T~0t ~ -~·--~«•HO-·-""'' ... '"'"""""'"'-"'""""'"".-........

~ C™-r;1rl..v· ewi. 0r 1..--wt.~ pte>c. fr,~ \Jec?c.r >< ~er t

[ E>u}h ~<u_ca. ~ ts. co.t ~"' (.(_(}i.v,, °"" )( [ ~1J ):>u J =o k q flo...td. 14

,, 11 (\

~ C.Ltw~,u~~~~ er'h'f",J( h-ncolta.\J~ b t-E ) c. s.'«t.112.; ~ Kci_

Ot~-c ol-'tl.~o. "IA

!Nt t,t,J J L M it.A. O<i.t ( f.A.., t tk ke__ f;(.Q k, Cr k ~f c.„/7-,- c d_

r~t~ J

Le,+. . ~ :: (N ~ 4 ) (k f-f-ite ettc_. ~\yai ~ J/ (1. N = ~ 1„. '"" ~

1 ~ >OCAlf"~ ) t11 -::: $ink

le. ~ / w, -r, L p..r·e;, ~-~ h~ va..cJcr x >

tA-l ~ ~ ()f o.- Q°"" crr:. 1 r a. H1 ~~ 1 f.o ~

i'f ~) J'f !

kE T ~€ 5 )

Page 3: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

(\

/ IP

1 ~

LJ l( 8e. 0p1i't..tJ fe-< i -7 Ur;>rk_ fO~k~ vi (><)

~ ~ Or 1h·IM.Jl \er l-e_ ~? 1-1.r:,c4 ro~ t,J.,..,. Tl.(~) t

=D Tr1 Cx. '> ::. 1i' ('t) =0 ·1

=o

~ r·~()('.t/Yl'iv~ H!A-t4 io.tre_ ~. a(ctfA.~J <m. '1{rCJ; of -(~ Ce.. t·

[ ~.rA. 1""'QY i eQ.~c.v~.~1

,,...„.,..~'

/ . S.~CJ ~ ~ r~<-tJ0trrJ DrC.~ ßy r

~--<teoL.Q..s. vm 67 oJ ee.aict &

........ ,_.._.._.__.,

(

E ve''( Cri fnc'l.Q (>O.. {-~ l.ttJv> 0t fc.~lCV J. <kc..,

. ;; 114

rkJ.u. r,eJ ~ 2 6

~ 1e.hc.tt_~ e,7 g b.

(f1.t)

Page 4: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

4 c,. t [$ r 1 1 ,-, • ;:;_~..{ _.Ed 1 '.V crii , ~ . , .eve ' 7 .: €c ~ "'"-

~ 11-t~~J · 9-r~ 1 -e7 a_ ol·l.{c.i.J ! rc.+h ~ s .

=/

-!) ~· r~ ~'4uul ~)(tfc 1P1 ß/ 6

::::::o rx1i >t tt ~ ~ . 'IA. fßcfm o-f , pet f ~ rr. 1\~~ T-

a.~- r;k.t..t~((-°"- fo! e-x:qcJ..e,7 ß ~o Tl"n, s4w-~J ~y 6 . ,

--~i.t~ viow A·oa,cl<tvettd ctilU. {k, i) k<kw.- '5211td~ . b

Page 5: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

- 19 .>-

kt L\ T J ·~ Ci ' ~(Yoot C~t

~~-1>1~ 1 cJJJ. ~-flt>C<.tJ CLf'C'.-J er &

~".)ikeh o.f.R_ ec._oL<cvc.JJ 4t1'CS. (]7 ~

7f Wi ts s. L//_~ el _, (l~ ~'l)

f,! g

.<:i""h C\. p0tn1 -t.v.1flt_ ~ ea.e~tv~&.o-e OetC

<5e.L.e,_,,t ~Lie !.1A.

Tu~ ~~.c<Zel.11J ~ ~ [3e>ö&_] Ct<f:

sln./~ o/!ß_ ~C.ftvOtl~ Gt~-C.S. Qf ~

~J~~-'1 a». eCtcktvM-et 4,(c.~ e1 & ( f tk1r r-rrnl>h·>•'J h'„1'~ Ft-l<A;L; '· e. ><v· < b1j' )

Page 6: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

(os,tr-a..k [s ,TJ -= Z_ c" > Ck.e IJ L~

(t')J) (k)~)

f c.nv~.t>l ({tc_ k) t 6c.ckt.oov-cl Qr-c

xkR <, bk~

n. X·- - q„ 'J 'j

Page 7: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

!~

.sJ. /

\._. e.t)-(?.tT J t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J hc... . .._~ <k.ccc-tii-.1S lo Q9.3)

Q( g 71 J)lr, ~t ~ 1,.., "'Q F CVY">t J h 'kA.R.. \/e~Jcr y 9 f c.r t -g .

'! 9 ::. .. 'J 0~>j ) fs Q

()"~ u.ri!>L

'

l q. 2 c.DR~ LLA re 'l , 1ie F(I) rcJ c.~~ Cr-t o-c„-~ ~ c t- ) ü r ie. CQ lvis.r CL.Qt\j-

~ J_ COvt l>e)( Ovt_ [ 4 IM;,_, > t i ... o,x ] 1v1· tlt

t !kt;.,,_ "'° c_ ( .. ) . & k.t 1'1-\ olu,,.ac_~,·~ r-u Jrtß IM.C,X ,_ Q'l )-··) qn

~l.-tC.X '.::-. C~W( c 61 . -- bn) C:- t.vta,..X: J..-ur°'th-~ pe,1- ·oe J

1+ v.._,._f ~ (C,w) kt~J ilJ, ~C>C.u!. !

(1} ~A~l ~{ { .-= .Ji..tt.X • ~-"" >( ~- ( hn ~·· bn) i'~ Dp k~.J.

(2-) "i4tr~t'J tw t..R. t l -=-, tll-t '"'

c~) ~s~cl <Dcri{ it,i~ ~~e.-1-- +o .)(

(6) i:-1 VlJ. i:t. ~ÖC)J Ü1-+ t<l;fh IM. ~· l't 1 ~ 1.4..t CO?} "TC( k t~"li- ~ g.l-;.d_ k skc.rk~J„

Page 8: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

(ci) :r~ t-~ ~ tmt11) ect.f: t 'F- f~W<i1.1

Ek?~ ~-J t:-=t-f ~~ 4A )(' L1e 14.e. ~lv f3f i-v-.~.

l,>-.e_C iu ~er 6 -& cJt~c_cvol~ to (i~ ,3)

S.o ~-ltu00 p~ e ~ ~ k U) c~rc.-..J {t> ( o...u. er· c..~~~) c~J~

w.~ c.~t +<i. ~- e,' tAJ{_ ~-() ~ sRor.e 1 +~" t r>' e. ~.

e:- C.·. 'J

~~t- ~k l;-

62.. ::: <r J' J ':: O<:l

c~~ ,s~,) --~p {..e..n.., .·1-1. 41,~·c.-..

Page 9: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

~ g ~ l

+ M.I\.\ ~ ~ ~o.Ji.QJ_

~2 ::: l

s :0 l 1

•' '

Ct;:)t -roJ-e lO t 10 = 20

$,z ~ 1 , ~3 -::: e6

"°""'~,lt- e~ s ~~4 'k).,.~J Ct'"'l U-t!H'e

Page 10: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

/~

l·HO

\-g

Gu.v,/nc-.. : !~rn.o frJ ~kJ H,..e_ c.Jr>ol Cu ~.i c&sen~t-~··<!.JP/

:ro&o..: fise_ ~t'Vwk fecrws

M (()( ~~ ~· K-! r'!.( C~ . .f- llt_e ~ ___ ..... ~ .... -----..-,,,_, . ....._ __ ,, __ .. ~--·-~ IM-4..;< i IM. t.i..t... \)~tA.e { a.

::: +~ l-IA r l.( •'L-t-ti.... k-\

~V?r'~-. Pe~

QCt, P°' c:-1~ @f ~ <: 1.( ./-

~0'1,\) ~.tr (.1c, ilÄA et{ ~ WI 7 K(')o-le [ f I,) Yl')

CJl r>Ot c.:1-i.n ~ Sn--P c 1-e J.. ~ „ ~ X" ~ u .. 1 ,-- u J 'J

- 2 j

1 f fuux, C.,C\fCr. c; ~f uppv Cßf<lC1' {f

~ <1t-C, ~~i)

Page 11: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

71\ 1 '

~ ) it..t ~~ C.l(!-f„e„J

cu ()_. ' ·-,-

~ Oö

1 c ..

Q.. J ~ "::.

'J 0

9 Av.1 IMo..x ,'IM. <.twt ~

~„vtJ ()( IMl\x i"'4 t"'-1

) L

x„ ) Q·· 'J u

Ll 1.

'J

c_„ u

~hve-rk 1.)c.~f ) rt,+-

r+ ><" ~

ö-~IV>·~

1 )(" ~

Ö~~N\q

> ~" 'J [ ( i)J) C."'-vi ~ ~~_a-/k~·cecJ ]

c :::: i> do ,,,.ff 4./A1'( t it!~ et....

Otrrc tf.( Q, Ct-.. f. ]

< bu· [ ( l„l) c_c.t..,, <k. ~n.)t~~~J

[ v.;, 1.2_ 1.<6( c.CH. l-i-: L. k ~~ C.cn f -rc. k J

p--r()olu.:c...,·~ sooJ. C1.J~ 1,v1lj_,

tt (~DoD( J Cl.ll of "'-t/414.{~-

6 ~'K.: ~-et{ ~ °"'"" & '"''~"-7n ~J p0t ~! ey 1S F.S.

lSFS $1.<..~~t ( evk ~te.- r> Vt() OV-t~ ~i·~ \ r4:+~ ) flto. 1

~ t.1.v1 I>: Se>~J.

Page 12: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

(>) E \/(>.I ( L"-<,7 . w. "kt IM.oM; '-« fA lr,.\ ('..r.fr;,.l rtit~k (._~ e(> f~a-l >:,,,.:

O( # &/~4,. '# 9.IJ'"{S. fe;j (~"~) <)) ::' 0 ( 113 R(!,><'!, h )

if' <J,rCS. ..J f\ ----------„„ ------. l....-- -~~~·• --- -~---~- A..._., ,.,..,__

().) lZw_ '&t(') - r..emu (> fe CV-,.t -~ Cl t t"" Ce)( •

~ c...k,,..~e,,,,.1 ~·~ 1-e.....vtßt,<•0 Q,~·iJ<ii evk.,. ~ c_c.ra...cfh„f:l °'II-€ c.l-t.cc.l'(~J. ""="D [+( f) C.(AAl.>V( !

~ # e.re.°'k P°'-..A.s

f li ;f- ex f~· 1t ,,,JLQ '?.

?to0~ ~ (1) ~ ~~; -) LV? c.t ... ,

(:2) eqy [J.e,.,• ~- c. 4, 1-. 'Cvi

(}) o{'.,Vi~ 0

Page 13: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

t tlc ~fftv ~kocr~

(T\ (10/(1)~~) y-i<1>~ 1

(Jf' /. (o, 2) (<t) (1) ', lo '@ 2-o

~~~•) ~- - ~~ lo >@~,,

s-~ ~01.u IAQ..b Cl 1-<

~~>V>) /fi>'"° "'·'> Cl)~ [fJ ~ /-,@ Oö

) // 4 (21ao) tf) (to

100) oD )0)/ 00

+ IM 1'~ 6-<?.Qc. tJ.eo{

Page 14: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

.ev.e. oy Jo-e ~ai s

OtU' :: 1 b6. :: 10

Cew_ s, kr f c 1 .{~'"') +~~\(1 ~\1.J. :x i:>p'fn .... a.~ ~r I t:-.

?rr,eiea l.c.t , ~ ()pk~J._ pro~,,J h~ v.ttcf~r r~ t - 8 U-<o( ~

a-B (_°"'. ~ al.... (] 'r s.L Ct ~.-.A i ~J Q,..R_~Jl J'ot> !. > C<lt. { lt-w-e_rl

:r?w- ~~ ~~~- IA,e, { 1iv c.r k

~~~ J,~Cß9 : .\-Lt,-.~ c~ ~ IC/'A,t . o.2_ ~1lJ:7 ·~ Ü1'\Q_ 301~J. cv.f a, t ll-.R ~~ ~\?. .. c.w~t

- c~ (l_v) k~02 ) ~! :::: 00 (ktl('..j a..re '-

~ ~ ~ ( ~,,Q_ QrC-5J, C<X,,.z ~ kcwß..S2J.. e7 9 ) "'°OS-==-? ~

-- ( ) (~ ':::. CO fit(? au-e CiJr.e(_ ~ ·lM C-l't.Ot ~~

~t Bo G' Jo) ~] cu,,) ·~-~ '( ~- ~ °'ft, Foc:. h·~ ve_c_fe.r

~·er t -30

Page 15: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

/!\ ' i 1

.~ ({ lS -

Tu.~-~ r u-- e.et~ E c V +~ p~> z~ k.1 d ,fp_"4tc.Q. J 7fi ~ ~· ("<) - a:_. C7)

Le.J ll ir, < 4 1T2. <: . . < 4 V~ rk. t4 olcf~~ t 8 ifi v& ~s. ~ ~ i .

(' '

() 3

2

- '

'­'

"' ' \

Page 16: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

(~)~ ~~,~ f.t04t~r~"rii·Ct-(_ ,t.r~r~n·d x. „4io 7 [ iu 'Dc.\17·+]

tu- k : : l to ..e - l clo

(i) L\k '·= 4irk - 4 'Tl" k -!

(~l) 7( •• . - )('. ' ' - <lk fcr a.QJL r~-1wc,.,.,.J Ct'..N:.~ (t ' ) lrn [~)Tl-\] IJ IJ . „q' "'

0_,i) K1-s ~ -::: )(, "t-s, tLl·

~. Cu ·fkP_ß_ l { J n(!C'-':!.Q•1H· M·C..S, ( "f)S) (,;,, [i T] k .1 ~ '

El<rQ: L\ k -· I r~ 0t.01l k u. o e !lt i:J< 1,,.,14 i J. o.ics. ·111 )

':::(;> r;;tAR, kll-lti? ()i,r, f C.f' UU, ~ al llu-LS ~rl 1 .evecr cf.,(..J.

=z:> 7

(~)

ki ~· ee. lt~ p-n.,c., (-.-G-i~. V~cil!..r aß /~·~~al GI clet„t~J

f:\, X. CA.( [5,t 1 T;. J ey So ( p~s.s«~ gt'f;(te, igo ~. s )

~1'1 ~ (5„ ~ri·!M.Q fc.t· f-90

e-1 z

k::q

e-1 ~ z

k.,. 1

II ' - X_,~

Page 17: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

- ttr+-

(lt-) „~Ct·€'47!S,(' 011 cu·l· c >1} ~ ] 1S ~r hi.iJ> ra. ~ Sc E: J C)) i.']

[ :?o lzCU> t?){.Q.t.. ~· K '(( J ~ Ccu- J

GJ g 1 ) S' L f ] V/ l] ~1t4 ~t c~ h c~ l > T; ] Cs:z ) s ] Clt tc.. ~o~ . .t' ~ ~o" (]. ) , Ac;~t-CtiA~ ev, Q. D. g. }k0i ~ ~ 1 -:;; g z..

g,~ocv .' 'CCl'>t :Ye- ~ [ ~ > T; J = (O;)f '"f'CI k [ s; ) ~ ]

,, ,, f ?. I~ < ) +~ .tle_ ~-CY'to,~ CM_ c ~ ) ~ ] e7 /M/l,{ 2 _C?, } ~2 J '"" 31

•-.;

~. tXJ:, °' ee_ /1.e; s. ~ t.i-c.,,, Pe-r t_ -!? 1 ) q (}_ o.Jy°' al_ '(! i ·ev-. .

-(>) ~ ~Cif ok_c„e0t~ ,e7:- ·~? ~-~I ;;.

WCTlv ßy a7 luo/)1 S ( clL~-~J e/1

' K.e c.u1 [>,11 ]

(9\ T\"l\v. l~. \ 01'tl1 ~1'1/tlt.vt~ · c~.f- "l"Ctk__ )

) '

~(} [>1 T J 1> .sl-i..eQ ~ ~J 4-/ t -.f ~-~ d_ :~ "1.U4J

fut-\ ~- ~ r ~I ckc__~<lt ~ t-lt-t ~ {!_ ~ 0

Page 18: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

y{f) ~ t«,·l-{ ? f [Q<0· -xuJ f] 1,J

~-„„ •• „„„ .• „„„.„„ •. „„„„.„„„ •. „„„ ..... „.„.-„„1~ ""--------) to

~~ lß".'2_ b) --=v j ?-<'A-~J~ Vou-i~- t w)f'-z. 1f ({) :: /E_[(?--t) t J

c-D ~-'° i P" e UL o4 1.f ( t) k ~ ~RC?fR- -1

c o_ rr(p frO ~ rY~ <0( p-e-cJ-eJ ~ ~t?e / ~U )

""" rt:rtJ . 1

>'e> f~ tk +cf() CClu( r IA10\ 7,·~ wit4 &», ;,, !~ !;{ ei~~( k ~ C><,J) = IE IT{'o -x~)t]

s~op tu~ +~ c~i -r-~k ~ t~ ~ rt{ k) u.cil-{ e,w. ·I ls. > 1 .,

·w w} {-~- s,g,F +o tk 1k_ ~ J.. ~r + ~ <:J.A i"r'~ J ~-IM.fL. to {-o - I

Page 19: Scheduling and Project Planning - TU Berlinpage.math.tu-berlin.de/~moehring/adm3-scheduling-2014-15/19.pdf · .sJ. / \._. e.t)-(?.tT . J . t ] 0, S] J +~ C..ket.,"(t~ ~f r~\J . hc

G .Q,Vl.Q_u-ai2t c_ e

~{kc:;o~~

kiJ (><~·)

-(q' l 9 -

+~ L('l'W( pvt 1Cr1eu._ (}~ li Ct) ey re<' V

-f0 fu Cac,~ ~A.f +k_ <'.0~~ fu.~ch~Cvi~

~ e <oe "r j <>ß (c:, .P Cl>t. f te ~ tuM p_,,~._r