{"id":1282,"date":"2025-07-23T17:45:08","date_gmt":"2025-07-23T09:45:08","guid":{"rendered":"http:\/\/heqiwei.cn\/?p=1282"},"modified":"2025-07-23T17:45:08","modified_gmt":"2025-07-23T09:45:08","slug":"%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e7%ba%bf%e6%80%a7%e8%a7%84%e5%88%92","status":"publish","type":"post","link":"https:\/\/heqiwei.cn\/index.php\/2025\/07\/23\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e7%ba%bf%e6%80%a7%e8%a7%84%e5%88%92\/","title":{"rendered":"\u6570\u5b66\u5efa\u6a21\u2014\u2014\u7ebf\u6027\u89c4\u5212"},"content":{"rendered":"\n

\u7ebf\u6027\u89c4\u5212\u7684\u5b9a\u4e49<\/h2>\n\n\n\n

\u6570\u5b66\u89c4\u5212\u662f\u8fd0\u7b79\u5b66\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u5b83\u7528\u6765\u7814\u7a76\u5728\u7ed9\u5b9a\u6761\u4ef6\u4e0b\uff08\u7ea6\u675f\u6761\u4ef6\uff09\uff0c\u5982\u4f55\u6309\u7167\u4e00\u8861\u91cf\u6307\u6807\uff08\u76ee\u6807\u51fd\u6570\uff09\u6765\u5bfb\u6c42\u8ba1\u5212\u3001\u7ba1\u7406\u5de5\u4f5c\u4e2d\u7684\u6700\u4f18\u65b9\u6848\u3002<\/p>\n\n\n\n

[math]\\min [\/math]\u6216[math]\\max f(x), \\text{ s.t. } g_i(x) \\leq 0 [\/math]\uff08\u5982\u679c\u662f\u5927\u4e8e\u7684\u5219\u8981\u624b\u52a8\u6539\u4e3a\u5c0f\u4e8e0\uff09<\/p>\n\n\n\n

\u8fd9\u91cc\u7684[math]x[\/math]\u79f0\u4e3a\u51b3\u7b56\u53d8\u91cf\uff1b[math]f(x)[\/math]\u79f0\u4e3a\u76ee\u6807\u51fd\u6570\uff1b[math]g_i(x) \\leq 0[\/math]\u79f0\u4e3a\u7ea6\u675f\u6761\u4ef6\u3002<\/p>\n\n\n\n

\u5982\u679c[math]f(x)[\/math]\u548c\u7ea6\u675f\u6761\u4ef6\u5747\u4e3a\u7ebf\u6027\u8868\u8fbe\u5f0f<\/mark>\uff0c\u5219\u6b64\u65f6\u5c31\u662f\u7ebf\u6027\u89c4\u5212\u3002<\/p>\n\n\n\n

\u7ebf\u6027\u89c4\u5212\u7684\u5e94\u7528<\/h2>\n\n\n\n

\u4f8b 1. \u5e02\u573a\u4e0a\u6709[math]n[\/math]\u79cd\u8d44\u4ea7[math]s_i (i = 1, 2, \\cdots, n)[\/math]\u53ef\u4ee5\u9009\u62e9\uff0c\u73b0\u7528\u6570\u989d\u4e3a[math]M[\/math]\u7684\u76f8\u5f53\u5927\u7684\u8d44\u91d1\u4f5c\u4e00\u4e2a\u65f6\u671f\u7684\u6295\u8d44\u3002\u8fd9[math]n[\/math]\u79cd\u8d44\u4ea7\u5728\u8fd9\u4e00\u65f6\u671f\u5185\u8d2d\u4e70[math]s_i[\/math]\u7684\u5e73\u5747\u6536\u76ca\u7387\u4e3a[math]r_i[\/math]\uff0c\u98ce\u9669\u635f\u5931\u7387\u4e3a[math]q_i[\/math]\uff0c\u6295\u8d44\u8d8a\u5206\u6563\uff0c\u603b\u7684\u98ce\u9669\u8d8a\u5c11\uff0c\u603b\u4f53\u98ce\u9669\u53ef\u7528\u6295\u8d44\u7684[math]s_i[\/math]\u4e2d\u6700\u5927\u7684\u4e00\u4e2a\u98ce\u9669\u6765\u5ea6\u91cf\u3002\u8d2d\u4e70[math]s_i[\/math]\u65f6\u8981\u4ed8\u4ea4\u6613\u8d39\uff0c\u8d39\u7387\u4e3a[math]p_i[\/math]\u3002\u53e6\u5916\uff0c\u5047\u5b9a\u540c\u671f\u94f6\u884c\u5b58\u6b3e\u5229\u7387\u662f[math]r_0[\/math]\uff0c\u65e2\u65e0\u4ea4\u6613\u8d39\u53c8\u65e0\u98ce\u9669[math]r_0 = 5\\%[\/math]\u3002\u5df2\u77e5[math]n = 4[\/math]\u65f6\u76f8\u5173\u6570\u636e\u5982\u4e0b\u8868\u6240\u5217\u3002\u8bf7\u4f60\u4e3a\u8be5\u516c\u53f8\u8bbe\u8ba1\u4e00\u79cd\u6295\u8d44\u65b9\u6848\uff0c\u4f7f\u51c0\u6536\u76ca\u5c3d\u53ef\u80fd\u5927\uff0c\u603b\u4f53\u98ce\u9669\u5c3d\u53ef\u80fd\u5c0f\u3002<\/p>\n\n\n\n

\n \n \n \n \n \n \n \n \n
[math]s_i[\/math]<\/th>\n [math]r_i\/\\%[\/math]<\/th>\n [math]q_i\/\\%[\/math]<\/th>\n [math]p_i\/\\%[\/math]<\/th>\n <\/tr>\n <\/thead>\n
[math]s_1[\/math]<\/td>\n 28<\/td>\n 2.5<\/td>\n 1<\/td>\n <\/tr>\n
[math]s_2[\/math]<\/td>\n 21<\/td>\n 1.5<\/td>\n 2<\/td>\n <\/tr>\n
[math]s_3[\/math]<\/td>\n 23<\/td>\n 5.5<\/td>\n 4.5<\/td>\n <\/tr>\n
[math]s_4[\/math]<\/td>\n 25<\/td>\n 2.6<\/td>\n 6.5<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n\n\n

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

\u786e\u5b9a\u76ee\u6807\u51fd\u6570 [math]\\begin{cases} \\max \\sum_{i = 0}^{n} (r_i – p_i) x_i \\\\ \\min \\left\\{ \\max_{1 \\leqslant i \\leqslant n} \\{ q_i x_i \\} \\right\\} \\end{cases}[\/math], \u7ea6\u675f\u6761\u4ef6\u4e3a [math]\\begin{cases} \\sum_{i = 0}^{n} (1 + p_i) x_i = M, \\\\ x_i \\geqslant 0, \\, i = 0, 1, \\cdots, n \\end{cases}[\/math]<\/p>\n\n\n\n

\u6211\u4eec\u7684\u76ee\u6807\u51fd\u6570\u6709\u4e24\u4e2a\uff0c\u8fd9\u5e76\u4e0d\u7b26\u5408\u6211\u4eec\u7684\u6a21\u578b\uff0c\u6240\u4ee5\u8fd9\u91cc\u6709\u4e00\u70b9\u4e0d\u540c\uff1a<\/p>\n\n\n\n

\u5b9e\u9645\u6295\u8d44\u4e2d\uff0c\u6211\u4eec\u5f80\u5f80\u662f\u628a\u98ce\u9669\u91cf\u5316\u5230\u4e00\u4e2a\u53ef\u63a7\u7684\u8303\u56f4\u5185\uff0c\u4f8b\u5982\u6700\u5927\u53ef\u63a5\u53d7\u98ce\u9669\u4e3a [math] a [\/math]\uff0c\u5373 <\/p>\n\n\n\n

[math]\\frac {q_i x_i}{M} \\leqslant a \\ (i = 1, 2, \\cdots, n)[\/math]<\/p>\n\n\n\n

\u6240\u4ee5\u8c03\u6574\u4e4b\u540e\u7684\u76ee\u6807\u51fd\u6570\u662f [math]\\max\\sum_{i = 0}^{n} (r_i – p_i) x_i [\/math]\uff0c\u800c\u6b64\u65f6\u7684\u7ea6\u675f\u6761\u4ef6\u591a\u4e86\u4e00\u4e2a\uff0c\u6700\u7ec8\u5f97\u5230\u7684\u7ea6\u675f\u96c6\u4e3a [math]\\begin{cases} \\sum_{i = 0}^{n} (1 + p_i) x_i = M, \\\\ x_i \\geqslant 0, i = 0, 1, \\cdots, n \\\\ \\frac{q_i x_i}{M} \\leqslant a \\end{cases}[\/math]<\/p>\n\n\n\n

    <\/ol>\n","protected":false},"excerpt":{"rendered":"

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