diff --git a/test/e2e_extra/gap/gap.jl b/test/e2e_extra/gap/gap.jl
new file mode 100644
index 000000000..3205993f0
--- /dev/null
+++ b/test/e2e_extra/gap/gap.jl
@@ -0,0 +1,309 @@
+function gap_small_instance()
+    data = ClD.GeneralizedAssignment.data("smallgap3.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm()),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    model, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+    BD.objectiveprimalbound!(model, 500.0)
+    BD.objectivedualbound!(model, 0.0)
+
+    JuMP.optimize!(model)
+    @test JuMP.objective_value(model) ≈ 438.0
+    @test JuMP.termination_status(model) == MOI.OPTIMAL
+    @test ClD.GeneralizedAssignment.print_and_check_sol(data, model, x)
+end
+register!(e2e_extra_tests, "gap", gap_small_instance; x = true)
+
+function gap_node_limit()
+    data = ClD.GeneralizedAssignment.data("mediumgapcuts3.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        CL.Optimizer,
+        "params" => CL.Params(
+            solver = ClA.BranchCutAndPriceAlgorithm(
+                maxnumnodes = 5
+            )
+        ),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    model, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+    BD.objectiveprimalbound!(model, 2000.0)
+    BD.objectivedualbound!(model, 0.0)
+
+    JuMP.optimize!(model)
+
+    @test JuMP.objective_bound(model) ≈ 1547.3889
+    @test JuMP.termination_status(model) == MathOptInterface.OTHER_LIMIT
+end
+register!(e2e_extra_tests, "gap", gap_node_limit; x = true)
+
+function gap_colgen_max_nb_iterations()
+    data = ClD.GeneralizedAssignment.data("smallgap3.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        CL.Optimizer,
+        "params" => CL.Params(
+            solver = ClA.TreeSearchAlgorithm(
+                conqueralg = ClA.ColCutGenConquer(
+                    stages = [ClA.ColumnGeneration(max_nb_iterations = 8)],
+                )
+            )
+        ),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+
+    JuMP.optimize!(problem)
+    @test abs(JuMP.objective_value(problem) - 438.0) <= 0.00001
+    @test JuMP.termination_status(problem) == MOI.OPTIMAL # Problem with final dual bound ?
+    @test ClD.GeneralizedAssignment.print_and_check_sol(data, problem, x)
+end
+register!(e2e_extra_tests, "gap", gap_colgen_max_nb_iterations; x = true)
+
+function gap_pure_master_variables()
+    data = ClD.GeneralizedAssignment.data("smallgap3.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm()),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, y, dec = ClD.GeneralizedAssignment.model_with_penalties(data, coluna)
+    JuMP.optimize!(problem)
+    @test JuMP.termination_status(problem) == MOI.OPTIMAL
+    @test abs(JuMP.objective_value(problem) - 416.4) <= 0.00001
+end
+register!(e2e_extra_tests, "gap", gap_pure_master_variables)
+
+function gap_maximisation_objective_function()
+    data = ClD.GeneralizedAssignment.data("smallgap3.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm()),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, dec = ClD.GeneralizedAssignment.model_max(data, coluna)
+    JuMP.optimize!(problem)
+    @test JuMP.termination_status(problem) == MOI.OPTIMAL
+    @test abs(JuMP.objective_value(problem) - 580.0) <= 0.00001
+end
+register!(e2e_extra_tests, "gap", gap_maximisation_objective_function; x = true)
+
+function gap_infeasible_master()
+    data = ClD.GeneralizedAssignment.data("master_infeas.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm()),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+
+    JuMP.optimize!(problem)
+    @test JuMP.termination_status(problem) == MOI.INFEASIBLE
+end
+register!(e2e_extra_tests, "gap", gap_infeasible_master)
+
+function gap_infeasible_master_2()
+    data = ClD.GeneralizedAssignment.data("master_infeas2.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm()),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+
+    JuMP.optimize!(problem)
+    @test JuMP.termination_status(problem) == MOI.INFEASIBLE
+end
+register!(e2e_extra_tests, "gap", gap_infeasible_master_2)
+
+function gap_infeasible_subproblem()
+    data = ClD.GeneralizedAssignment.data("sp_infeas.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm()),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+
+    JuMP.optimize!(problem)
+    @test JuMP.termination_status(problem) == MOI.INFEASIBLE
+end
+register!(e2e_extra_tests, "gap", gap_infeasible_subproblem)
+
+function gap_with_all_phases_in_colgen()
+    data = ClD.GeneralizedAssignment.data("mediumgapcuts1.txt")
+    for m in data.machines
+        data.capacity[m] = floor(Int, data.capacity[m] * 0.5)
+    end
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.TreeSearchAlgorithm(
+            conqueralg = ClA.ColCutGenConquer(
+                stages = [ClA.ColumnGeneration(opt_rtol = 1e-4, smoothing_stabilization = 0.5)]
+            )
+        )),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    problem, x, y, dec = ClD.GeneralizedAssignment.model_with_penalty(data, coluna)
+
+    JuMP.optimize!(problem)
+    @test abs(JuMP.objective_value(problem) - 31895.0) <= 0.00001
+end
+register!(e2e_extra_tests, "gap", gap_with_all_phases_in_colgen; x = true)
+
+function gap_with_max_obj_pure_master_vars_and_stab()
+    data = ClD.GeneralizedAssignment.data("gapC-5-100.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        CL.Optimizer,
+        "params" => CL.Params(
+            solver = ClA.BranchCutAndPriceAlgorithm(
+                colgen_stabilization = 1.0,
+                maxnumnodes = 300
+            )
+        ),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    model, x, y, dec = ClD.GeneralizedAssignment.max_model_with_subcontracts(data, coluna)
+
+    JuMP.optimize!(model)
+
+    @test JuMP.objective_value(model) ≈ 3520.1
+    @test JuMP.termination_status(model) == MOI.OPTIMAL
+end
+register!(e2e_extra_tests, "gap", gap_with_max_obj_pure_master_vars_and_stab; x = true)
+
+function gap_with_no_solver()
+    data = ClD.GeneralizedAssignment.data("play2.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm())
+    )
+
+    problem, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+    try
+        JuMP.optimize!(problem)
+    catch e
+        @test e isa ErrorException
+    end
+end
+register!(e2e_extra_tests, "gap", gap_with_no_solver)
+
+# We solve the GAP but only one set-partionning constraint (for job 1) is
+# put in the formulation before starting optimization.
+# Other set-partionning constraints are added in the essential cut callback.
+function gap_with_lazy_cuts()
+    data = ClD.GeneralizedAssignment.data("play2.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => CL.Params(solver = ClA.BranchCutAndPriceAlgorithm(
+            max_nb_cut_rounds = 1000
+        )),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    model = BlockModel(coluna, direct_model = true)
+    @axis(M, data.machines)
+    @variable(model, x[m in M, j in data.jobs], Bin)
+    @constraint(model, cov, sum(x[m,1] for m in M) == 1)  # add only covering constraint of job 1
+    @constraint(model, knp[m in M],
+        sum(data.weight[j,m]*x[m,j] for j in data.jobs) <= data.capacity[m]
+    )
+    @objective(model, Min,
+        sum(data.cost[j,m]*x[m,j] for m in M, j in data.jobs)
+    )
+    @dantzig_wolfe_decomposition(model, dec, M)
+    subproblems = BlockDecomposition.getsubproblems(dec)
+    specify!.(subproblems, lower_multiplicity = 0)
+
+    cur_j = 1
+    # Lazy cut callback (add covering constraints on jobs on the fly)
+    function my_callback_function(cb_data)
+        for j in 1:cur_j
+            @test sum(callback_value(cb_data, x[m,j]) for m in M) ≈ 1
+        end
+        if cur_j < length(data.jobs)
+            cur_j += 1
+            con = @build_constraint(sum(x[m,cur_j] for m in M) == 1)
+            MOI.submit(model, MOI.LazyConstraint(cb_data), con)
+        end
+    end
+    MOI.set(model, MOI.LazyConstraintCallback(), my_callback_function)
+    optimize!(model)
+    @test JuMP.objective_value(model) ≈ 75.0
+    @test JuMP.termination_status(model) == MOI.OPTIMAL
+end
+register!(e2e_extra_tests, "gap", gap_with_lazy_cuts; x = true)
+
+function gap_with_best_dual_bound()
+    data = ClD.GeneralizedAssignment.data("play2.txt")
+
+    coluna = JuMP.optimizer_with_attributes(
+        CL.Optimizer,
+        "params" => CL.Params(
+            solver = Coluna.Algorithm.TreeSearchAlgorithm(
+                explorestrategy = Coluna.Algorithm.BestDualBoundStrategy()
+            )
+        ),
+        "default_optimizer" => GLPK.Optimizer
+    )
+
+    model, x, dec = ClD.GeneralizedAssignment.model(data, coluna)
+
+    optimize!(model)
+    @test JuMP.objective_value(model) ≈ 75.0
+    @test JuMP.termination_status(model) == MOI.OPTIMAL
+end
+register!(e2e_extra_tests, "gap", gap_with_best_dual_bound; x = true)
+
+function gap_with_obj_const()
+    M = 1:3;
+    J = 1:15;
+    c = [12.7 22.5 8.9 20.8 13.6 12.4 24.8 19.1 11.5 17.4 24.7 6.8 21.7 14.3 10.5; 19.1 24.8 24.4 23.6 16.1 20.6 15.0 9.5 7.9 11.3 22.6 8.0 21.5 14.7 23.2;  18.6 14.1 22.7 9.9 24.2 24.5 20.8 12.9 17.7 11.9 18.7 10.1 9.1 8.9 7.7; 13.1 16.2 16.8 16.7 9.0 16.9 17.9 12.1 17.5 22.0 19.9 14.6 18.2 19.6 24.2];
+    w = [61 70 57 82 51 74 98 64 86 80 69 79 60 76 78; 50 57 61 83 81 79 63 99 82 59 83 91 59 99 91;91 81 66 63 59 81 87 90 65 55 57 68 92 91 86; 62 79 73 60 75 66 68 99 69 60 56 100 67 68 54];
+    Q = [1020 1460 1530];
+
+    coluna = optimizer_with_attributes(
+        Coluna.Optimizer,
+        "params" => Coluna.Params(
+            solver = Coluna.Algorithm.TreeSearchAlgorithm() # default branch-cut-and-price
+        ),
+        "default_optimizer" => GLPK.Optimizer # GLPK for the master & the subproblems
+    );
+
+    model = BlockModel(coluna)
+    @axis(M_axis, M);
+    @variable(model, x[m in M_axis, j in J], Bin);
+    @constraint(model, cov[j in J], sum(x[m, j] for m in M_axis) >= 1);
+    @constraint(model, knp[m in M_axis], sum(w[m, j] * x[m, j] for j in J) <= Q[m]);
+    @objective(model, Min, sum(c[m, j] * x[m, j] for m in M_axis, j in J) + 250);
+    @dantzig_wolfe_decomposition(model, decomposition, M_axis)
+    subproblems = getsubproblems(decomposition)
+    specify!.(subproblems, lower_multiplicity = 0, upper_multiplicity = 1)
+    optimize!(model)
+
+    @test JuMP.objective_value(model) ≈ 250 + 166.5
+    return
+end
+register!(e2e_extra_tests, "gap", gap_with_obj_const)
diff --git a/test/revise.jl b/test/revise.jl
index a2b4dcf8b..18b84c11e 100644
--- a/test/revise.jl
+++ b/test/revise.jl
@@ -17,7 +17,8 @@ typical_test_dirs = [
     joinpath("integration", "custom_data"),
     joinpath("integration", "parser"),
     joinpath("integration", "pricing_callback"),
-    joinpath("e2e_extra", "advanced_colgen")
+    joinpath("e2e_extra", "advanced_colgen"),
+    joinpath("e2e_extra", "gap")
 ]
 tracked_dirs = filter(isdir, typical_test_dirs)