Question

The cost of transportation from 3 sources to four destinations are given in the follow¬ing table. Obtain an initial basic feasible solution using 

(i) North West Corner Rule (NWC) 

(ii) Least Cost Method (LCM) and 

(iii) Vogel’s Approximation Method (VAM)

Answer 1

(i) North West Corner Rule 

We start by allotting the units to the North -West Comer cell. We show all the allocations in a single table.

Total transportation cost is (200 × 4) + (50 × 2) + (350 × 7) + (100 × 5) + (200 × 3) + (1 × 300) 

= 800 + 100 + 2450 + 500 + 600 + 300 

= Rs. 4750

(ii) Least cost method (LCM)

Transportation cost is = (250 × 2) + (200 × 3) + (150 × 7) + (100 × 5) + (200 × 3) + (300 × 1) 

= 500 + 600+ 1050 + 500 + 600 + 300 

= Rs. 3550

(iii) Vogel Approximation Method (VAM)

There are five penalties which have the maximum value 2. The cell with the least cost is row 3 and hence select cell (3, D) for allocation.

There are four penalties which have maximum value 2. Select cell (1, B) which has the least cost for allocation.

The largest penalty is 6. Allot units to cell (2, A)

The largest penalty is 3. Allot units to cell (3, B)

We first allot 50 units to cell (3, C) which has less cost. Then the balance units we allot to cell (2, C). We get the final allocation table as follows.

Transportation cost is = (250 × 2) + (200 × 3) + (250 × 5) + (150 × 4) + (50 × 3) + (300 × 1) 

= 500 + 600 + 1250 + 600 + 150 + 300 

= Rs. 3400