diff --git a/Notebook_final.ipynb b/Notebook_final.ipynb
index f0c41aaf61d81179c36d6e6498fb82ea5c8f868b..ce1e64859e8e00486d98874aa632153aaefd12e6 100644
--- a/Notebook_final.ipynb
+++ b/Notebook_final.ipynb
@@ -689,6 +689,30 @@
     "probleme.solve(solver=cp.GLPK_MI, warm_start=True, verbose=False)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4189d852",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Duree = 8\n",
+    "x_i = cp.Variable(n//Duree, boolean=True) #Allumage\n",
+    "\n",
+    "# Formulation et résolution du problème\n",
+    "objectif = cp.Minimize(c.T@(p_n_i+p_r_i))\n",
+    "contraintes = [T_i[0] == T_initial, T_i[n] == T_final, T_min <= T_i, T_i <= T_max, T_i[1:n+1] == T_i[0:n]+deltaT_i, p_n_i>=0, p_r_i>=0, \n",
+    "               deltaT_i == -(1-eta)*(T_i[0:n]-T_ext)+(cp.multiply(p_n_i,COP_normal(T_ext)))*0.25/(V*Cx)-p_r_i*COP_reverse*0.25/(V*Cx)]\n",
+    "\n",
+    "for i in range(n):\n",
+    "    contraintes.append((p_n_i[i]+p_r_i[i])<=p_max*x_i[i//Duree])\n",
+    "    contraintes.append((p_n_i[i]+p_r_i[i])>=0.25*p_max*x_i[i//Duree])\n",
+    "#contraintes.append((p_n_i+p_r_i)<=p_max)\n",
+    "\n",
+    "probleme = cp.Problem(objectif, contraintes)\n",
+    "probleme.solve(solver=cp.GLPK_MI, warm_start=True, verbose=False)"
+   ]
+  },
   {
    "attachments": {},
    "cell_type": "markdown",