Dear all,
I am trying to find the solution for the optimization problem focused on
the finding minimum cost.
I used the solution proposed by excel solver, but there is a restriction
in the number of variables.
My data consists of 300 rows represent cities and 6 columns represent the
centres. It constitutes a cost matrix, where the cost are distances between
each city and each of six centres.
..+ 1 column contains variables, represents number of firms.
I want to calculate the minimum cost between cities and centres. Each city
can belong only to one of the centres.
(1) The solution you say the Excel Solver returns does not appear to be
correct: The column sum in columns 3 to 5 is not (greater or) equal
to 1 as you request.
(2) lpSolve does not return an error, but says "no feasible solution found",
which seems to be correct: The equality constraints are too strict.
(3) If you relieve these constraints to inequalities, lpSolves does find
a solution:
costs <- matrix(c(
30, 20, 60, 40, 66, 90,
20, 30, 60, 40, 66, 90,
25, 31, 60, 40, 66, 90,
27, 26, 60, 40, 66, 90), 4, 6, byrow = TRUE)
firms <- c(15, 10, 5, 30)
row.signs <- rep (">=", 4)
row.rhs <- firms
col.signs <- rep (">=", 6)
col.rhs <- c(1,1,1,1,1,1)
require("lpSolve")
T <- lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve = 0, compute.sens = 0)
T$solution
sum(T$solution * costs) # 1557
Of course, I don't know which constraints you really want to impose.
Hans Werner
A model example:
costs: distance between municipalities and centres + plus number of firms
in each municipality
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5"
"Centre6"
"Firms"
"Muni1" 30 20 60 40 66 90 15
"Muni2" 20 30 60 40 66 90 10
"Muni3" 25 31 60 40 66 90 5
"Muni4" 27 26 60 40 66 90 30
The outcome of excel functon Solver is:
cost assigned
"Municipality" "Centre1" "Centre2" "Centre3" "Centre4" "Centre5" "Centre6"
"Solution"
"Muni1" 0 20 0 0 0 0 300
"Muni2" 20 0 0 0 0 0 200
"Muni3" 25 0 0 0 0 0 125
"Muni4" 0 26 0 0 0 0 780
objective : 1405
I used package "lpSolve" but there is a problem with variables "firms":
s <- as.matrix(read.table("C:/R/OPTIMALIZATION/DATA.TXT", dec = ",",
sep=";",header=TRUE))
[2] [3] [4] [5] [6]
[1] 30 20 60 40 66 90
[2] 20 30 60 40 66 90
[3] 25 31 60 40 66 90
[4] 27 26 60 40 66 90
row.signs <- rep ("=", 4)
row.rhs <- c(15,10,5,30)
col.signs <- rep ("=", 6)
col.rhs <- c(1,1,1,1,1,1)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)
lp.transport (costs, "min", row.signs, row.rhs, col.signs, col.rhs,
presolve=0, compute.sens=0)$solution
Outcome:
Error in lp.transport(costs, ...):
Error: We have 6 signs, but 7 columns
Does anyone know where could the problem ?
Does there exist any other possibility how to perform that analysis in R ?
I am bit confused here about how can I treat with the variables "firms".
Thanks
Pavel