SP_Simplex_method _for_linear_optimization_problems

SP_Simplex_for_4_or_More_than_4_Variable_LPP.py

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+import numpy as np
+from fractions import Fraction
+
+def simplex_algorithm():
+    print("\n**** Simplex Algorithm ****\n\n")
+
+    # User inputs
+    num_constraints = int(input("Enter the number of constraints: "))
+    num_variables = int(input("Enter the number of variables: "))
+
+    A = []
+    print("Enter the coefficients of the constraints (row-wise):")
+    for i in range(num_constraints):
+        row = list(map(float, input(f"Constraint {i + 1}: ").split()))
+        A.append(row)
+
+    A = np.array(A)
+
+    b = []
+    print("Enter the amount of resources for each constraint:")
+    for i in range(num_constraints):
+        resource = float(input(f"Resource for constraint {i + 1}: "))
+        b.append(resource)
+
+    b = np.array(b)
+
+    c = list(map(float, input("Enter the coefficients of the objective function: ").split()))
+
+    B = np.array([[num_variables + i] for i in range(1, num_constraints + 1)])
+    cb = np.array([0 for i in range(num_constraints)])
+    xb = np.transpose([b])
+
+    table = np.hstack((B, np.transpose([cb])))
+    table = np.hstack((table, xb))
+    table = np.hstack((table, A))
+    table = np.array(table, dtype='float')
+
+    MIN = 0
+    print("Table at itr = 0")
+    print("B \tCB \tXB \t" + "\t".join([f"y{i+1}" for i in range(num_variables + num_constraints)]))
+    for row in table:
+        for el in row:
+            print(Fraction(str(el)).limit_denominator(100), end='\t')
+        print()
+
+    print("Simplex Working....")
+
+    reached = 0
+    itr = 1
+    unbounded = 0
+    alternate = 0
+
+    while reached == 0:
+        print("Iteration: ", end=' ')
+        print(itr)
+        print("B \tCB \tXB \t" + "\t".join([f"y{i+1}" for i in range(num_variables + num_constraints)]))
+        for row in table:
+            for el in row:
+                print(Fraction(str(el)).limit_denominator(100), end='\t')
+            print()
+
+        rel_prof = []
+        for i in range(len(A[0])):
+            rel_prof.append(c[i] - np.sum(table[:, 1] * table[:, 3 + i]))
+
+        print("rel profit: ", end=" ")
+        for profit in rel_prof:
+            print(Fraction(str(profit)).limit_denominator(100), end=", ")
+        print()
+
+        b_var = table[:, 0]
+
+        for i in range(len(A[0])):
+            present = False
+            for j in range(len(b_var)):
+                if int(b_var[j]) == i:
+                    present = True
+                    break
+            if not present and rel_prof[i] == 0:
+                alternate = 1
+                print("Case of Alternate found")
+
+        if all(profit <= 0 for profit in rel_prof):
+            print("All profits are <= 0, optimality reached")
+            reached = 1
+            break
+
+        k = rel_prof.index(max(rel_prof))
+        min_ratio = 99999
+        r = -1
+
+        for i in range(len(table)):
+            if table[:, 2][i] > 0 and table[:, 3 + k][i] > 0:
+                val = table[:, 2][i] / table[:, 3 + k][i]
+                if val < min_ratio:
+                    min_ratio = val
+                    r = i
+
+        if r == -1:
+            unbounded = 1
+            print("Case of Unbounded")
+            break
+
+        print("pivot element index:", end=' ')
+        print(np.array([r, 3 + k]))
+        pivot = table[r][3 + k]
+        print("pivot element: ", end=" ")
+        print(Fraction(pivot).limit_denominator(100))
+
+        table[r, 2:] = table[r, 2:] / pivot
+
+        for i in range(len(table)):
+            if i != r:
+                table[i, 2:] = table[i, 2:] - table[i][3 + k] * table[r, 2:]
+
+        table[r][0] = k
+        table[r][1] = c[k]
+
+        print()
+        itr += 1
+        print()
+        print("*")
+
+    if unbounded == 1:
+        print("UNBOUNDED LPP")
+        return
+
+    if alternate == 1:
+        print("ALTERNATE Solution")
+
+    print("Optimal table:")
+    print("B \tCB \tXB \t" + "\t".join([f"y{i+1}" for i in range(num_variables + num_constraints)]))
+    for row in table:
+        for el in row:
+            print(Fraction(str(el)).limit_denominator(100), end='\t')
+        print()
+
+    print()
+    print("Value of Z at optimality: ", end=" ")
+    sum = 0
+    for i in range(len(table)):
+        sum += table[i][1] * table[i][2]
+    if MIN == 1:
+        print(-Fraction(str(sum)).limit_denominator(100))
+    else:
+        print(Fraction(str(sum)).limit_denominator(100))
+
+    basis = []
+    for i in range(len(table)):
+        temp = "x" + str(int(table[i][0]) + 1)
+        basis.append(temp)
+
+    print("Final Basis: ", end=" ")
+    print(basis)
+    print("Simplex Finished...")
+
+# To run the function
+simplex_algorithm()