diff --git a/src/pmedian.jl b/src/pmedian.jl
index e280be6..8e60bbe 100644
--- a/src/pmedian.jl
+++ b/src/pmedian.jl
@@ -117,6 +117,8 @@ function pmedian_with_distances(distancematrix::Matrix, ncenters::Int)::PMedianR
 
     distances = distancematrix
 
+    M = 100000.0 * n
+
 
     model = Model(HiGHS.Optimizer)
     MOI.set(model, MOI.Silent(), true)
@@ -127,9 +129,7 @@ function pmedian_with_distances(distancematrix::Matrix, ncenters::Int)::PMedianR
     @constraint(model, sum(y) == ncenters)
 
     for i = 1:n
-        for j = 1:n
-            @constraint(model, z[i, j] .<= y[j])
-        end
+        @constraint(model, sum(z[:, i]) <= M * y[i])
     end
 
     for i = 1:n
diff --git a/test/testpmedian.jl b/test/testpmedian.jl
index ae737b0..d22a32c 100644
--- a/test/testpmedian.jl
+++ b/test/testpmedian.jl
@@ -73,7 +73,8 @@
         result2 = pmedian_with_distances(distance_matrix, 3)
         result3 = pmedian_with_distances(distance_matrix, 4)
 
-        @test sort(result1.centers) == [3, 4]
+
+        @test (sort(result1.centers) == [3, 4]) || (sort(result1.centers) == [1, 2])
         @test result1.objective == 22.0
 
         @test sort(result2.centers) == [3, 4, 5]