Created
October 17, 2018 22:06
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"from numpy import *\n", | |
"from cvxpy import *" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"**Дано**\n", | |
"\n", | |
"* $n$ - ко-во складов\n", | |
"* $R_i$ - ко-во ресурсов на складе $i$\n", | |
"* $m$ - ко-во заводов\n", | |
"* $S_j$ - ко-во потребляемых зводом ресурсов\n", | |
"* $c_{i,j}$ - стоимость доставки единицы ресурса со склада $i$ на завод $j$\n", | |
"* $x_{i,j}$ - ко-во доставленного на завод $j$ ресурса со склада $i$\n", | |
"\n", | |
"**Нобходимо**\n", | |
"* Найти такие $x_{i,j}$ при которых $\\sum\\limits_{i=1}^m \\sum\\limits_{j=1}^n c_{ij} x_{ij} \\rightarrow min$" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 93, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"n = 3\n", | |
"m = 9\n", | |
"R = around(random.uniform(size=n)*1000)\n", | |
"S = around(random.uniform(size=m)*100)+100\n", | |
"c = around(random.uniform(size=(n,m))*10)+1" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 94, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"x = Variable((n,m), integer=True)\n", | |
"cond = [\n", | |
" x>=0,\n", | |
" x*ones(m)<=R,\n", | |
" x.T*ones(n)==S\n", | |
"]\n", | |
"obj = sum(multiply(x,c))\n", | |
"prob = Problem(Minimize(obj), cond)\n", | |
"result = prob.solve()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 95, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Минимальный расход на доставку: 5646.0\n", | |
"План доставки:\n", | |
" [[ 10. 109. -0. 0. 57. 0. -0. 0. -0.]\n", | |
" [ 0. -0. 149. 74. 134. 110. -0. 0. -0.]\n", | |
" [109. -0. -0. 92. 0. 0. 117. 101. 103.]]\n" | |
] | |
} | |
], | |
"source": [ | |
"print(\"Минимальный расход на доставку:\",round(result))\n", | |
"print(\"План доставки:\\n\", around(x.value))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 98, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Потребности производства в ресурсах:\n", | |
" [119. 109. 149. 166. 191. 110. 117. 101. 103.]\n", | |
"Доставлено ресурсов на производства:\n", | |
" [119. 109. 149. 166. 191. 110. 117. 101. 103.]\n", | |
"\n", | |
"Начальные ресурсы на складах:\n", | |
" [176. 467. 722.]\n", | |
"Отправлено со складов:\n", | |
" [176. 467. 522.]\n", | |
"Остаток на складах:\n", | |
" [ 0. -0. 200.]\n" | |
] | |
} | |
], | |
"source": [ | |
"print(\"Потребности производства в ресурсах:\\n\",S)\n", | |
"print(\"Доставлено ресурсов на производства:\\n\", dot(x.value.T, ones(n)))\n", | |
"print()\n", | |
"print(\"Начальные ресурсы на складах:\\n\", R)\n", | |
"print(\"Отправлено со складов:\\n\", around(dot(x.value, ones(m))))\n", | |
"print(\"Остаток на складах:\\n\", around(R-dot(x.value,ones(m))));" | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.6.6" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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