Question

Solve by least cost method and apply UV method to optimize the solution.
19 30 50 13 Supply
70 30 40 60 7
40 10 60 20 10
Demand 5 8 7 15 18

Answer 1

Answer to Question #72475, Math / Discrete Mathematics

Solve by least cost method and apply UV method to optimize the solution.

Solution.

$$Total Cost = 7 \cdot 13 + 3 \cdot 70 + 7 \cdot 40 + 2 \cdot 40 + 8 \cdot 10 + 8 \cdot 20 = 901$$

UV method:

$$c_{ij} = u_i + v_j \text{ for occupied cells}$$

The reduced costs for unoccupied cells:

$$reduced cost = c_{ij} - u_i - v_j$$ $$c_{11} = 19 - 1 = 18; \quad c_{12} = 30 - 7 = 23; \quad c_{13} = 50 - 5 = 45$$ $$c_{22} = 30 - 2 - 7 = 21; \quad c_{24} = 60 - 2 - 7 = 51; \quad c_{33} = 60 - 1 - 5 = 54$$

Since all the current reduced costs are non-negative, this is the optimal solution.

$$The minimum cost = Total Cost = 901$$

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