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