Linear Programming with R

文章信息
作者： kaiwu
点击数：828

 

 

1.参考资料

1.1 Modern optimization with R

Cortez, P. (2021). Modern optimization with R.Springer.

springer link

amazon link

library genesis

cover_modern_optimization_with_R.jpg

1.3 Linear Programming with R: Exploring the “lpSolve” R package

Roberto Salazar,Nov 17, 2019

Linear Programming with R: Exploring the “lpSolve” R package

1.4 lpSolveAPI Package Users Guide by Kjell Konis

lpSolveAPI Package Users Guide

2. prepraration

2.1 import libraries

# Import lpSolve package
library(lpSolve)
library(XLConnect)

2.2 the problem: 班次安排问题

imagename ## 2.3 连接Excel文件

mybook<-loadWorkbook("D:/kedu/teaching_datasets/Excel_model/sm_solver.xls")
rsheets<-getSheets(mybook)
rsheets
[1] "table-chair" "beef"        "transport"   "staff"

3. linear programming

3.1 Set coefficients of the objective function

设定目标函数，因为是求和，所以矩阵是1，1，1，1，1，1 matrix在这里非常重要 研究一下如何生成重复的相同元素

#f.obj <- c(4, 2)
f.obj <-as.matrix(rep(1,each=7))

3.2 Set matrix corresponding to coefficients of constraints by rows

Do not consider the non-negative constraint; it is automatically assumed

就是员工工作的可用矩阵 注意：这里面通常包含标题，默认header=TRUE，那么startRow=7

#f.con <- matrix(c(5, 15,20, 5), nrow = 2, byrow = TRUE)

f.con <-as.matrix(readWorksheet(mybook, sheet = "staff", startRow = 8, endRow = 14,
startCol = 17, endCol = 23,header=FALSE))

3.3 Set unequality signs

设置不等式符号 可以每行设置不同的符号

f.dir <- as.matrix(rep(">=",each=7))

3.4 Set right hand side coefficients

约束条件的范围

#f.rhs <- c(50,40)
f.rhs <-as.matrix(readWorksheet(mybook, sheet = "staff", startRow = 8, endRow =14,
startCol = 27, endCol = 27,header=FALSE))

3.5 设定变量取整数 f.intvec，例如f.intvec <- c(1,2)表示x1，x2取整数

如果自变量全都是整数，那么 all.int = TRUE就可以了

#f.intvec <- c(1,2)

3.6 Final value (z)

计算结果

#report_lp<-lp("min", f.obj, f.con, f.dir, f.rhs,int.vec = f.intvec)
# 部分变量取整数：int.vec = f.intvec

report_lp<-lp("min", f.obj, f.con, f.dir, f.rhs, all.int = TRUE)
report_lp
Success: the objective function is 9 
report_lp$objval
[1] 9
# output the final value
writeWorksheet(mybook,report_lp$objval,sheet = "staff", startRow =16,startCol = 25,header = FALSE)
saveWorkbook(mybook)

3.7 Variables final values

report_solution<-report_lp$solution
report_solution
[1] 0 1 0 0 1 3 4
## 保存变量取值
## 结果是一个矩阵（1列），所以为了在excel变为1行，需要转置，t()
writeWorksheet(mybook,t(report_solution),sheet = "staff", startRow =16,startCol = 17,header = FALSE)
saveWorkbook(mybook)

3.8 Sensitivities

敏感度分析

report_lp<-lp("min", f.obj, f.con, f.dir, f.rhs, all.int = TRUE,compute.sens=TRUE)
report_lp$sens.coef.from
[1]  1e+00 -1e+30  0e+00  0e+00  0e+00  0e+00  0e+00
report_lp$sens.coef.to
[1] 1.000000e+30 1.000000e+30 1.333333e+00 1.000000e+00 1.333333e+00
[6] 1.333333e+00 1.333333e+00

3.9 Dual Values (first dual of the constraints and then dual of the variables)

Duals of the constraints and variables are mixed

report_lp$duals
 [1] 0 1 0 0 0 0 0 0 1 0 0 0 0 0

3.10 Duals lower and upper limits

report_lp$duals.from
 [1] -1e+30 -1e+30  7e+00  6e+00  6e+00  5e+00  4e+00 -1e+30 -1e+30 -1e+30
[11] -1e+30 -1e+30 -1e+30 -1e+30
report_lp$duals.to
 [1] 1.000000e+30 1.000000e+30 8.333333e+00 8.666667e+00 8.666667e+00
 [6] 9.000000e+00 9.333333e+00 1.250000e+00 2.500000e-01 1.000000e+30
[11] 1.000000e+30 1.000000e+30 1.000000e+30 1.000000e+30
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