MIP (ompr) model taking too much time to solve in R

Question

I am trying to solve a capacitated facility location problem in R. The sample data for that:

n<- 500 #number of customers
m<- 20 #number of facility centers

set.seed(1234)

fixedcost <- round(runif(m, min=5000, max=10000))

warehouse_locations <- data.frame(
  id=c(1:m),
  y=runif(m, 22.4, 22.6),
  x= runif(m, 88.3, 88.48)
)

customer_locations <- data.frame(
  id=c(1:n),
  y=runif(n, 22.27, 22.99),
  x= runif(n, 88.12, 88.95)
)

capacity <- round(runif(m, 1000, 4000))
demand <- round(runif(n, 5, 50))

The model with the cost functions:

library(geosphere)

transportcost <- function(i, j) {
  customer <- customer_locations[i, ]
  warehouse <- warehouse_locations[j, ]
  (distm(c(customer$x, customer$y), c(warehouse$x, warehouse$y), fun = distHaversine)/1000)*20
}


library(ompr)
library(magrittr)
model <- MIPModel() %>%
  # 1 iff i gets assigned to SC j
  add_variable(x[i, j], i = 1:n, j = 1:m, type = "binary") %>%
  
  # 1 if SC j is built
  add_variable(y[j], j = 1:m, type = "binary") %>%
  
  # Objective function
  set_objective(sum_expr(transportcost(i, j) * x[i, j], i = 1:n, j = 1:m) + 
                  sum_expr(fixedcost[j] * y[j], j = 1:m), "min") %>%
  
  #Demand of customers shouldn't exceed total facility capacities
  add_constraint(sum_expr(demand[i] * x[i, j], i = 1:n) <= capacity[j] * y[j], j = 1:m) %>%
  
  # every customer needs to be assigned to a SC
  add_constraint(sum_expr(x[i, j], j = 1:m) == 1, i = 1:n) %>% 
  
  # if a customer is assigned to a SC, then this SC must be built
  add_constraint(x[i,j] <= y[j], i = 1:n, j = 1:m)
model



library(ompr.roi)
library(ROI.plugin.glpk)
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))

At this moment, the computation is being done for the results.

Is there any way I can reduce the computation times? If I understand it correctly then 0.4% is the difference between the current model and the desired outcome. I will be happy even if the difference is far greater than that and I can obtain a suitable model. Is there any way I can set that? Like 5-6% difference will be good enough.

Answer 1

Took the help from @Erwin Kalvelagen's comment. Used the symphony solver and edited one line:

library(ROI.plugin.symphony)
result <- solve_model(model, with_ROI(solver = "symphony",
                                      verbosity=-1, gap_limit=1.5))

Processing time reduced a lot and got the answer!

Answer 2

You can try the below 3 approaches

1. You can test by reformulating the last constraint.

if a customer is assigned to a SC, then this SC must be built

You can use the following instead of the current constraint add_constraint(sum_expr(x[i,j], i = 1:n)<= y[j], j = 1:m)

This should reduce the run time without affecting the output.

2. Apart from that, you can add termination criteria based on minimum optimality gap you want or/and maximum run time you want the model to run.

3. You can also try to use some other solver instead of glpk and see it helps.

Answer 3

R and Python libraries are very slow for MIP try with lp solve open source solver