Optimization/Approximation.py at main · scruffyscarf/Optimization · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
s = list(map(int, input().split()))
c = [list(map(int, input().split())) for i in range(3)]
d = list(map(int, input().split()))


def print_matrix(supply, costs, demand):
    print("       | ", "1  2  3",  " | Supply")
    print("—" * 25)
    for i in range(len(supply)):
        print(i + 1, "     | ", *costs[i], " | ", supply[i])
    print("—" * 25)
    print("Demand | ", *demand,  " | ")


def north_west(supply, costs, demand):

    supply = supply[:]
    demand = demand[:]
    costs = [row[:] for row in costs]
    north_west_allocation_matrix = [[0] * len(demand) for _ in range(len(supply))]
    north_west_total_cost = 0

    i, j = 0, 0

    while i < len(supply) and j < len(demand):
        quantity = min(supply[i], demand[j])
        north_west_allocation_matrix[i][j] = quantity
        north_west_total_cost += costs[i][j] * quantity

        supply[i] -= quantity
        demand[j] -= quantity

        if supply[i] == 0:
            i += 1
        elif demand[j] == 0:
            j += 1

    return north_west_allocation_matrix, north_west_total_cost


def vogel(supply, costs, demand):

    supply = supply[:]
    demand = demand[:]
    costs = [row[:] for row in costs]
    vogel_allocation_matrix = [[0] * len(demand) for i in range(len(supply))]
    vogel_total_cost = 0

    while any(supply) and any(demand):

        minimal_values = []

        for i in range(len(supply)):
            if supply[i] > 0:
                line = costs[i][:]
                first_min = min(line)
                line.remove(first_min)
                second_min = min(line) if line else float('inf')
                minimal_values.append((abs(first_min - second_min), i, 'row'))

        for j in range(len(demand)):
            if demand[j] > 0:
                col = [costs[i][j] for i in range(len(supply))]
                first_min = min(col)
                col.remove(first_min)
                second_min = min(col) if col else float('inf')
                minimal_values.append((abs(first_min - second_min), j, 'col'))

        maximal_value, index, direction = max(minimal_values)

        if direction == 'row':
            row_index = index
            col_index = costs[row_index].index(min(costs[row_index]))
        else:
            col_index = index
            row_index = [costs[i][col_index] for i in range(len(supply))].index(min([costs[i][col_index] for i in range(len(supply))]))

        quantity = min(supply[row_index], demand[col_index])
        vogel_allocation_matrix[row_index][col_index] = quantity
        vogel_total_cost += quantity * costs[row_index][col_index]

        supply[row_index] -= quantity
        demand[col_index] -= quantity

        if supply[row_index] == 0:
            for j in range(len(demand)):
                costs[row_index][j] = float('inf')

        if demand[col_index] == 0:
            for i in range(len(supply)):
                costs[i][col_index] = float('inf')

    return vogel_allocation_matrix, vogel_total_cost


def russell(supply, costs, demand):

    supply = supply[:]
    demand = demand[:]
    costs = [row[:] for row in costs]
    russell_allocation_matrix = [[0] * len(demand) for i in range(len(supply))]
    russell_total_cost = 0

    while sum(supply) > 0 and sum(demand) > 0:
        max_supply = [max(costs[i]) if supply[i] > 0 else float('-inf') for i in range(len(supply))]
        max_demand = [max((costs[j][i] for j in range(len(supply)) if demand[i] > 0), default=float('-inf')) for i in range(len(demand))]

        adjusted_costs = [[costs[i][j] - max_supply[i] - max_demand[j] for j in range(len(demand))] for i in range(len(supply))]

        min_value = float('inf')
        row_index, col_index = -1, -1

        for i in range(len(supply)):
            for j in range(len(demand)):
                if supply[i] > 0 and demand[j] > 0 and adjusted_costs[i][j] < min_value:
                    min_value = adjusted_costs[i][j]
                    row_index, col_index = i, j

        quantity = min(supply[row_index], demand[col_index])
        russell_allocation_matrix[row_index][col_index] = quantity
        russell_total_cost += quantity * costs[row_index][col_index]

        supply[row_index] -= quantity
        demand[col_index] -= quantity

        if supply[row_index] == 0:
            for j in range(len(demand)):
                costs[row_index][j] = float('inf')

        if demand[col_index] == 0:
            for i in range(len(supply)):
                costs[i][col_index] = float('inf')

    return russell_allocation_matrix, russell_total_cost


if sum(s) != sum(d):
    print("The problem is not balanced!")
else:
    north_west_allocation_matrix, north_west_total_cost = north_west(s, c, d)
    vogel_allocation_matrix, vogel_total_cost = vogel(s, c, d)
    russell_allocation_matrix, russell_total_cost = russell(s, c, d)

    print()
    print_matrix(s, c, d)


    print("\nFeasible solutions for North-West method:")
    for row in north_west_allocation_matrix:
        print(row)
    print("Total cost for North-West method:", north_west_total_cost)

    print("\nFeasible solutions for Vogel's approximation:")
    for row in vogel_allocation_matrix:
        print(row)
    print("Total cost for Vogel's approximation:", vogel_total_cost)

    print("\nFeasible solutions for Russell's approximation:")
    for row in russell_allocation_matrix:
        print(row)
    print("Total cost for Russell's approximation:", russell_total_cost)