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E L-LOVELY-H math27-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12
noEPk;soh dk rfDs
B'N 27H4 o/yh gq'rokfwzr dhnK ;hwktK (Limitations of Linear Programming)
o/yh gq'rokfwzr noEPk;so ftZu pj[s jh bkGdkfJe ;kXB f;ZX j'fJnk j?. gozs{ fJ; dhnK
nkgDhnK ;hwktK jB. n;b ftZu, fJBQK d/ gqfspzXK d/ ekoB n;b ;wZf;nktK o/yh gq'rokfwzr
seBhe d[nkok jZb BjhA ehsh ik ;edhnK. gfjbh, fJZe ftfPPN T[d/P cbB B{z gfoGkfPs
eoBk ;ob BjhA j?. d{i/, i/eo fJZe ftP/P T[d/P cbB fBoXkfos eo th fdZsk ikt/ sK fdZs/
j'J/ T[d/P dh fdqPNh d/ wkor ftZu gquZbs ftfGzB ;wkfie, ;z;EkfBe ftZsh ns/ j'o gqfspzXK B{z
ikDBk e'Jh n;kB ezw BjhA j?. fsZi/, fJZe ftfPPN T[d/P ns/ gqfspzXK dk ;?N fdZs/ j'D s/,
fJj io{oh j? fe gqfspzX o/yh n;wkBsktK d/ o{g ftZu gqsZy o{g s'A ftnes Bk ehsk ik ;eD.
u"E/, i/eo toDs ;wZf;nktK gko eoB :'r th j'D sK fJZe w[Zy ;wZf;nk ftfGzB ;fEo r[DKeK
d/ ;zpzX ftZu nkrDB dh j? fijVh fJZe o/yh gq'rokfwzr ;wZf;nk fit/A ehwsK nkfd ftZu gqt/P
eodh j?. gzit/A fJ; seBhe dh w[Zy ewh fJj j? fe fJj nkrsK ns/ fBorsK ftZu o/yh ;zpzX
dh ;EkgBk T[Zs/ nXkfos j? fi;dk Gkt fJj j? fe ftfGzB nkrsK ns/ fBorsK ftZu :'r, r[DB
ns/ ftGkiesk d/ ;zpzX gkJ/ iKd/ jB. gozs{ fJj ;zpzX jo/e o/yh gq'rokfwzr ;wZf;nk T[Zs/ BjhA
j[zd/ feT[Afe pj[s ;kohnK ;wZf;nktK ftZu no/yh (non-linear) ;zpzX gkJ/ iKd/ jB. S/t/A,
seBhe t;s{ ns/ ;kXB pkIkoK ftZu g{oD gqfs:'rsk dh wkBsk T[Zs/ nXkfos j?. gozs{ ftZu
g{oD gqfs:'rsk dh nt;Ek BjhA d/yh iKdh. ;Zst/A, o/yh gq'rokfwzr noEftt;Ek ftZu
gqfscbK dh wkBsk b?e/ uZbdh j?, go n;b ftZu iK sK gqfscb xNd/ j'J/ iK tXd/ j'J/ j[zd/
jB. nkyoh, fJj fJZe pj[s fInkdk rfDse ns/ ifNb seBhe j?. o/yh gq'rokfwzr d/ Bkb
;wZf;nk dk jZb fJZe ;gPN nkdoP uo d/ nfXeheoD iK fBT{BswheoD dh ng/fynk eodk
j?. fJZe o/yh gq'rokfwzr ;wZf;nk dk jZb f;wgb?e; ftXh (simplex method) fij/ ifNb
sohfenK Bkb th gqkgs ehsk iKdk j?, fiBQK ftZu pj[s ;ko/ rfDse gforDB eoB g?Ad/ jB.
fJ;d/ bJh ftP/P rDB^seBhe (computational technique) fit/A fpibJh rDe (electric
computer) iK v/;e rDe (desk calculator) dh io{os j[zdh j?. nfij/ rDe e/tb wfjzr/ jh
BjhA j[zd/ pbfe T[jBK B{z ubkT[D d/ bJh ftP/PZrK dh th Io{os g?Adh j?.
eh s[;hA ikDd/ j' o/yh gq'rokfwzr wkvb fInkdkso ‘gqhyD ns/ u{e’ jZb (trial and error
solutions) g/P eod/ jB. ftfGzB nkofEe ;wZf;nktK dk n;b ftZu
nkPktkdh jZb y'iDk w[Pfeb j[zdk j?.
27H5 ;koKP (Summary)
• o/yh gq'rokfwzr fJZe rfDse ftXh j? fi;dk rfDs ftfrnkBh ikoe v?Bfir (George
Dantzig) B/, ;/BktK B{z g{osh gj[zukT[D dh ;wZf;nk Bkb ;zpzXs nwohek dh jtkJh
;/Bk d/ ftfGzB ekoi^ebkgK dh :'iBk pDkT[D d/ bJh, 1947 ftZu ftef;s ehsk ;h.
cow d/ nkofEe f;XKs, gqpzXkswe noEPk;so, nzdo{Bh gqd/fPe tgko, ;XkoD
;zs[bB ftPb/PD, efbnkD noEPk;so ns/ ftek; :'iBk ftZu gq:'r d/ bJh th fJ;dk
ftek; j'fJnk j?.
• nfXeheoD ns/ fBT{BswheoD dhnK ;wZf;nktK B{z nkPktkdh (optimisation) dhnK
;wZf;nktK th efjzd/ jB fJBQK ;wZf;nktK B{z jZb eoB d/ bJh noEPk;sohnK d[nkok
fijVhnK seBheK ngDkJhnK iKdhnK jB T[jBK B{z o/yh gq'rokfwzr efjzd/ jB.
348 LOVELY PROFESSIONAL UNIVERSITY
