up

Author: TahaHammadia

.ipynb_checkpoints/INF421 P 2021 _ Matching under constraints-checkpoint.ipynb

@@ -475,6 +475,26 @@
    "source": [
     "## Test Instance 3:"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Task 11:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Here we use an Integer Linear Programing algorithm. Since no algorithm has been proposed in the course and the implementation of the usual algorithms is complicated, we have chosen to use the library ```pulp``` of Python that implements the ILP.\n",
+    "\n",
+    "The problem corresponds to the following model :\n",
+    "\n",
+    "\\begin{center}\n",
+    "Maximize c^{T} x\n",
+    "\\end{center}"
+   ]
   }
  ],
  "metadata": {

INF421 P 2021 _ Matching under constraints.ipynb

@@ -489,7 +489,11 @@
    "source": [
     "Here we use an Integer Linear Programing algorithm. Since no algorithm has been proposed in the course and the implementation of the usual algorithms is complicated, we have chosen to use the library ```pulp``` of Python that implements the ILP.\n",
     "\n",
-    "The problem correspond"
+    "The problem corresponds to the following model :\n",
+    "\n",
+    "\\begin{center}\n",
+    "Maximize $c^{T} x$\n",
+    "\\end{center}"
    ]
   }
  ],

Task11.py

@@ -1,25 +1,31 @@
 import numpy as np
 from pulp import LpMaximize, LpProblem, LpStatus, lpSum, LpVariable
 
-def optimize(w, p, Ws):
+def optimize(w, n, Ws):
     """
     w is the list of costs of the different groups.
-    p is the list of the proportions of different groups.
+    n is the number of candidate students from each group.
     Ws is the budget of the school.
     """
-    G = len(p)
+    G = len(n)
+    N = sum(n) # total number of all students
+    p = np.array([n[i] / N for i in range(G)])
     model = LpProblem(name="Task_5.1", sense=LpMaximize)
     groups = np.array([[LpVariable(name="x" + str(i), lowBound=0, cat="Integer")] for i in range(G)]) # variables
     model += lpSum(groups) # objective function
-    print(lpSum(groups))
 
-    # Constraints
+    # #Constraints
+    # Cost constraint
     cost = []
     for i in range(G):
         cost.append(w[i,0] * groups[i, 0])
     model += lpSum(cost) <= Ws
-    print(lpSum(cost) <= Ws)
 
+    # Number constraint
+    for i in range(G):
+        model += 1 * groups[i,0] <= n[i,0]
+
+    #4/5- rule
     A1 = np.array([[6 / 5 * p[i, 0]] * G for i in range(G)])
     A2 = np.array([[-4 / 5 * p[i, 0]] * G for i in range(G)])
     for i in range(G):
@@ -31,16 +37,15 @@ def optimize(w, p, Ws):
 
     for i in range(G):
         model += set1[i, 0] >= 0
-        print(set1[i, 0] >= 0)
         model += set2[i, 0] >= 0
-        print(set2[i, 0] >= 0)
 
+    # Solution
     status = model.solve()
 
     for var in model.variables():
         print(f"{var.name}: {var.value()}")
 
 w = np.array([[1], [10]])
-p = np.array([[3/4], [1/4]])
-Ws = 11
-optimize(w, p, Ws)
+n = np.array([[3], [1]])
+Ws = 1000
+optimize(w, n, Ws)