{"id":28903,"date":"2023-12-07T05:26:51","date_gmt":"2023-12-07T05:26:51","guid":{"rendered":"https:\/\/masterskills.org\/blog\/qui-hoach-tuyen-tinh-linear-programming-la-gi-cong-thuc-va-vi-du.html"},"modified":"2023-12-23T06:07:11","modified_gmt":"2023-12-22T23:07:11","slug":"qui-hoach-tuyen-tinh-linear-programming-la-gi-cong-thuc-va-vi-du","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/qui-hoach-tuyen-tinh-linear-programming-la-gi-cong-thuc-va-vi-du.html","title":{"rendered":"Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh (Linear programming) l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"
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H\u00ecnh minh h\u1ecda. Ngu\u1ed3n: studentfeels1211<\/p>\n<\/div>\n<\/div>\n

Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh (Linear programming)<\/font><\/h2>\n

Kh\u00e1i ni\u1ec7m<\/b><\/p>\n

Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh<\/b> trong ti\u1ebfng Anh g\u1ecdi l\u00e0 Linear programming<\/b>, vi\u1ebft t\u1eaft l\u00e0 LP<\/b>.<\/p>\n

Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh (LP)<\/b> l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n nh\u1eb1m t\u00ecm ra ph\u01b0\u01a1ng \u00e1n t\u1ed1i \u01b0u (ho\u1eb7c k\u1ebf ho\u1ea1ch t\u1ed1i \u01b0u) t\u1eeb v\u00f4 s\u1ed1 c\u00e1c ph\u01b0\u01a1ng \u00e1n quy\u1ebft \u0111\u1ecbnh. Ph\u01b0\u01a1ng \u00e1n t\u1ed1i \u01b0u l\u00e0 ph\u01b0\u01a1ng \u00e1n th\u1ecfa m\u00e3n \u0111\u01b0\u1ee3c c\u00e1c m\u1ee5c ti\u00eau \u0111\u1ec1 ra c\u1ee7a m\u1ed9t h\u00e3ng, ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e1c h\u1ea1n ch\u1ebf v\u00e0 c\u00e1c r\u00e0ng bu\u1ed9c.\u00a0<\/p>\n

LP \u0111\u1ec1 c\u1eadp \u0111\u1ebfn v\u1ea5n \u0111\u1ec1 ph\u00e2n b\u1ed5 ngu\u1ed3n l\u1ef1c khan hi\u1ebfm gi\u1eefa c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ea1nh tranh trong m\u1ed9t ph\u01b0\u01a1ng th\u1ee9c t\u1ed1i \u01b0u. Quy\u1ebft \u0111\u1ecbnh t\u1ed1i \u01b0u mang l\u1ea1i hi\u1ec7u qu\u1ea3 cao nh\u1ea5t, l\u00e3i g\u1ed9p (Contribution Margin – CM) cao nh\u1ea5t hay doanh thu ho\u1eb7c chi ph\u00ed th\u1ea5p nh\u1ea5t. M\u00f4 h\u00ecnh LP g\u1ed3m 2 th\u00e0nh ph\u1ea7n:<\/p>\n

– H\u00e0m m\u1ee5c ti\u00eau<\/i>: H\u00e3ng ph\u1ea3i x\u00e1c \u0111\u1ecbnh m\u1ee5c ti\u00eau c\u1ee5 th\u1ec3 ph\u1ea3i \u0111\u1ea1t t\u1edbi<\/p>\n

– C\u00e1c r\u00e0ng bu\u1ed9c<\/i>: C\u00e1c r\u00e0ng bu\u1ed9c d\u01b0\u1edbi d\u1ea1ng c\u00e1c h\u1ea1n ch\u1ebf v\u1ec1 s\u1ef1 s\u1eb5n c\u00f3 c\u1ee7a ngu\u1ed3n l\u1ef1c hay th\u1ecfa m\u00e3n c\u00e1c y\u00eau c\u1ea7u t\u1ed1i thi\u1ec3u. Nh\u01b0 t\u00ean g\u1ecdi qui ho\u1ea1ch tuy\u1ebfn t\u00ednh, c\u1ea3 h\u00e0m m\u1ee5c ti\u00eau v\u00e0 c\u00e1c r\u00e0ng bu\u1ed9c ph\u1ea3i d\u01b0\u1edbi d\u1ea1ng tuy\u1ebfn t\u00ednh.\u00a0<\/p>\n

V\u00ed d\u1ee5:<\/b><\/p>\n

M\u1ed9t h\u00e3ng mu\u1ed1n t\u00ecm k\u1ebft h\u1ee3p s\u1ea3n ph\u1ea9m t\u1ed1i \u01b0u. K\u1ebft h\u1ee3p t\u1ed1i \u01b0u l\u00e0 k\u1ebft h\u1ee3p t\u1ed1i \u0111a h\u00f3a t\u1ed5ng hi\u1ec7u qu\u1ea3 hay l\u00e3i g\u1ed9p (CM) trong ng\u00e2n s\u00e1ch \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n v\u00e0 c\u00f4ng su\u1ea5t s\u1ea3n xu\u1ea5t. Ho\u1eb7c l\u00e0 h\u00e3ng c\u00f3 th\u1ec3 mu\u1ed1n x\u00e1c \u0111\u1ecbnh k\u1ebft h\u1ee3p nguy\u00ean li\u1ec7u \u0111\u1ea7u v\u00e0o c\u00f3 chi ph\u00ed nh\u1ecf nh\u1ea5t trong khi v\u1eabn \u0111\u00e1p \u1ee9ng \u0111\u01b0\u1ee3c c\u00e1c \u0111\u00f2i h\u1ecfi c\u1ee7a s\u1ea3n xu\u1ea5t, t\u1eadn d\u1ee5ng c\u00f4ng su\u1ea5t s\u1ea3n xu\u1ea5t v\u00e0 s\u1eed d\u1ee5ng nh\u00e2n c\u00f4ng s\u1eb5n c\u00f3.\u00a0<\/p>\n

\u1ee8ng d\u1ee5ng c\u1ee7a Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh<\/font><\/h2>\n

Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh<\/b> c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng ch\u1eb3ng h\u1ea1n nh\u01b0:<\/p>\n

– L\u1ef1a ch\u1ecdn k\u1ebft h\u1ee3p \u0111\u1ea7u v\u00e0o c\u00f3 chi ph\u00ed th\u1ea5p nh\u1ea5t cho s\u1ea3n ph\u1ea9m s\u1ea3n xu\u1ea5t ra<\/p>\n

– X\u00e1c \u0111\u1ecbnh ng\u00e2n s\u00e1ch t\u1ed1i \u01b0u<\/p>\n

– Quy\u1ebft \u0111\u1ecbnh danh m\u1ee5c \u0111\u1ea7u t\u01b0 t\u1ed1i \u01b0u (hay ph\u00e2n b\u1ed5 t\u00e0i s\u1ea3n)<\/p>\n

– Ph\u00e2n b\u1ed5 ng\u00e2n s\u00e1ch qu\u1ea3ng c\u00e1o cho c\u00e1c ph\u01b0\u01a1ng ti\u1ec7n th\u00f4ng tin<\/p>\n

– L\u00ean k\u1ebf ho\u1ea1ch s\u1eed d\u1ee5ng m\u00e1y m\u00f3c<\/p>\n

– Quy\u1ebft \u0111\u1ecbnh ph\u01b0\u01a1ng th\u1ee9c v\u1eadn chuy\u1ec3n c\u00f3 chi ph\u00ed th\u1ea5p nh\u1ea5t<\/p>\n

\u00a0– L\u00ean k\u1ebf ho\u1ea1ch cho c\u00e1c chuy\u1ebfn bay<\/p>\n

– Ph\u00e2n b\u1ed1 nh\u00e2n l\u1ef1c t\u1ed1i \u01b0u<\/p>\n

– L\u1ef1a ch\u1ecdn v\u1ecb tr\u00ed \u0111\u1eb7t nh\u00e0 x\u01b0\u1edfng ph\u00f9 h\u1ee3p nh\u1ea5t<\/p>\n

C\u00f4ng th\u1ee9c c\u1ee7a Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh<\/font><\/h3>\n

\u0110\u1ec3 x\u00e2y d\u1ef1ng m\u1ed9t b\u00e0i to\u00e1n Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh<\/b>, c\u1ea7n l\u00e0m theo c\u00e1c b\u01b0\u1edbc sau:<\/p>\n

– X\u00e1c \u0111\u1ecbnh bi\u1ebfn quy\u1ebft \u0111\u1ecbnh ph\u1ea3i t\u00ecm<\/p>\n

– Bi\u1ec3u di\u1ec5n h\u00e0m m\u1ee5c ti\u00eau c\u00e1c c\u00e1c r\u00e0ng bu\u1ed9c theo c\u00e1c bi\u1ebfn quy\u1ebft \u0111\u1ecbnh n\u00e0y. C\u00e1c ph\u01b0\u01a1ng tr\u00ecnh ph\u1ea3i c\u00f3 d\u1ea1ng tuy\u1ebfn t\u00ednh.<\/p>\n

V\u00ed d\u1ee5<\/i><\/b><\/p>\n

C\u00f4ng ty s\u1ea3n xu\u1ea5t \u0111\u1ed3 n\u1ed9i th\u1ea5t XXX s\u1ea3n xu\u1ea5t 2 s\u1ea3n ph\u1ea9m: b\u00e0n gi\u1ea5y v\u00e0 b\u00e0n \u0103n. C\u1ea3 2 s\u1ea3n ph\u1ea9m c\u1ea7n th\u1eddi gian \u0111\u1ec3 \u0111\u01b0\u1ee3c x\u1eed l\u00ed trong 2 b\u1ed9 ph\u1eadn: b\u1ed9 ph\u1eadn l\u1eafp r\u00e1p v\u00e0 b\u1ed9 ph\u1eadn ho\u00e0n thi\u1ec7n. D\u1eef li\u1ec7u v\u1ec1 hai s\u1ea3n ph\u1ea9m n\u00e0y nh\u01b0 sau:<\/p>\n

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C\u00f4ng ty mu\u1ed1n t\u00ecm \u0111\u01b0\u1ee3c c\u00e1ch k\u1ebft h\u1ee3p 2 lo\u1ea1i s\u1ea3n ph\u1ea9m n\u00e0y sao cho c\u00f3 l\u1ee3i nh\u1ea5t.\u00a0<\/p>\n

B\u01b0\u1edbc 1<\/i>, x\u00e1c \u0111\u1ecbnh c\u00e1c bi\u1ebfn quy\u1ebft \u0111\u1ecbnh nh\u01b0 sau:<\/p>\n

x1<\/sub>= S\u1ed1 l\u01b0\u1ee3ng b\u00e0n gi\u1ea5y<\/p>\n

x2<\/sub>= S\u1ed1 l\u01b0\u1ee3ng b\u00e0n \u0103n<\/p>\n

B\u01b0\u1edbc 2<\/i>, h\u00e0m m\u1ee5c ti\u00eau \u0111\u1ec3 t\u1ed1i \u0111a h\u00f3a hi\u1ec7u qu\u1ea3 (Z) \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n

Z = 25x1<\/sub> + 40x2<\/sub><\/p>\n

Sau \u0111\u00f3 l\u1eadp c\u00f4ng th\u1ee9c c\u00e1c r\u00e0ng bu\u1ed9c nh\u01b0 l\u00e0 c\u00e1c b\u1ea5t \u0111\u1eb3ng th\u1ee9c:<\/p>\n

2x1<\/sub> + 4x2<\/sub> < 100 (r\u00e0ng bu\u1ed9c l\u1eafp r\u00e1p)<\/p>\n

3x1<\/sub> + 2x2<\/sub> <90 (r\u00e0ng bu\u1ed9c ho\u00e0n thi\u1ec7n)<\/p>\n

Th\u00eam v\u00e0o \u0111\u00f3, \u1ea9n trong b\u1ea5t k\u00ec c\u00f4ng th\u1ee9c LP n\u00e0o ph\u1ea3i c\u00f3 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 l\u00e0m cho x1 v\u00e0 x2 kh\u00f4ng \u00e2m, t\u1ee9c l\u00e0 x1<\/sub>, x2<\/sub> >= 0<\/p>\n

T\u1ed1i \u01b0u h\u00f3a: Z = 25x1<\/sub> + 40x2<\/sub><\/p>\n

R\u00e0ng bu\u1ed9c: 2x1<\/sub> + 4x2<\/sub> < 100<\/p>\n

3x1<\/sub> + 2x2<\/sub> < 90<\/p>\n

x1<\/sub>, x2<\/sub> >= 0<\/p>\n

(Theo Gi\u00e1o tr\u00ecnh Qu\u1ea3n tr\u1ecb kinh doanh, NXB \u0110\u1ea1i h\u1ecdc Kinh t\u1ebf Qu\u1ed1c d\u00e2n<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n Qui ho\u1ea1ch tuy\u1ebfn t\u00ednh (ti\u1ebfng Anh: Linear programming) l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n nh\u1eb1m t\u00ecm ra ph\u01b0\u01a1ng \u00e1n t\u1ed1i \u01b0u (ho\u1eb7c k\u1ebf ho\u1ea1ch t\u1ed1i \u01b0u) t\u1eeb v\u00f4 s\u1ed1 c\u00e1c ph\u01b0\u01a1ng \u00e1n quy\u1ebft \u0111\u1ecbnh.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[416],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/28903"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=28903"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/28903\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=28903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=28903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=28903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}