ILP Mevo

ILP MEVo v.2

This is an ILP model version 2.

printSolution <- function(solx){
  if (sum(solx$value) == 0){
    cat("No solution found.\n")
    return
  }
  cat("Zone | alpha |   h   |  m  | Stations \n")
  for (i in c(1:NZones)){
    cat(" ",i," |  ", alpha[i], " | ", h[i], " | ", m[i], " | ")
    for (j in c(1:NLocations))
      if (N[j,i] && solx$value[j])
        cat(j, "  ")
    cat("\n")
  }
  
  cat("\nZone |sum(x_j * c_j)| alpha * h \n")
  objective = 0
  for (i in c(1:NZones)){
    objective <- objective + (solx$value * N[ , i]) %*% C
    cat(" ",i," |     ", (solx$value * N[ , i]) %*% C , "     | ", alpha[i] * h[i], "\n")
  }
  
  cat("\nTotal sum(x_j * c_j): ", objective)
  cat("\nTotal number of stations: ", sum(solx$value))
  
}

library("igraph")

## 
## Dołączanie pakietu: 'igraph'

## Następujące obiekty zostały zakryte z 'package:stats':
## 
##     decompose, spectrum

## Następujący obiekt został zakryty z 'package:base':
## 
##     union

library(ROI)

## ROI: R Optimization Infrastructure

## Registered solver plugins: nlminb, glpk.

## Default solver: auto.

library(Rglpk)

## Ładowanie wymaganego pakietu: slam

## Using the GLPK callable library version 5.0

library(ompr)
library(ompr.roi)
library(ROI.plugin.glpk)

NZones = 5
NLocations = 25

# N_i - The set of candidate parking locations that are in zone i
N1 <- c(rep(1, 5), rep(0, 20))
N2 <- c(rep(0, 5), rep(1, 5), rep(0, 15))
N3 <- c(rep(0, 10), rep(1, 5), rep(0, 10))
N4 <- c(rep(0, 15), rep(1, 5), rep(0, 5))
N5 <- c(rep(0, 20), rep(1, 5))

N <- array(c(N1, N2, N3, N4, N5), dim=c(NLocations, NZones))

# cj = Capacity of candidate bicycle parking location j
C <- c(rep(25, NLocations))

#hi = Demand (number of bicycle users) in zone i
h <- round(runif(n=NZones, min=20, max=100))

# alphai : The minimum percentage of demand that needs to be satisfied for zone i
#alpha <- round(runif(n=NZones, min=1, max=100))
alpha <- c(rep(0.7,NZones))

# mi: Minimum number of covering stations required for zone i (redundancy)
m <- round(runif(n=NZones, min=1, max=5))

# B = Maximum number of bicycle parking stations that can be built (due to budget constraints)
B <- sum(m)


model <- MIPModel() %>%
  add_variable(x[j], j = 1:NLocations, type = "integer", lb = 0, ub = 1) %>%
  set_objective(sum_expr(x[j] * C[j], j = 1:NLocations), "max") %>%
  add_constraint(sum_expr(x[j] * C[j] * N[j ,i] , j = 1:NLocations) >= alpha[i] * h[i], i = 1:NZones) %>%
  add_constraint(sum_expr(x[j] * N[j ,i], j = 1:NLocations) >= m[i], i = 1:NZones) %>%
  add_constraint(sum_expr(x[j], j = 1:NLocations) <= B) 
  
result <- solve_model(model, with_ROI(solver = "glpk", verbose = TRUE))

## <SOLVER MSG>  ----
## GLPK Simplex Optimizer 5.0
## 11 rows, 25 columns, 75 non-zeros
##       0: obj =  -0.000000000e+00 inf =   2.132e+02 (10)
##      21: obj =   3.250000000e+02 inf =   1.520e+00 (1)
## LP HAS NO PRIMAL FEASIBLE SOLUTION
## GLPK Integer Optimizer 5.0
## 11 rows, 25 columns, 75 non-zeros
## 25 integer variables, all of which are binary
## glp_intopt: optimal basis to initial LP relaxation not provided
## <!SOLVER MSG> ----

solx <- get_solution(result, x[j])
#sol <- list("x" = solx)
printSolution(solx)

## No solution found.
## Zone | alpha |   h   |  m  | Stations 
##   1  |   0.7  |  60  |  2  | 
##   2  |   0.7  |  39  |  5  | 
##   3  |   0.7  |  90  |  1  | 
##   4  |   0.7  |  54  |  2  | 
##   5  |   0.7  |  43  |  3  | 
## 
## Zone |sum(x_j * c_j)| alpha * h 
##   1  |      0      |  42 
##   2  |      0      |  27.3 
##   3  |      0      |  63 
##   4  |      0      |  37.8 
##   5  |      0      |  30.1 
## 
## Total sum(x_j * c_j):  0
## Total number of stations:  0