Question

Solve by NWCM (north-west corner method) and find optimal solution by UV method
3 1 7 4 Supply
2 6 5 9 250
8 3 3 2 350
Demand 200 300 350 400

Answer 1

Answer to Question #72476, Math / Discrete Mathematics

Solve by NWCM (north-west corner method) and find optimal solution by UV method

Solution.

$$\text{Total Cost} = 150 \cdot 3 + 100 \cdot 1 + 100 \cdot 6 + 250 \cdot 5 + 50 \cdot 3 + 350 \cdot 2 = 3250$$ $$c_{ij} = u_i + v_j \text{ for occupied cells}$$

The reduced costs for unoccupied cells:

$$\text{reduced cost} = c_{ij} - u_i - v_j$$ $$c_{13} = 7; \; c_{14} = 4 + 1 = 5; \; c_{21} = 2 - 5 - 3 = -6$$ $$c_{24} = 9 - 5 + 1 = 5; \; c_{31} = 8 - 3 - 3 = 2; \; c_{32} = 3 - 3 - 1 = -1$$

UV method:

The closed path: cells

$$(2,1), (1,1), (1,2), (1,3), (1,4), (2,4), (3,4), (3,3), (3,2), (2,2), (2,1)$$

The smallest value with a negative position on the closed path is 2.

It indicates the number of units that can be shipped to the entering cell. Now we add this quantity to all the cells on the corner points of the closed path marked with plus signs and subtract it from those cells marked with minus signs.

Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/)

Answer to Question #72476, Math / Discrete Mathematics

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

$$150 \cdot 1 + 100 \cdot 1 + 100 \cdot 4 + 250 \cdot 5 + 50 \cdot 3 = 2050$$

Answer provided by AssignmentExpert.com

Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/)