L
mai 7
hywwlluaj~
(Transportation Problem)
(Supply)
3 1 8
3 3
- cllxll+c12x12+c13x13+c21x21+c22x22+c23x23
+c31x31+c32x32+c33x33
3
bwufl 1 : - xll+x12+x13 \<a 1
ln4vlii 2 :3
fi= x2J - x21+x22+x23 y< a2
- x31+x32+x33 Ga3
&&l&d 1 :- X11+x21+x31~ 1<b
fl;42URY7d 2 : - x12+'c22+x32 iSb2
3 1 9
m
is= xlj ,< bj J = 1,2 l oo....n
l&f$q--.
1
2
3
1
___--
=I1
=21
=31
..- --
2 3
=12 c13
"22 '23
'32 =33
7 =11 =12 x13 ai
2 x21 x22 =23 '2
3 x31 =32 x33
zi?mix bl b2 b3 &i.,~g.,fwx.Amf
322
K0
: +
03
x0
:
wII
IN w
III
sG
0 0
03
-1’
n :c
+ ?5 + 5 + Yl 0 +
-J 0
wl
0
3 3
F;= ai = 40*70+50 = 160 F;= bj = 30+50+20 = 100
325
1 2 3
-T-----T"12 p
1 x11 x12 x13
c2L - L5
2
3
x21 '22
1 x31
3:
Ix32 x33-I
--___30 50 20
fiullii otn(a 1
0
2Hi4
40-
:24 --
5 0I34--I_
-----t----l60 160
I I I I131 12 I 131 17 I
XT..u. I.. -IL - Xl4, I‘ , I,
Ill 11151 I4 3
150
x21 x22 x23 x243 5 4 6
80x31 x32 x33 =34
327
7
3 80
R7l$mn7shl-'/ li%U 90 70 50 60 270
I I I I I 1
x11 = Min (al,bl) = Mln (150,90) - 90
&ii 2d~ufwm Xl1 = bl - 9 0 nn?~~ttrnv=l~~,nz?T~nl;lnvl~~Buo?
mud 1 a1 = 150 Glarorlh%lJ 90 u'Ji&%h 60 IhlA XI2
Y2 - Min (al-xll,b2) P Min (15090,70) - 60
u'Jtw%&7 30 1IsytihFT~ x23
x23 = Min (a,- x22, b3) = Min (40-10,50) E 30
x23 * 30
x34 = 60
- ~si~3~+~6ox2~+~1ux5)t(9c~t4)+(2~44)+(6ck6)
=m+n-1
1I&! .:3+4-l
,6 &
3 3 1
1.2 North to South row rule
1 l-2 150
2 OL 1 4LOL 3 4010 30
3 3 q?-ig@k lzo
R37J&Plm&=nl&u 90 70 50 60 270
1 &Q l-2 150
2 4OL 1 LOL 3 4010 30
3 3 q?-ig@k lzo
I
R37J&Plm&=nl&u 90 70 50 60 270
@i%~aUn~dWDi~nti% North to South row rule ml?f7Ji!
7-7 lhdt Y ,
ciJviqnlntrn cl2 p 2 6ao?"l5l~\rao?ru,
x12 = Min (al,b2) = Min (150,70) - 70
3 3 2
x34 = Min (a, - x33, b4- ~2~ > = piin (80-50,60-30) = 30
3 3 3
3-l 5-2 4-3 6-3
2 -3-1
1+4-3
ll?lnnmnll&wnt/ lkll 90 70 50 60 270
Iuamwmtna&
-z - i i3-1 4-3 6-3
i;fl1 2 3 4
m'n rhl
I '1 I 7 3 7 150
4 340
4 680
2-3-1
1 @"@'@j /-- 150 m
1 5 4 32 / / 40
1
2 -93-l
3 5 4 63 8 0 3-6-3/ /
ll?u1wl??ll?kN”V I l%lll 9 0 70 50 6 0 270
540
/ /
13 I5 I4 16
150
3 -/-/- L 80 3-b6-3
1
24 3
/ 40
3 t---w-? 4 6, 80
~himnummt/ &I 90 70 50 60 270
3*
339
I I I I It
mtmnm~m~ 2 3* 1 3
u& 2 - 1 3
2 - - 3
2 - - T
3 - - CT
3 - - -
x11 = 30
x12 P 70
x13 = 50
x24 - 40
x31 - 60
x34 - 20
3 4 1
2 ~@~& k 405 4 6
3 LOLOL2 0 60 80
Ralll~~~nlT~URY7 ‘30 70 50 60 270P-L r%mI
344
345
nmd 7-15
11 22
11 &&: L&&: L1 51 5
22 LdLLdLIC -IC -
'3 3
I IY
40
SO
50 60 270
P
=14 - =12 + =22- '23 + '33 - '34
= 7-2+5-4+4-6
I’ll 4 1?ium x31;a (+)x3,+ (-)x3,--+ (+)x2,--+ (-)x2-p
*
=22 + =12 - =11
-3
Ml4 r%ml;l x32&I (+)x3,--+ (-)x33~(+)x23~-)x22
n7ri~~oualinj?w"snrEis~~~u I c32 - c33 + =23 - =22
p1lmla'4 = +5 -4+4-5/-
= 0
348
1 2
1
90-10 @
2
IO-IO -0, 0
= 80, xl2 = 70, x.21 = 10, x23 = 30
x33 = 20, x34 = 60
Y t Inu?lwlaunJr3~ m (80x3) + (70x2) + (10x1) + (30x4)
+(20x4) + (60x6)
P 950 WM
x21 =0 + 90 - 90
x22 - 10 - 90 - -80.
x12 -60 + 90 = 150
352
n-lm!J! 7-20
x13
=14
=22
x24
x31
=32
+3-2t1-4 I - 3
+7-3+-l-4+4-6 P -1
+5-2+3-l = +5
+3-4+4-6 P -3
+3-4+4-l = +2
+5-4+4-1+3-2 = +5
353
w-If7 d1
x,,wL 3
80-30 -0 50
.,,o
10+30 - 0 40
7-21
3
y3(+) 3L0+30= 300
x2,(-) L4
30-30 @
V177$! 7-22
2
1 2 34-b@j) 3@ 2@ 3
40
OL 60 6 80
60 270
x14 +x14-x13+x33-x34 +7-3+4-6 t +2
x22 +x22-x12+xll-x21 +5-2+3-l I +5
x23 +x23-x13'xll+x21 +4-3+3-l = +3
x24 +x24-x21+x11-x13+x33-x~ +3-1+3-34-6 P 0
x31 +x31-x33+x13-xll +3-4+3-3 s -1
x32 +x32-x33+x13-x12 +5-4+3-2 P 2
355
50 - 20 5 0 30 30 + 20 = 0 50
x3,(+) x3,(->
0 + 20 = 0 20 20-20 - @
356
uan’w;~m~a xl1 pED30, x12 = 70, Xl3 = 50
x21 = 40, x31 - 20, xN - 60
= (30x3) + (70x2) + wx3) + (40x1)
+ (20x3) + (60x6)
P 840 llw
+7 - 3+3-6 = +l
+5 -2+3-l = +5
+4 -3+3-l - +3
+3-1+3-6 = -1