R语言解决最优化运营研究问题-线性优化(LP)问题
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使用R中的线性编程工具来解决优化问题。
优化通常用于运营研究领域，以解决生产计划，运输网络设计，仓库位置分配和调度等问题，我们尝试最大化或最小化具有决策变量和约束数量的线性函数。
在这里，我使用了我的一个咨询项目，帮助我们的投资组合公司选择一个无线供应商，其中包含可以满足所有要求（总线数和汇总数据量）的数据计划组合，同时花费最少的金钱。
这种优化通常可以在Excel求解器中解决。但是，由于我有20个投资组合公司有2个提供商和2个方案进行分析，要在Excel中完成，我将不得不运行80次。使用R会容易得多。
加载包
<span style="color:#333333"><code><span style="color:#990000"><strong>library</strong></span><span style="color:#687687">(</span><span style="color:#000000">lpSolve</span><span style="color:#687687">)</span></code></span>
加载数据
<span style="color:#333333"><code><span style="color:#000000">usage</span> <span style="color:#687687"><-</span> <span style="color:#000000">read.csv</span><span style="color:#687687">(</span><span style="color:#dd1144">"usage.csv"</span><span style="color:#687687">)</span>
<span style="color:#000000">plan</span> <span style="color:#687687"><-</span> <span style="color:#000000">read.csv</span><span style="color:#687687">(</span><span style="color:#dd1144">"wireless_data_plan.csv"</span><span style="color:#687687">)</span></code></span>使用数据
<span style="color:#333333"><code><span style="color:#000000">head</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">)</span></code></span>## Company Num_Lines Data_Usage
## 1 A 134 397.5
## 2 B 350 1037.5
## 3 C 1510 3462.5
## 4 D 2260 4437.5
## 5 E 750 2875.0
## 6 F 410 612.5<span style="color:#333333"><code><span style="color:#000000">str</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">)</span></code></span>## ‘data.frame‘: 20 obs. of 3 variables:
## $ Company : Factor w/ 20 levels "A","B","C","D",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ Num_Lines : int 134 350 1510 2260 750 410 2930 1091 3350 7760 ...
## $ Data_Usage: num 398 1038 3462 4438 2875 ...我们可以看到，我们在数据集中共有20家公司，平均线数和过去3个月的月度数据使用量。
现在，我查看摘要统计信息和公司数据的直方图。
- 行数：我们可以看到平均行数约为1800，但大多数公司的行数少于2000行。只有一家公司有超过7000条线路的异常值。
- 数据使用情况：每行的平均使用量约为2.5GB，范围从1GB到4GB。
<span style="color:#333333"><code><span style="color:#000000">summary</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Num_Lines</span><span style="color:#687687">)</span></code></span>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 134.0 779.2 1083.0 1774.0 1909.0 7760.0<span style="color:#333333"><code><span style="color:#000000">summary</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Data_Usage</span><span style="color:#687687">/</span><span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Num_Lines</span><span style="color:#687687">)</span></code></span>## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.004 1.674 2.527 2.547 3.075 4.475<span style="color:#333333"><code><span style="color:#000000">par</span><span style="color:#687687">(</span><span style="color:#000000">mfrow</span> <span style="color:#687687">=</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#009999">1</span>,<span style="color:#009999">2</span><span style="color:#687687">)</span><span style="color:#687687">)</span>
<span style="color:#000000">hist</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Num_Lines</span>, <span style="color:#000000">main</span> <span style="color:#687687">=</span> <span style="color:#dd1144">"Number of Lines"</span>, <span style="color:#000000">xlab</span> <span style="color:#687687">=</span> <span style="color:#dd1144">"Number of Lines"</span><span style="color:#687687">)</span>
<span style="color:#000000">hist</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Data_Usage</span><span style="color:#687687">/</span><span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Num_Lines</span>, <span style="color:#000000">main</span> <span style="color:#687687">=</span> <span style="color:#dd1144">"Data Usage"</span>, <span style="color:#000000">xlab</span> <span style="color:#687687">=</span> <span style="color:#dd1144">"Data Usage - GB"</span><span style="color:#687687">)</span></code></span>
? 计划数据
<span style="color:#333333"><code><span style="color:#000000">head</span><span style="color:#687687">(</span><span style="color:#000000">plan</span><span style="color:#687687">)</span></code></span>## Wireless_Carrier Data_GB Plan_Rate
## 1 ATT 3 60
## 2 ATT 4 75
## 3 ATT 5 85
## 4 ATT 6 100
## 5 VZW 1 56
## 6 VZW 2 60<span style="color:#333333"><code><span style="color:#000000">str</span><span style="color:#687687">(</span><span style="color:#000000">plan</span><span style="color:#687687">)</span></code></span>## ‘data.frame‘: 10 obs. of 3 variables:
## $ Wireless_Carrier: Factor w/ 2 levels "ATT","VZW": 1 1 1 1 2 2 2 2 2 2
## $ Data_GB : int 3 4 5 6 1 2 4 6 8 10
## $ Plan_Rate : int 60 75 85 100 56 60 70 80 90 100我们还可以看到我们有来自AT＆T和Verizon Wireless的不同级别的数据计划供我们选择。此分析的目标是选择具有最低总成本的不同数据计划组合的运营商，同时满足线路数量和总数据要求
创建目标函数，约束和约束方向对象
<span style="color:#333333"><code><span style="color:#000000">obj.fun.att</span> <span style="color:#687687"><-</span> <span style="color:#000000">plan</span><span style="color:#687687">[</span><span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">4</span>, <span style="color:#009999">3</span><span style="color:#687687">]</span>
<span style="color:#000000">obj.fun.vzw</span> <span style="color:#687687"><-</span> <span style="color:#000000">plan</span><span style="color:#687687">[</span><span style="color:#009999">5</span><span style="color:#687687">:</span><span style="color:#009999">10</span>, <span style="color:#009999">3</span><span style="color:#687687">]</span>
<span style="color:#000000">constr.att</span> <span style="color:#687687"><-</span> <span style="color:#000000">matrix</span><span style="color:#687687">(</span><span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#000000">as.vector</span><span style="color:#687687">(</span><span style="color:#000000">plan</span><span style="color:#687687">[</span><span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">4</span>, <span style="color:#009999">2</span><span style="color:#687687">]</span><span style="color:#687687">)</span><span style="color:#687687">)</span>, <span style="color:#000000">ncol</span> <span style="color:#687687">=</span> <span style="color:#009999">4</span>, <span style="color:#000000">byrow</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span><span style="color:#687687">)</span>
<span style="color:#000000">constr.vzw</span> <span style="color:#687687"><-</span> <span style="color:#000000">matrix</span><span style="color:#687687">(</span><span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#009999">1</span>, <span style="color:#000000">as.vector</span><span style="color:#687687">(</span><span style="color:#000000">plan</span><span style="color:#687687">[</span><span style="color:#009999">5</span><span style="color:#687687">:</span><span style="color:#009999">10</span>, <span style="color:#009999">2</span><span style="color:#687687">]</span><span style="color:#687687">)</span><span style="color:#687687">)</span>, <span style="color:#000000">ncol</span> <span style="color:#687687">=</span> <span style="color:#009999">6</span>, <span style="color:#000000">byrow</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span><span style="color:#687687">)</span>
<span style="color:#000000">constr.dir</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#dd1144">"="</span>, <span style="color:#dd1144">">="</span><span style="color:#687687">)</span></code></span>我们有两个目标函数，因为我们希望找到AT＆T和Verizon成本最低的计划组合。并且有两个限制因素。一个是总行数和总（合并）数据量。对于总行数，我希望数据计划具有完全相同的数量，因此我使用“=”。但是对于总的数据量，只要有比所消耗的数据更多的数据，就可以接受。所以我用“> =”表示数据量约束。
创建空矩阵以存储结果
<span style="color:#333333"><code><span style="color:#000000">result.att</span> <span style="color:#687687"><-</span> <span style="color:#000000">matrix</span><span style="color:#687687">(</span><span style="color:#009999">0</span>, <span style="color:#000000">nr</span> <span style="color:#687687">=</span> <span style="color:#009999">20</span>, <span style="color:#000000">nc</span> <span style="color:#687687">=</span> <span style="color:#009999">5</span><span style="color:#687687">)</span>
<span style="color:#000000">row.names</span><span style="color:#687687">(</span><span style="color:#000000">result.att</span><span style="color:#687687">)</span> <span style="color:#687687"><-</span> <span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Company</span>
<span style="color:#000000">colnames</span><span style="color:#687687">(</span><span style="color:#000000">result.att</span><span style="color:#687687">)</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#dd1144">"3GB"</span>, <span style="color:#dd1144">"4GB"</span>, <span style="color:#dd1144">"5GB"</span>, <span style="color:#dd1144">"6GB"</span>, <span style="color:#dd1144">"Cost"</span><span style="color:#687687">)</span>
<span style="color:#000000">result.vzw</span> <span style="color:#687687"><-</span> <span style="color:#000000">matrix</span><span style="color:#687687">(</span><span style="color:#009999">0</span>, <span style="color:#000000">nr</span> <span style="color:#687687">=</span> <span style="color:#009999">20</span>, <span style="color:#000000">nc</span> <span style="color:#687687">=</span> <span style="color:#009999">7</span><span style="color:#687687">)</span>
<span style="color:#000000">row.names</span><span style="color:#687687">(</span><span style="color:#000000">result.vzw</span><span style="color:#687687">)</span> <span style="color:#687687"><-</span> <span style="color:#000000">usage</span><span style="color:#687687">$</span><span style="color:#000000">Company</span>
<span style="color:#000000">colnames</span><span style="color:#687687">(</span><span style="color:#000000">result.vzw</span><span style="color:#687687">)</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#dd1144">"1GB"</span>, <span style="color:#dd1144">"2GB"</span>, <span style="color:#dd1144">"4GB"</span>, <span style="color:#dd1144">"6GB"</span>, <span style="color:#dd1144">"8GB"</span>, <span style="color:#dd1144">"10GB"</span>, <span style="color:#dd1144">"Cost"</span><span style="color:#687687">)</span></code></span>创建循环以针对每个提供商为每个投资组合公司运行解算器
<span style="color:#333333"><code><span style="color:#990000"><strong>for</strong></span> <span style="color:#687687">(</span><span style="color:#000000">i</span> <span style="color:#990000"><strong>in</strong></span> <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">20</span><span style="color:#687687">)</span> <span style="color:#687687">{</span>
<span style="color:#000000">rhs</span> <span style="color:#687687"><-</span> <span style="color:#000000">usage</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">2</span><span style="color:#687687">:</span><span style="color:#009999">3</span><span style="color:#687687">]</span>
<span style="color:#000000">prod.sol</span> <span style="color:#687687"><-</span> <span style="color:#000000">lp</span><span style="color:#687687">(</span><span style="color:#dd1144">"min"</span>, <span style="color:#000000">obj.fun.att</span>, <span style="color:#000000">constr.att</span>, <span style="color:#000000">constr.dir</span>, <span style="color:#000000">rhs</span>, <span style="color:#000000">compute.sens</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span>, <span style="color:#000000">all.int</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span><span style="color:#687687">)</span>
<span style="color:#000000">result.att</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">5</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">objval</span>
<span style="color:#000000">result.att</span><span style="color:#687687">[</span><span style="color:#000000">i</span>, <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">4</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">solution</span>
<span style="color:#687687">}</span>
<span style="color:#990000"><strong>for</strong></span> <span style="color:#687687">(</span><span style="color:#000000">i</span> <span style="color:#990000"><strong>in</strong></span> <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">20</span><span style="color:#687687">)</span> <span style="color:#687687">{</span>
<span style="color:#000000">rhs</span> <span style="color:#687687"><-</span> <span style="color:#000000">usage</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">2</span><span style="color:#687687">:</span><span style="color:#009999">3</span><span style="color:#687687">]</span>
<span style="color:#000000">prod.sol</span> <span style="color:#687687"><-</span> <span style="color:#000000">lp</span><span style="color:#687687">(</span><span style="color:#dd1144">"min"</span>, <span style="color:#000000">obj.fun.vzw</span>, <span style="color:#000000">constr.vzw</span>, <span style="color:#000000">constr.dir</span>, <span style="color:#000000">rhs</span>, <span style="color:#000000">compute.sens</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span>, <span style="color:#000000">all.int</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span><span style="color:#687687">)</span>
<span style="color:#000000">result.vzw</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">7</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">objval</span>
<span style="color:#000000">result.vzw</span><span style="color:#687687">[</span><span style="color:#000000">i</span>, <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">6</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">solution</span>
<span style="color:#687687">}</span></code></span>AT＆T优化结果
<span style="color:#333333"><code><span style="color:#000000">result.att</span></code></span>## 3GB 4GB 5GB 6GB Cost
## A 134 0 0 0 8040
## B 350 0 0 0 21000
## C 1510 0 0 0 90600
## D 2260 0 0 0 135600
## E 438 0 311 1 52815
## F 410 0 0 0 24600
## G 2930 0 0 0 175800
## H 286 0 805 0 85585
## I 3350 0 0 0 201000
## J 7760 0 0 0 465600
## K 4920 0 0 0 295200
## L 594 0 335 1 64215
## M 960 0 0 0 57600
## N 1792 0 0 0 107520
## O 1730 0 0 0 103800
## P 1406 0 247 1 105455
## Q 316 0 472 1 59180
## R 297 0 0 0 17820
## S 1075 0 0 0 64500
## T 796 0 0 0 47760正如我们在这里看到的，大多数分配是3GB计划，这是有道理的，因为大多数公司使用的不到3GB。但是，如果公司使用超过3GB，由于每GB成本较低，似乎更好地使用更高的数据计划。
Verizon优化结果
<span style="color:#333333"><code><span style="color:#000000">result.vzw</span></code></span>## 1GB 2GB 4GB 6GB 8GB 10GB Cost
## A 0 69 65 0 0 0 8690
## B 0 258 66 0 1 25 22690
## C 1 1405 64 1 0 39 92816
## D 82 2178 0 0 0 0 135272
## E 1 528 65 0 1 155 51876
## F 207 203 0 0 0 0 23772
## G 785 2145 0 0 0 0 172660
## H 1 704 64 0 1 321 78966
## I 3337 13 0 0 0 0 187652
## J 1 7174 64 0 1 520 487066
## K 4215 705 0 0 0 0 278340
## L 1 680 64 1 0 184 63816
## M 645 315 0 0 0 0 55020
## N 0 1573 1 0 0 218 116250
## O 1 1571 66 0 1 91 108126
## P 1 1336 64 0 0 253 109996
## Q 0 523 65 0 1 200 56020
## R 148 149 0 0 0 0 17228
## S 1 890 66 0 0 118 69876
## T 0 796 0 0 0 0 47760至于Verizon，我们可以看到大多数公司都有2GB和10GB的混合计划，以利用2GB计划中更便宜的总速率，但从10GB计划中降低每GB速率。
比较AT＆T和Verizon Wireless的总体成本
<span style="color:#333333"><code><span style="color:#000000">comp</span> <span style="color:#687687"><-</span> <span style="color:#000000">as.data.frame</span><span style="color:#687687">(</span><span style="color:#000000">cbind</span><span style="color:#687687">(</span><span style="color:#000000">result.att</span><span style="color:#687687">[</span>,<span style="color:#009999">5</span><span style="color:#687687">]</span>, <span style="color:#000000">result.vzw</span><span style="color:#687687">[</span>,<span style="color:#009999">7</span><span style="color:#687687">]</span><span style="color:#687687">)</span><span style="color:#687687">)</span>
<span style="color:#000000">comp</span><span style="color:#687687">$</span><span style="color:#000000">lowest</span> <span style="color:#687687"><-</span> <span style="color:#000000">ifelse</span><span style="color:#687687">(</span><span style="color:#000000">comp</span><span style="color:#687687">[</span>,<span style="color:#009999">1</span><span style="color:#687687">]</span> <span style="color:#687687">></span> <span style="color:#000000">comp</span><span style="color:#687687">[</span>,<span style="color:#009999">2</span><span style="color:#687687">]</span>, <span style="color:#dd1144">"vzw"</span>, <span style="color:#dd1144">"att"</span><span style="color:#687687">)</span>
<span style="color:#000000">colnames</span><span style="color:#687687">(</span><span style="color:#000000">comp</span><span style="color:#687687">)</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#dd1144">"ATT"</span>, <span style="color:#dd1144">"VZW"</span>, <span style="color:#dd1144">"Lowest"</span><span style="color:#687687">)</span>
<span style="color:#000000">comp</span></code></span>## ATT VZW Lowest
## A 8040 8690 att
## B 21000 22690 att
## C 90600 92816 att
## D 135600 135272 vzw
## E 52815 51876 vzw
## F 24600 23772 vzw
## G 175800 172660 vzw
## H 85585 78966 vzw
## I 201000 187652 vzw
## J 465600 487066 att
## K 295200 278340 vzw
## L 64215 63816 vzw
## M 57600 55020 vzw
## N 107520 116250 att
## O 103800 108126 att
## P 105455 109996 att
## Q 59180 56020 vzw
## R 17820 17228 vzw
## S 64500 69876 att
## T 47760 47760 att第二种情景
现在我们知道根据我们当前的行数和用途选择什么提供商和计划。然而，公司可能希望购买的数据超过他们现在消费的数据，因为数据的使用一直在增长，并且预计会继续这样做，其次，他们希望避免潜在的超额费用。
所以现在，我将建立一个新变量，作为公司过去使用的数据的百分比。
<span style="color:#333333"><code><span style="color:#000000">buffer</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#009999">1.2</span><span style="color:#687687">)</span>
<span style="color:#990000"><strong>for</strong></span> <span style="color:#687687">(</span><span style="color:#000000">i</span> <span style="color:#990000"><strong>in</strong></span> <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">20</span><span style="color:#687687">)</span> <span style="color:#687687">{</span>
<span style="color:#000000">rhs</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">2</span><span style="color:#687687">]</span>,<span style="color:#000000">usage</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">3</span><span style="color:#687687">]</span> <span style="color:#687687">*</span> <span style="color:#000000">buffer</span><span style="color:#687687">)</span>
<span style="color:#000000">prod.sol</span> <span style="color:#687687"><-</span> <span style="color:#000000">lp</span><span style="color:#687687">(</span><span style="color:#dd1144">"min"</span>, <span style="color:#000000">obj.fun.att</span>, <span style="color:#000000">constr.att</span>, <span style="color:#000000">constr.dir</span>, <span style="color:#000000">rhs</span>, <span style="color:#000000">compute.sens</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span>, <span style="color:#000000">all.int</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span><span style="color:#687687">)</span>
<span style="color:#000000">result.att</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">5</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">objval</span>
<span style="color:#000000">result.att</span><span style="color:#687687">[</span><span style="color:#000000">i</span>, <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">4</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">solution</span>
<span style="color:#687687">}</span>
<span style="color:#990000"><strong>for</strong></span> <span style="color:#687687">(</span><span style="color:#000000">i</span> <span style="color:#990000"><strong>in</strong></span> <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">20</span><span style="color:#687687">)</span> <span style="color:#687687">{</span>
<span style="color:#000000">rhs</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#000000">usage</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">2</span><span style="color:#687687">]</span>,<span style="color:#000000">usage</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">3</span><span style="color:#687687">]</span> <span style="color:#687687">*</span> <span style="color:#000000">buffer</span><span style="color:#687687">)</span>
<span style="color:#000000">prod.sol</span> <span style="color:#687687"><-</span> <span style="color:#000000">lp</span><span style="color:#687687">(</span><span style="color:#dd1144">"min"</span>, <span style="color:#000000">obj.fun.vzw</span>, <span style="color:#000000">constr.vzw</span>, <span style="color:#000000">constr.dir</span>, <span style="color:#000000">rhs</span>, <span style="color:#000000">compute.sens</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span>, <span style="color:#000000">all.int</span> <span style="color:#687687">=</span> <span style="color:#990073">TRUE</span><span style="color:#687687">)</span>
<span style="color:#000000">result.vzw</span><span style="color:#687687">[</span><span style="color:#000000">i</span>,<span style="color:#009999">7</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">objval</span>
<span style="color:#000000">result.vzw</span><span style="color:#687687">[</span><span style="color:#000000">i</span>, <span style="color:#009999">1</span><span style="color:#687687">:</span><span style="color:#009999">6</span><span style="color:#687687">]</span> <span style="color:#687687"><-</span> <span style="color:#000000">prod.sol</span><span style="color:#687687">$</span><span style="color:#000000">solution</span>
<span style="color:#687687">}</span></code></span><span style="color:#333333"><code><span style="color:#000000">result.att</span></code></span>## 3GB 4GB 5GB 6GB Cost
## A 97 0 36 1 8980
## B 253 0 96 1 23440
## C 1510 0 0 0 90600
## D 2260 0 0 0 135600
## E 150 0 600 0 60000
## F 410 0 0 0 24600
## G 2930 0 0 0 175800
## H 0 0 687 404 98795
## I 3350 0 0 0 201000
## J 7513 0 246 1 471790
## K 4920 0 0 0 295200
## L 248 0 681 1 72865
## M 960 0 0 0 57600
## N 1282 0 510 0 120270
## O 1730 0 0 0 103800
## P 860 0 794 0 119090
## Q 0 0 757 32 67545
## R 297 0 0 0 17820
## S 753 0 321 1 72565
## T 796 0 0 0 47760<span style="color:#333333"><code><span style="color:#000000">result.vzw</span></code></span>## 1GB 2GB 4GB 6GB 8GB 10GB Cost
## A 1 57 66 0 1 9 9086
## B 1 231 66 0 1 51 23726
## C 1 1318 65 0 1 125 96276
## D 1 2109 65 1 0 84 139626
## E 0 504 3 0 0 243 54750
## F 85 325 0 0 0 0 24260
## G 0 2899 3 0 0 28 176950
## H 1 581 65 1 0 443 83846
## I 2665 685 0 0 0 0 190340
## J 1 6678 65 0 1 1015 506876
## K 3090 1830 0 0 0 0 282840
## L 1 593 65 0 1 270 67276
## M 390 570 0 0 0 0 56040
## N 0 1439 2 0 0 351 121580
## O 0 1513 1 0 0 216 112450
## P 0 1199 66 0 1 388 115450
## Q 1 440 64 0 0 284 59336
## R 59 238 0 0 0 0 17584
## S 0 860 0 0 0 215 73100
## T 1 707 64 0 0 24 49356<span style="color:#333333"><code><span style="color:#000000">comp</span> <span style="color:#687687"><-</span> <span style="color:#000000">as.data.frame</span><span style="color:#687687">(</span><span style="color:#000000">cbind</span><span style="color:#687687">(</span><span style="color:#000000">result.att</span><span style="color:#687687">[</span>,<span style="color:#009999">5</span><span style="color:#687687">]</span>, <span style="color:#000000">result.vzw</span><span style="color:#687687">[</span>,<span style="color:#009999">7</span><span style="color:#687687">]</span><span style="color:#687687">)</span><span style="color:#687687">)</span>
<span style="color:#000000">comp</span><span style="color:#687687">$</span><span style="color:#000000">lowest</span> <span style="color:#687687"><-</span> <span style="color:#000000">ifelse</span><span style="color:#687687">(</span><span style="color:#000000">comp</span><span style="color:#687687">[</span>,<span style="color:#009999">1</span><span style="color:#687687">]</span> <span style="color:#687687">></span> <span style="color:#000000">comp</span><span style="color:#687687">[</span>,<span style="color:#009999">2</span><span style="color:#687687">]</span>, <span style="color:#dd1144">"vzw"</span>, <span style="color:#dd1144">"att"</span><span style="color:#687687">)</span>
<span style="color:#000000">colnames</span><span style="color:#687687">(</span><span style="color:#000000">comp</span><span style="color:#687687">)</span> <span style="color:#687687"><-</span> <span style="color:#000000">c</span><span style="color:#687687">(</span><span style="color:#dd1144">"ATT"</span>, <span style="color:#dd1144">"VZW"</span>, <span style="color:#dd1144">"Lowest"</span><span style="color:#687687">)</span>
<span style="color:#000000">comp</span></code></span>## ATT VZW Lowest
## A 8980 9086 att
## B 23440 23726 att
## C 90600 96276 att
## D 135600 139626 att
## E 60000 54750 vzw
## F 24600 24260 vzw
## G 175800 176950 att
## H 98795 83846 vzw
## I 201000 190340 vzw
## J 471790 506876 att
## K 295200 282840 vzw
## L 72865 67276 vzw
## M 57600 56040 vzw
## N 120270 121580 att
## O 103800 112450 att
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