[R] Optimization in R similar to MS Excel Solver

[Pavel_K]

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.

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, "min", row.signs, row.rhs, col.signs, col.rhs, 
: 
  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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