# Facility location problem
**URL:** https://discourse.julialang.org/t/facility-location-problem/123068
**Category:** Optimization (Mathematical)
**Tags:** question
**Created:** [November 26, 2024, 1:04am UTC](https://discourse.julialang.org/t/facility-location-problem/123068 "2024-11-26T01:04:09Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@aditya\_lokesh](https://discourse.julialang.org/u/aditya_lokesh)
#### Post date: [November 26, 2024, 1:04am UTC](https://discourse.julialang.org/t/facility-location-problem/123068/1 "2024-11-26T01:04:09Z")
facing a issue with my implementation of the facility location problem.
I tried implementing the problem however the optimization model just does not seem to stop even after 3 hours not sure if I have slow computer.
```julia
n = 5 # <- number of candidate facilities
m = 100 # <- number of customers
# Location of facilities and customers are assumed to be normalized so that they belong to [0,1] × [0,1]
## location of facilities
f_x, f_y = rand(n), rand(n) # x- and y-coordinates
## location of customers
c_x, c_y = rand(m), rand(m) # x- and y-coordinates
# Costs
## installation cost of each facility; it is assumed that all facilities have the same normalized installation cost of 9
b = 20 * ones(n)
## delivery cost from facility i to customer j is computed based on the distance between the facility and the customer
c = zeros(n,m)
for i=1:n, j=1:m
c[i,j] = norm([f_x[i]; f_y[i]] - [c_x[j]; c_y[j]])
end
# Demand and capacity
## demand of each customer
d = 5 * rand(m)
## capacity of each facility
M = 200 * rand(n)
# 'fig' plots the geographic information
fig = scatter(f_x, f_y, label="candidate facilities", xlim=[0,1], ylim=[0,1], aspect_ratio = 1, legend = :outertopright, xticks=:false, yticks=:false)
scatter!(fig, c_x, c_y, label="customers")
display(fig)
```
This is the initialization provided on the Julia programming site
my implementation of the facility location problem model
````model
@variable(model,y[1:n], Bin)
@variable(model,x[1:m,1:n],Bin)
@constraint(model,demand,x'*d .<= m.*y)
@constraint(model,client_service[i in 1:m], sum(x[i,:])== 1)
@objective(model,Min, b'*y+ sum(c* x) )```
The optimize command keeps running it does not end even after hours
The same uncapacited location problem provides a solution of 281
````
uc\_model = Model(GLPK.Optimizer)
@variable(uc\_model,x[i in 1:m,j in 1:n],Bin)
@variable(uc\_model,y[i in 1:n],Bin)
@constraint(uc\_model,uncapacity\_demand[i in 1:m,j in 1:n],x[i,j] \<= y[j])
@constraint(uc\_model,demand[i in 1:m, j in 1:n], sum( x[i,:]) ==1)
@objective(uc\_model, Min, sum(c\* x) + b’\*y)
optimize!(uc\_model)
```julia
the model for the same
Just not able to figure out the issue here.
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [November 26, 2024, 1:39am UTC](https://discourse.julialang.org/t/facility-location-problem/123068/2 "2024-11-26T01:39:28Z")
Hi @aditya_lokesh, welcome to the forum 😄
I’ve moved your question to the “Optimization (Mathematical)” section.
Don’t use GLPK.jl Use a solver like HiGHS.jl instead.
Here’s how I would write your model:
```Julia
julia> using JuMP, HiGHS, LinearAlgebra
julia> begin
n = 5
m = 100
f_x, f_y = rand(n), rand(n) # x- and y-coordinates
c_x, c_y = rand(m), rand(m) # x- and y-coordinates
b = 20 * ones(n)
c = zeros(n,m)
for i in 1:n, j in 1:m
c[i, j] = norm([f_x[i]; f_y[i]] - [c_x[j]; c_y[j]])
end
d = 5 * rand(m)
M = 200 * rand(n)
uc_model = Model(HiGHS.Optimizer)
set_silent(uc_model)
@variable(uc_model, x[1:m, 1:n], Bin)
@variable(uc_model, y[1:n], Bin)
@constraint(uc_model, x' * d .<= M .* y)
@constraint(uc_model, [i in 1:m], sum(x[i, :]) == 1)
@objective(uc_model, Min, sum(c * x) + b' * y)
optimize!(uc_model)
solution_summary(uc_model)
end
* Solver : HiGHS
* Status
Result count : 1
Termination status : OPTIMAL
Message from the solver:
"kHighsModelStatusOptimal"
* Candidate solution (result #1)
Primal status : FEASIBLE_POINT
Dual status : NO_SOLUTION
Objective value : 3.08230e+02
Objective bound : 3.08230e+02
Relative gap : 0.00000e+00
Dual objective value : NaN
* Work counters
Solve time (sec) : 7.46224e-03
Simplex iterations : 181
Barrier iterations : -1
Node count : 1
```