Least cost method (LCM) Assignment Help

Transportation Problem in Linear Programming - Least cost method (LCM)

Least cost method (LCM)

In this method, allocations are made on the basis of unit transportation costs. The method is explained below.

Step 1: Select the cell with the least unit transportation cost and allocate as many units as possible to that cell.

Step 2: If the minimum cost exists in several cells, select a cell arbitrarily and assign the possible number of goods. Then consider the remaining cells of the same unit transportation cost.

Step 3: Select a cell with the next higher unit transportation cost and continue the process till all requirements are met.

Problem

Distances between factory and its warehouses and demand at each warehouse are given in the table.

Table: Transportation Table

Factory/Warehouse                 

W1

W2

W3

Supply

F1

16

22

14

200

F2

18

14

18

150

F3

8

14

16

100

Demand

175

125

150

 

Solve the problem using least cost method.

Solution

Step 1: First, we consider the cell when the unit cost of transportation is the least; i.e. the cell (F3, W1) with a cost of Rs. 8

Step 2: The possible number of goods that can be assigned to the cell (F3, W1) is 100.

Step 3: Next, we move to that cell where the next higher unit cost of transportation exists and assign the possible number of goods.

Step 4: The process is continued till the entire goods are assigned.

The solution is shown below:

The number of occupied cells is 5, that is equal to the value of (m+n-1), i.e. (3+3-1). So the solution is a feasible solution.

Therefore, the cost associated with the solution is, (50 × 16) + (25 × 18) + (100 × 8) + (125 × 14) + (150 × 14) = Rs. 5900. 

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