Pavel_K <kuk064 <at> vsb.cz> writes:
>
> 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
>
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