Answer to Question #243629 in Operations Research for mafi

Question

Consider the following transportation problem:

To/From Store 1 Store 2 Store 3 Store 4 Supply_

Plant 1 19 30 50 10 7

Plant 2 70 30 40 60 9

Plant 3 40 8 70 20 18

Demand 5 8 7 14 34

Required:

i. Set Up The Transportation Tableau For This Problem And Determine

The InitialSolution

Using The Minimum Cell Cost Method.

ii. Solve Using MODI

iii. Formulate This Problem As A Linear Programming Model

Answer 1

(i)

TOTAL number of supply constraints : 3

TOTAL number of demand constraints: 4

Problem Table is:

The smallest transportation cost is 8 in cell $S_3D_2$

The allocation to this cell is min(18,8) = 8.

This satisfies the entire demand of $D_2$  and leaves 18 - 8=10 units with $S_3$ .

Initial feasible solution is:

The minimum total transportation cost:$=10×7+70×2+40×7+40×3+8×8+20×7=814$

Here, the number of allocated cells = 6 is equal to m + n - 1 = 3 + 4 - 1 = 6

∴ This solution is non-degenerate.

(ii)

TOTAL number of supply constraints : 3

TOTAL number of demand constraints: 4

Problem Table is:

The smallest transportation cost is 8 in cell $S_3D_2$

The allocation to this cell is min(18,8) = 8.

This satisfies the entire demand of $D_2$  and leaves 18 - 8=10 units with $S_3$ .

Optimality test using modi method...

Allocation Table is:

 Final optimal solution:

The minimum total transportation cost =19×5+10×2+30×2+40×7+8×6+20×12=743

(iii) LPP model solved by Least Cost method (optimal solution using stepping stone method)

TOTAL number of supply constraints : 3

TOTAL number of demand constraints: 4

Problem Table is:

Initial feasible solution is:

The minimum total transportation cost =10×7+70×2+40×7+40×3+8×8+20×7=814

Here, the number of allocated cells = 6 is equal to m + n - 1 = 3 + 4 - 1 = 6

∴ This solution is non-degenerate.

Optimality test using stepping stone method...

Allocation Table is:

Final optimal solution is:

The minimum total transportation cost =19×5+10×2+30×2+40×7+8×6+20×12=743