diff --git a/src/algorithms/TambyVanderpooten.jl b/src/algorithms/TambyVanderpooten.jl
index 02f6def..b4b0a96 100644
--- a/src/algorithms/TambyVanderpooten.jl
+++ b/src/algorithms/TambyVanderpooten.jl
@@ -30,19 +30,20 @@ function _update_search_region(
     y::Vector{Float64},
     yN::Vector{Float64},
 )
-    bounds_to_remove = Vector{Float64}[]
     p = length(y)
+    bounds_to_remove = Vector{Float64}[]
+    bounds_to_add = Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}}()
     for u in keys(U_N)
         if all(y .< u)
             push!(bounds_to_remove, u)
             for l in 1:p
                 u_l = _get_child(u, y, l)
                 N = [
-                    k != l ? [yi for yi in U_N[u][k] if yi[l] < y[l]] : [y]
+                    k == l ? [y] : [yi for yi in U_N[u][k] if yi[l] < y[l]]
                     for k in 1:p
                 ]
-                if all(!isempty(N[k]) for k in 1:p if u_l[k] ≠ yN[k])
-                    U_N[u_l] = N
+                if all(!isempty(N[k]) for k in 1:p if k != l && u_l[k] != yN[k])
+                    bounds_to_add[u_l] = N
                 end
             end
         else
@@ -53,27 +54,31 @@ function _update_search_region(
             end
         end
     end
-    for bound_to_remove in bounds_to_remove
-        delete!(U_N, bound_to_remove)
+    for u in bounds_to_remove
+        delete!(U_N, u)
     end
+    merge!(U_N, bounds_to_add)
     return
 end
 
 function _get_child(u::Vector{Float64}, y::Vector{Float64}, k::Int)
     @assert length(u) == length(y)
-    return vcat(u[1:k-1], y[k], u[k+1:length(y)])
+    return vcat(u[1:(k-1)], y[k], u[(k+1):length(y)])
 end
 
 function _select_search_zone(
     U_N::Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}},
     yI::Vector{Float64},
+    yN::Vector{Float64},
 )
-    i, j =
-        argmax([
-            prod(_project(u, k) - _project(yI, k)) for k in 1:length(yI),
-            u in keys(U_N)
-        ]).I
-    return i, collect(keys(U_N))[j]
+    upper_bounds = collect(keys(U_N))
+    p = length(yI)
+    hvs = [
+        u[k] == yN[k] ? 0.0 : prod(_project(u, k) .- _project(yI, k)) for
+        k in 1:p, u in upper_bounds
+    ]
+    k_star, j_star = argmax(hvs).I
+    return k_star, upper_bounds[j_star]
 end
 
 function optimize_multiobjective!(
@@ -100,7 +105,6 @@ function optimize_multiobjective!(
         warm_start_supported = true
     end
     solutions = Dict{Vector{Float64},Dict{MOI.VariableIndex,Float64}}()
-    YN = Vector{Float64}[]
     variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
     n = MOI.output_dimension(model.f)
     yI, yN = zeros(n), zeros(n)
@@ -114,7 +118,7 @@ function optimize_multiobjective!(
             return status, nothing
         end
         _, Y = _compute_point(model, variables, f_i)
-        yI[i] = Y + 1
+        yI[i] = Y
         model.ideal_point[i] = Y
         MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MAX_SENSE)
         MOI.optimize!(model.inner)
@@ -124,7 +128,7 @@ function optimize_multiobjective!(
             return status, nothing
         end
         _, Y = _compute_point(model, variables, f_i)
-        yN[i] = Y
+        yN[i] = Y + 1
     end
     MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     U_N = Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}}()
@@ -136,7 +140,7 @@ function optimize_multiobjective!(
             status = MOI.TIME_LIMIT
             break
         end
-        k, u = _select_search_zone(U_N, yI)
+        k, u = _select_search_zone(U_N, yI, yN)
         MOI.set(
             model.inner,
             MOI.ObjectiveFunction{typeof(scalars[k])}(),
diff --git a/test/algorithms/TambyVanderpooten.jl b/test/algorithms/TambyVanderpooten.jl
index 97d8582..33356ac 100644
--- a/test/algorithms/TambyVanderpooten.jl
+++ b/test/algorithms/TambyVanderpooten.jl
@@ -621,7 +621,44 @@ function test_vector_of_variables_objective()
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     MOI.add_constraint(model, sum(1.0 * xi for xi in x), MOI.GreaterThan(1.0))
     MOI.optimize!(model)
-    MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+    @test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMAL
+    return
+end
+
+function test_issue_105()
+    cost = [100.0, 120.0, 150.0, 110.0, 200.0, 170.0]
+    time = [8.0, 3.0, 4.0, 2.0, 5.0, 4.0]
+    capacity = [10.0, 8.0]
+    demand = [5.0, 8.0, 5.0]
+    m, n = 2, 3
+    model = MOI.instantiate(; with_bridge_type = Float64) do
+        return MOA.Optimizer(HiGHS.Optimizer)
+    end
+    MOI.set(model, MOA.Algorithm(), MOA.TambyVanderpooten())
+    MOI.set(model, MOI.Silent(), true)
+    x = MOI.add_variables(model, m * n)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint.(model, x, MOI.Integer())
+    X = reshape(x, m, n)
+    for i in 1:m
+        f_i = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(1.0, X[i, :]), 0.0)
+        MOI.add_constraint(model, f_i, MOI.LessThan(capacity[i]))
+    end
+    for j in 1:n
+        f_j = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(1.0, X[:, j]), 0.0)
+        MOI.add_constraint(model, f_j, MOI.EqualTo(demand[j]))
+    end
+    f = MOI.Utilities.operate(
+        vcat,
+        Float64,
+        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(cost, x), 0.0),
+        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(time, x), 0.0),
+        MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(1.0, x), 0.0),
+    )
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
+    MOI.optimize!(model)
+    @test MOI.get(model, MOI.ResultCount()) == 6
     return
 end