Question

The starting solution using the intuitive lowest-cost method is: (Note: You must enter a shipment in every cell, even if the shipment is 0.) To From C Dummy Supply A $10 $19 $12 X 100 50 5 20 25 $13 $9 $1 Y 50 50 0 0 0 $14 $20 $18 0 Z 75 0 75 0 50 80 Demand 70 b) The total cost of the initial solution developed using the intuitive lowest-cost method $2635 c) The total cost of the optimal solution $

Answer 1

Use the following method to conduct the transportation simplex algorithm:

• Assign u_i for each i-th row and vj for each j-th column.
• Start with u₁=0 and compute the values of other u_i's and v_j's using the formula u_i + v_j = c_ij for the basic cells only. c_ij be the cost figures.
• Compute w_ij = u_i + v_j - c_ij for the non-basic cells.
• Perform loop pivoting for w_ij having the highest positive value.
• If all w_ij's are less than or equal to zero, then the solution is an optimal solution.

V4 V4 V1 V2 V3 V1 V2 V3 10 19 12 0 10 16 12 0 $0 $10 $19 $12 $0 $10 $19 $12 i0 50 5 25 50 25 25 W12= -3 $0 $17 $13 $9 $0 $17 $13 $9 U2-3 U2-3 = 3 50 5 45 W21= -10W2= W21= -10 W24 -3 W24= -3 $14 $20 $18 $14 $0 $20 $18 $0 -1 U3 2 U3 75 - 3 -1 W31 -8 75 W33 C 2 W33 W34 W34 W31 -11 Second iteration First iteration O 20 OC

V2 V3 V4 V1 -2 10 16 12 $10 $19 $12 $0 50 W12= -3 50 W14 2 $17 $13 $9 $0 U2 -3 W21 -1030 20 W24= -5 $20 $18 $14 $0 u3 2 50 W330 25 W31 8 Third iteration

Note that at the end of the third iteration all the w_ij's are less than or equal to zero. So, we have reached an optimal solution which can be stated as follows:

To Dummy $12 From B C Supply $10 $19 0 100 0 0 $9 $17 $13 0 50 Y 0 0 30 20 $20 $18 $14 0 75 50 0 0 70 Demand 50 80 25 50 50

Total cost of the optimal solution = 50*10 + 50*12 + 30*13 + 20*9 + 50*18 + 25*0 = $2,570