Question

For the following transportation problem, obtain the Initial basic feasible solution by:-  N.W.C.R and 

Answer 1

1. By N.W.CR:- Start allocating at north corner cell at the cell (1, 1): X₁₁ = Min (a₁ b₁)

= min (5, 7) = 5

Here O₁ is satisfied, next allocate at (2, 1) as: 

X₂₁ = Min (a₂, b₁ – X₁₁) = Min (8, 7-5) 

= Min (8, 2) = 2 

D₁ satisfied and next allocation is made at (2, 2): 

X₂₂ = Min (a₂ – X₂₁, b₂) 

= Min (8-2, 9) 

= Min (6, 9) = 6

O₂ availabilities are allocated, next allocate at (3, 2): X₃₂ 

= Min (a₃, b₃₂ – X₂₂) 

= Min (7, 9 – 6) = Min (7, 3) = 3 

D₂ Satisfied, next allocate at (3, 3) as: 

X₃₃ = Min (a₃ – X₃₂, b₃) 

= Min (7-3, 18) = min (4, 18) = 4 

O₃ Satisfied, Allocate at (4, 3) as: 

X₄₃ = Min (a₄, b₃ – X₃₃) 

= Min (14, 18, -4) = Min (14,14) = 14

The Initial Basic feasible solution (I. B. F.S) is: