diff --git a/ILP/caffeinesynthesis.py b/ILP/caffeinesynthesis.py
index c54eeea..87bfad5 100644
--- a/ILP/caffeinesynthesis.py
+++ b/ILP/caffeinesynthesis.py
@@ -1,3 +1,101 @@
 import gurobipy as gp
-from gurobipy import GRB
+from gurobipy import GRB, Model, quicksum
 
+HYPEREDGES = {
+    1: ([], ["Xanthine"])
+    2: (["Xanthine"], ["p_{0,0}"])
+    3: (["Xanthine"], ["p_{0,1}"])
+    4: (["Xanthine"], ["p_{0,2}"])
+    5: (["p_{0,0}"], ["p_{0,3}"])
+    6: (["p_{0,0}"], ["p_{0,4}"])
+    7: (["p_{0,1}"], ["p_{0,3}"])
+    8: (["p_{0,1}"], ["p_{0,5}"])
+    9: (["p_{0,2}"], ["p_{0,4}"])
+    10: (["p_{0,2}"], ["p_{0,5}"])
+    11: (["p_{0,3}"], ["Caffeine"])
+    12: (["p_{0,4}"], ["Caffeine"])
+    13: (["p_{0,5}"], ["Caffeine"])
+    14: (["Caffeine"], [])
+}
+#Similyrity of Nodes NMR to Measured NMR
+VERTICES = {
+    1: ([0, 0], ["Xanthine"])
+    2: ([0, 0], ["p_{0,0}"])
+    3: ([0, 0], ["p_{0,1}"])
+    4: ([1, 0], ["p_{0,2}"])
+    5: ([0, 0], ["p_{0,3}"])
+    6: ([0, 0], ["p_{0,4}"])
+    7: ([0, 1], ["p_{0,5}"])
+    8: ([0, 0], ["Caffeine"])
+}
+FIXED_FLOWS = {
+    1: 1,
+    14: 1,
+}
+
+def build_model(name, hyperedges, vertices,  excluded_support=None):
+    model = Model(name)
+
+    x = {e_id: model.addVar(vtype=GRB.INTEGER, lb=0, name=f"x_{e_id}") for e_id in hyperedges}
+    b = {e_id: model.addVar(vtype=GRB.BINARY, name=f"b_{e_id}") for e_id in hyperedges}
+
+    vertices = set(v for tails, heads in hyperedges.values() for v in tails + heads)
+
+    for v in vertices:
+        inflow = quicksum(x[e_id] for e_id, (_, heads) in hyperedges.items() if v in heads)
+        outflow = quicksum(x[e_id] for e_id, (tails, _) in hyperedges.items() if v in tails)
+        model.addConstr(inflow == outflow, name=f"flow_conservation_{v}")
+
+    for e_id, value in FIXED_FLOWS.items():
+        model.addConstr(x[e_id] == value, name=f"fixed_flow_{e_id}")
+
+    for e_id in hyperedges:
+
+    model.addGenConstrIndicator(b[e_id], 0, x[e_id] == 0, name=f"unused_implies_zero_{e_id}")
+    model.addConstr(x[e_id] >= b[e_id], name=f"used_implies_positive_flow_{e_id}")
+
+    if excluded_support:
+        model.addConstr(quicksum(b[e_id] for e_id in excluded_support) <= len(excluded_support) - 1, name="different_hyperedges",)
+
+    model.setObjective(quicksum(quicksum(x[v_id]) for v_id in vertices), GRB.MAXIMIZE) #Maximize Similarity of Nodes
+    return model, x, b
+
+def positive_entries(variable_dict, threshold=0.5):
+    return {e_id: var.X for e_id, var in variable_dict.items() if var.X > threshold}
+
+def print_solution(title, flow_solution, binary_solution, hyperedges):
+    print(f"\n{title}:")
+    for e_id in sorted(flow_solution):
+        flow = flow_solution[e_id]
+        tails, heads = hyperedges[e_id]
+        print(f"Hyperedge {e_id}: Flow = {flow}, Tails = {tails}, Heads = {heads}")
+    print("\nBinary Variables:")
+    for e_id in sorted(binary_solution):
+        print(f"Binary Variable b_{e_id} = {binary_solution[e_id]}")
+
+    print(f"\nTotal flow: {sum(flow_solution.values())}")
+    print(f"Number of used hyperedges: {len(binary_solution)}")
+
+def main():
+    model, x, b = build_model("HypergraphFlow", HYPEREDGES, NODES)
+    model.optimize()
+    if model.status != GRB.Status.OPTIMAL:
+        print("No optimal solution found for the first model.")
+        return
+    optimal_solution = positive_entries(x)
+    optimal_binary_solution = positive_entries(b)
+    print_solution("Optimal Solution", optimal_solution, optimal_binary_solution, HYPEREDGES)
+
+    excluded_support = list(optimal_binary_solution.keys())
+    second_model, x2, b2 = build_model("SecondBestHypergraphFlow", HYPEREDGES, excluded_support=excluded_support,)
+
+    second_model.optimize()
+    if second_model.status == GRB.Status.OPTIMAL:
+        second_solution = positive_entries(x2)
+        second_binary_solution = positive_entries(b2)
+        print_solution("Second Best Solution", second_solution, second_binary_solution, HYPEREDGES, VERTICES)
+    else:
+        print("No optimal solution found for the second best model.")
+
+if __name__ == "__main__":
+    main()
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