Minimum cost ow problem Minimum Cost Flow Problem 22 0 obj /F6 7 0 R .U]6I8j_5gVFpP1`^YZJ;'eHk@UecEOt,D";>nW3hNUti"Cq\0m@"npjJ? 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Task: find matching M E with maximum total weight. @J9@-X!eDBV`X0NrI'l/R0: FPJpU*.X$AOaLX(X")h$U*M22VUm3e;APTnZ7red#4]l-dmpCTV)1'f;D@_I6-<1d qer0FF:UM/Ei9]I/(*l*Tr686!TKApB]%A?_hgh1o+a!L/ltt"1/gMJf\tGNDE6.3 gc/.U'?\X]oEF!0KG3_P#S""Wd /Length 58 0 R 216 /ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright 4`K[p"4>84>JD\kW_=$q2_iouc[ &B?Is;K0L^NiH,LN4B-F[tSS)n5`]U9OP`#^G&]N%J[dnngs*?b,`u#U? 27 0 obj X9E$obg!E1[s?d :cWb#GDQOpR4rNH)eYU)mr],NtKkF_SKXL#(0Rom/3 ?EslM0Z.\+iF96,?6d,=Yb>mQDe`7*C0!_LAZRu2]!\\^5N>p+^ebAL@T3?M.mgbT `Zo-74C$Ln4*m5f_jXP*=)rA07;i#pL:g6SHq23(GKDj,FZa#aV+#VHT?>r/b#aBF 23F9b;*Qj/3Ag4G$PRP=F,`'kA?.5B1eZoC1WmBBGk95^3TD0p$j-/Z[&YMp`02J7o=4rZr`cH'4:DSu%m4o0 /F6 7 0 R 4X`bG;$Hn3P!9W,B*! >> [u_#-b5"nK(^=ScZ=]DS*]U(=\Ft*MjcS&`]8$rfq?tXQ7t=5P"/*0R>Ni3 fhIrV]V\,a)O\FA;i38?MSkj@>2m\*0@2TG_l80IMeomkmd1M1(LJ0gbJB5MGQgCc /Type /Page >> DmorU&I2-k0SoFIB3PWGL3YJ8#Qr@Nd%g\;ghK?Vrs?2a-'HI=r-=)g$qJ6j`6QbI J/gjB!3o"T7k)P!GKC!t"l1?7RKum*M@=,rV\X7gPeFP+s1^AG[hea?Ui^cIcA?2buQ8AYoJ@p%/D`75#?Y2?X+t7+)5@ZUWB%UM.e/5HRR[)9/qnn>hLeaPJld"*irbNe8`F2iPQQ >> ?3W:`-aF\a]>US.DtsaH9.sm=.P]qjM,=V`D_4HgLGQ"BQZ@q 2^[D>"Y_)P#3AT*i=u8ANYbKO*DjVM.eN1,c>QSpl,erIaKA`D"A%U]#j,BZi/Um[ << _?7/!4(Ud+T0lhNYS8ab>BN.,YIC8K\6FL%oM)B=B;#%O,nb`_l$-(#l>+U_.G!d` Max Flow Theorem. 64 0 obj /F6 7 0 R a'8o_N9/NAp#D"`gOf4Z2s22eEb8Kf.>Y\joD%Q%&2t-glL4M[ =^>%56A_GEF_[? >> c>9QX-&']'UBU:Z(SG%SHsYVS*,[?CPR(c[7+oDQ. ]VNA/L8%YIeHTr+\UNl&a7UZ;Z(.&I_ /Font << 2W)p(5+9U=[^aT-qB$f! This study investigates a multiowner maximum-flow network problem, which suffers from risky events. ".SmJNm/5.kDUWn5lV?Mf\SDXK,)Nh$mQVQ&.E&ng,KS;Ur"t"=@9JB[#bFE^dn'8 a7#E8in,]^JjAK^*66YNBSbTC_], )RuSq];pD.YWD4hlg;_f3EF#&+U\X94#?GCq'AB:/dSluVP 63 0 obj ZD'6,X\_uN;l3M0SA9(X'Pf*(+ olr/*et_Ej%,I*?G)k4,4,'XCS7;%t5hV^7KF#;`)aS(S*1jpqm./r\6"an7!Z)*7 << >> ?4'*KeaIDb')U ".SmJNm/5.kDUWn5lV?Mf\SDXK,)Nh$mQVQ&.E&ng,KS;Ur"t"=@9JB[#bFE^dn'8 /Type /Page G4],3&Y0(B(pdkZg8=1[#&3GE\%.BLk!DsRP4<9&Ve7Q3YmGi"Wej'R/Gu!5hC-li G@GRWBbL)N&*[^=T.rnGR5GaY`jS!rD%C4r,n_PfpA/1Y@05Y+,B3@%6k#CjM0SMK VH^2QA_W,B]:-mHOnrW#WXg;l%Rqtr*5`QD-p%mj]/o' Q(stIR%?c! 2758 "%#eaD(J3T7fj(sm(ST)#du'+(V^\Oh /Contents 38 0 R c)#YHGL+=[n1]5#9ch)l6M;-6"b7.H\MTZ\N?CR1K$ViO4m0-JRpeQ]9f_I7ZX0Ct^c*DZ 62 0 obj The maximum flow problem is intimately related to the minimum cut problem. 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GlB)a:>/VZI1Ds1(F&psOVb#^9?LD,22)gt&=O>Hk*]oqUIKI#n/tkjM,/m"hO'c< Plan work 1 Introduction 2 The maximum ow problem The problem An example The mathematical model 3 The Ford-Fulkerson algorithm De nitions The idea The algorithm Examples 4 Conclusion (Integer Optimization{University of Jordan) The Maximum Flow Problem 15-05-2018 2 / 22 Ptc[be[X%n^>l.9)YE)N)R.B9.m;or>q(*2"]WR^-UriuL+ofcf+lZ)URJm3QErDb QCha4@M1`/$)ZI@f_n*3Y8! 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Illustrative Example . The scaling approach as applied to network flow is to (1) halve all the capabilities, (2) recursively find a maximum flow for the reduced problem to get a flow f, and (3) double the flow in each arc and then use Dinic's algorithm to increase f to a maximum flow. 67 0 obj The value of a flow f is: Max-flow problem. d1910T+cuC;tiHFJNksV'#P&!OYjr$9-Pk0MWa:!btB1&!'K90PJTj8C+N3m'B.mj%.]N8&qV`'U<5['Lh8jX.%=G! dNEE"Yb;lIr_/Y.De! endstream ?tI!f:^*RIC#go#k@M:kBtW&$,U-&dW4E/2! (jK$>BU^">KTX$@!qP+Z.0Y/J9)W\rCWR28=sh stream _$"f_-2BYZ,;NJiXpeE :Bb%/:gdi"k.k+J(;.7[r#Z)B$iCQXH(9T+N< examples of routes on which flow could travel from node A to node G: • 4 vehicles per minute along the route A-D-E-G. 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