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LEAST COST METHOD

In this method, we allocate as much as possible in the lowest cost cell or cells and then move to the next lowest cost cell/cells and so on. Let us solve the above problem using the least cost method.

Distribution centers

A

X

Y

Supply

Rs.2000 Rs.=5380

1000

Plants

B

X11-1000

X12-0

1500

Rs.2500

Rs.2700

C

X21-1300

X22=200

1200

Rs.2550

Rs.1700

X21=0

X32=1200

Demand

2300

1400

Here the lowest cost cell is CY (Rs. 1700) and maximum possible allocation, meting supply and demand requirement is made here i.e., 1200. This meets the supply position of row 3 and hence it is crossed out.

The next least cost cell is AX (2000). Maximum possible allocation of 1000 is made here and row one is crossed out. Next lowest cost cell is BX (2500) and maximum possible allocation of 1300 is made here as the total demand in column X is 2300 and we have already allocated 1O00 in cell AX. Next lowest cost cell is CX (2550) only 0 can be allocated here to meet the demand (2300) and supply (1200) position. Next cell with lowest cost is BY (2700). Here allocation of 200 is possible. The next lowest cost cell is A Y where only 0 allocation is possible.

Hence

Z = Rs. (2000 × 1000 + 2500 × 1300 + 2700 × 200 + 1700 × 1200)

= Rs. 78,30,000.