{"id":1322,"date":"2025-07-28T16:29:59","date_gmt":"2025-07-28T08:29:59","guid":{"rendered":"http:\/\/heqiwei.cn\/?p=1322"},"modified":"2025-07-28T16:29:59","modified_gmt":"2025-07-28T08:29:59","slug":"%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e6%95%b4%e6%95%b0%e8%a7%84%e5%88%92","status":"publish","type":"post","link":"https:\/\/heqiwei.cn\/index.php\/2025\/07\/28\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e6%95%b4%e6%95%b0%e8%a7%84%e5%88%92\/","title":{"rendered":"\u6570\u5b66\u5efa\u6a21\u2014\u2014\u6574\u6570\u89c4\u5212"},"content":{"rendered":"\n

\u6574\u6570\u89c4\u5212\u7684\u5b9a\u4e49<\/h2>\n\n\n\n

\u5f53\u6a21\u578b\u4e2d\u7684\u53d8\u91cf (\u90e8\u5206\u6216\u5168\u90e8) \u88ab\u9650\u5236\u4e3a\u6574\u6570\u65f6\uff0c\u79f0\u4e3a\u6574\u6570\u89c4\u5212\u3002<\/p>\n\n\n\n

[math]\\text{\u6574\u6570\u89c4\u5212}\\begin{cases}\\text{\u6574\u6570\u7ebf\u6027\u89c4\u5212(\u7ebf\u6027\u89c4\u5212 + \u53d8\u91cf\u53d6\u6574)} \\\\ \\text{\u6574\u6570\u975e\u7ebf\u6027\u89c4\u5212(\u65e0\u6c42\u89e3\u7b97\u6cd5\uff0c\u53ea\u80fd\u6a21\u62df\uff0c\u5982\u8499\u7279\u5361\u6d1b\u7b97\u6cd5\u3001\u667a\u80fd\u7b97\u6cd5)}\\end{cases}[\/math]<\/p>\n\n\n\n

\u95ee\u9898\uff1a\u628a\u7ebf\u6027\u89c4\u5212\u7684\u6700\u4f18\u89e3\u7684\u81ea\u53d8\u91cf\u53d6\u6574\u5c31\u662f\u6574\u6570\u89c4\u5212\u7684\u6700\u4f18\u89e3\u5417\uff1f<\/p>\n\n\n\n

    \n
  1. [math]\\min z = x_1 + x_2, \\ \\text {s.t.} \\begin {cases} 2x_1 + 4x_2 = 5 \\\\ x_1 \\geqslant 0, x_2 \\geqslant 0 \\end {cases}[\/math]\uff0c\u6b64\u65f6\u6700\u4f18\u89e3 [math] x_1 = 0, x_2 = \\min \\ z = \\dfrac {5}{4}[\/math]\uff0c\u6b64\u65f6\u6574\u6570\u89c4\u5212\u65e0\u89e3\u3002<\/li>\n\n\n\n
  2. [math]\\min z = x_1 + x_2, \\ \\text {s.t.} \\begin {cases} 2x_1 + 4x_2 = 6 \\\\ x_1 \\geqslant 0, x_2 \\geqslant 0 \\end {cases}[\/math]\uff0c\u6b64\u65f6\u6700\u4f18\u89e3 [math] x_1 = 0, x_2 = \\dfrac {3}{2}, \\min z = \\dfrac {3}{2}[\/math]\uff0c\u82e5\u9650\u5236\u4e3a\u6574\u6570 [math] x_1 = 1, x_2 = 1, \\min z = 2 [\/math]\uff0c\u6709\u89e3\u3002<\/li>\n<\/ol>\n\n\n\n

    \u6574\u6570\u89c4\u5212\u7684\u4f8b\u9898<\/h2>\n\n\n\n

    \u76f8\u4e92\u6392\u65a5\u7684\u7ea6\u675f\u6761\u4ef6\/01\u80cc\u5305\u95ee\u9898<\/h3>\n\n\n\n

    \u4f8b 1. \u67d0\u5e02\u4e3a\u65b9\u4fbf\u5c0f\u5b66\u751f\u4e0a\u5b66\uff0c\u62df\u5728\u65b0\u5efa\u7684 8 \u4e2a\u5c45\u6c11\u5c0f\u533a [math] A_1, A_2, \\dots, A_8 [\/math] \u589e\u8bbe\u82e5\u5e72\u6240\u5c0f\u5b66\uff0c\u7ecf\u8fc7\u8bba\u8bc1\uff0c\u77e5\u5907\u9009\u6821\u5740\u6709 [math] B_1, B_2, \\dots, B_6 [\/math]\uff0c\u5b83\u4eec\u80fd\u8986\u76d6\u7684\u5c45\u6c11\u5c0f\u533a\u5982\u8868\u6240\u793a\u3002<\/p>\n\n\n\n

    \n \n \n \n \n \n
    \u5907\u9009\u6821\u5740<\/th>\n B1<\/th>\n B2<\/th>\n B3<\/th>\n B4<\/th>\n B5<\/th>\n B6<\/th>\n <\/tr>\n <\/thead>\n
    \u8986\u76d6\u5c0f\u533a<\/td>\n A1,A5,A7<\/td>\n A1,A2,A5,A8<\/td>\n A1,A3,A5<\/td>\n A2,A4,A8<\/td>\n A3,A6<\/td>\n A4,A6,A8<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n\n\n

    \u89e3\u9898\u601d\u8def<\/mark><\/strong><\/p>\n\n\n\n

    \u8bbe [math] x_i = \\begin {cases} 1, & \\text {\u5728\u5907\u9009\u6821\u5740 } B_i \\text { \u5efa\u5b66\u6821}, \\\\ 0, & \\text {\u5728\u5907\u9009\u6821\u5740 } B_i \\text { \u4e0d\u5efa\u5b66\u6821}. \\end {cases}[\/math]<\/p>\n\n\n\n

    \u76ee\u6807\u662f\u8ba9\u8986\u76d6\u6240\u6709\u5c0f\u533a\uff0c\u4e14\u6821\u533a\u6570\u91cf\u6700\u5c11\uff0c\u5373 [math]\\min \\sum_{i = 1}^{6} x_i [\/math]\u3002<\/p>\n\n\n\n

    \u5bf9\u4e8e[math]A_1[\/math]\u5230[math]A_7[\/math]\uff0c\u5206\u522b\u627e\u51fa\u5305\u542b\u5b83\u4eec\u7684\u5907\u9009\u6821\u5740\uff0c\u53ef\u4ee5\u5f97\u5230\u7ea6\u675f\u6761\u4ef6\uff1a<\/p>\n\n\n\n

    [math]\\text {s. t.}\\begin {cases}x_1 + x_2 + x_3 \\geqslant 1 \\\\x_4 + x_6 \\geqslant 1 \\\\x_3 + x_5 \\geqslant 1 \\\\x_2 + x_4 \\geqslant 1 \\\\x_5 + x_6 \\geqslant 1 \\\\x_1 \\geqslant 1 \\\\x_2 + x_4 + x_6 \\geqslant 1\\end {cases}[\/math]<\/p>\n\n\n\n

    \u6307\u6d3e\u95ee\u9898<\/h3>\n\n\n\n

    \u4f8b 2. \u67d0\u516c\u53f8\u65b0\u8d2d\u7f6e\u4e86\u67d0\u79cd\u8bbe\u5907 6 \u53f0\uff0c\u6b32\u5206\u914d\u7ed9\u4e0b\u5c5e\u7684 4 \u4e2a\u4f01\u4e1a\uff0c\u5df2\u77e5\u5404\u4e2a\u4f01\u4e1a\u83b7\u5f97\u8fd9\u79cd\u8bbe\u5907\u540e\u521b\u5e74\u5229\u6da6\u5982\u8868\u6240\u793a\uff0c\u6bcf\u4e2a\u4f01\u4e1a\u81f3\u5c11\u5206\u914d 1 \u53f0\u8bbe\u5907\uff0c\u95ee\u5e94\u8be5\u5982\u4f55\u5206\u914d\u8fd9\u4e9b\u8bbe\u5907\u624d\u80fd\u4f7f\u5e74\u521b\u603b\u5229\u6da6\u6700\u5927\uff0c\u6700\u5927\u4e3a\u591a\u5c11\uff1f<\/p>\n\n\n\n\n \n \n \n \n \n \n \n \n \n
    \u8bbe\u5907\\\u4f01\u4e1a<\/th>\n \u7532<\/th>\n \u4e59<\/th>\n \u4e19<\/th>\n \u4e01<\/th>\n <\/tr>\n <\/thead>\n
    1<\/td>\n 4<\/td>\n 2<\/td>\n 3<\/td>\n 4<\/td>\n <\/tr>\n
    2<\/td>\n 6<\/td>\n 4<\/td>\n 5<\/td>\n 5<\/td>\n <\/tr>\n
    3<\/td>\n 7<\/td>\n 6<\/td>\n 7<\/td>\n 6<\/td>\n <\/tr>\n
    4<\/td>\n 7<\/td>\n 8<\/td>\n 8<\/td>\n 6<\/td>\n <\/tr>\n
    5<\/td>\n 7<\/td>\n 9<\/td>\n 8<\/td>\n 6<\/td>\n <\/tr>\n
    6<\/td>\n 7<\/td>\n 10<\/td>\n 8<\/td>\n 6<\/td>\n <\/tr>\n <\/tbody>\n<\/table>\n\n\n\n

    \u89e3\u9898\u601d\u8def<\/mark><\/strong><\/p>\n\n\n\n

    \u7528 [math] j = 1, 2, 3, 4 [\/math] \u5206\u522b\u8868\u793a\u7532\u3001\u4e59\u3001\u4e19\u3001\u4e01\u56db\u4e2a\u4f01\u4e1a\uff0c[math] c_{ij}[\/math] \u8868\u793a\u7b2c [math] i (i = 1, \u2026, 6)[\/math] \u53f0\u8bbe\u5907\u5206\u914d\u7ed9\u7b2c [math] j [\/math] \u4e2a\u4f01\u4e1a\u521b\u9020\u7684\u5229\u6da6\uff0c\u8bbe\uff1a[math]
    x_{ij} =
    \\begin {cases}
    1, & \\text {\u7b2c} i\\text {\u53f0\u8bbe\u5907\u5206\u914d\u7ed9\u7b2c} j\\text {\u4e2a\u4f01\u4e1a} \\\\
    0, & \\text {\u7b2c} i\\text {\u53f0\u8bbe\u5907\u4e0d\u5206\u914d\u7ed9\u7b2c} j\\text {\u4e2a\u4f01\u4e1a}
    \\end {cases},
    i = 1, \\cdots, 6; j = 1, 2, 3, 4.
    [\/math]<\/p>\n\n\n\n

    \u76ee\u6807\u51fd\u6570\u4e3a\uff1a[math]\\max \\sum_{i = 1}^{6} \\sum_{j = 1}^{4} c_{ij} x_{ij}[\/math]<\/p>\n\n\n\n

    \u7ea6\u675f\u6761\u4ef6\uff08s.t.\uff09\uff1a[math]
    \\begin {cases}
    \\sum_{i = 1}^{6} x_{ij} \\geqslant 1, & j = 1, 2, 3, 4, \\\\
    \\sum_{j = 1}^{4} x_{ij} = 1, & i = 1, \\cdots, 6, \\\\
    x_{ij} = 0 \\text { \u6216 } 1, & i = 1, \\cdots, 6; j = 1, 2, 3, 4.
    \\end {cases}
    [\/math]<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u6574\u6570\u89c4\u5212\u7684\u5b9a\u4e49 \u5f53\u6a21\u578b\u4e2d\u7684\u53d8\u91cf (\u90e8\u5206\u6216\u5168\u90e8) \u88ab\u9650\u5236\u4e3a\u6574\u6570\u65f6\uff0c\u79f0\u4e3a\u6574\u6570\u89c4\u5212\u3002 [math]\\text{\u6574\u6570\u89c4 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-1322","post","type-post","status-publish","format-standard","hentry","category-19"],"_links":{"self":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1322","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1322"}],"version-history":[{"count":27,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1322\/revisions"}],"predecessor-version":[{"id":1350,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1322\/revisions\/1350"}],"wp:attachment":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1322"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1322"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}