UGC NET CSE | Junet 2015 | Part 3 | Question: 68

Question

Consider the following transportation problem:

The initial basic feasible solution of the above transportation problem using Vogel's Approximation method (VAM) is given below:

The solution of the above problem:

• A. is degenerate solution
• B. is optimum solution
• C. needs to improve
• D. is infeasible solution

Answer 1

answer is B

Answer 2

Since number of allocation =5 which is m+n-1 (3+3-1)  m, n are no of rows and column it can not be Degenerate soln

Also Total supply=Total demand=450 so soln is not infeasible  , hence choice A, D are out

for optimality we will check whether each (Cij)'  for non allocated cell is non negative

for this first we look for allocated cells

select the row and column with max allocation here we can take first row and assign U1=0

then V1=16  as C11=U1+V1  simialrly  U2=-2 as  C21=U2+V1 simlarly U3=-4  and V2=10, V3=20

now compute (Cij)' for uncoccupied cell with (Cij)'=Cij-(Ui+Vj)

For C12=20-(0+10) =10  C23=18-(-2+20)=0  C31=26-(-4+16)=14  C32=24-(-4+10)=18  which all are +ve and so soln s optimal and hence needs no improvement

Hence Ans is B

Comments

How to determine u1 v1 value as well as u2 v2 u3 v3

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assume one of them as 0 ( preferably asscociated with the row or column that have max allocations)

Answer 3

B . The optimum solution