Consider the following transportation problem From To Cost S

Consider the following transportation problem: From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150 Demand 110 140 100 Solve it by using the computer.

Solution

sol)

               1              2                     3               supply

A           8                 14                    8               120

B            6                   17                   7                80

C            9                   24                  10               150

Demand   110               140                 100

Here sum of supply= sum of demand .It is balanced transportation problem.

TOTAL no. of supply constraints : 3
TOTAL no. of demand constraints : 3
Problem Table is

Table-1

The maximum penalty, 3, occurs in column D₂.
Allocate At [1][2] = 120
The minimum Cij in this column is C₁₂ = 14.
The maximum allocation in this cell is 120.
It satisfy supply of S₁ and adjust the demand of D₂ from 140 to 20 (140 - 120 = 20).
Table-2

The maximum penalty, 7, occurs in column D₂.
Allocate At [2][2] = 20
The minimum Cij in this column is C₂₂ = 17.
The maximum allocation in this cell is 20.
It satisfy demand of D₂ and adjust the supply of S₂ from 80 to 60 (80 - 20 = 60).
Table-3

The maximum penalty, 3, occurs in column D₁.
Allocate At [2][1] = 60
The minimum Cij in this column is C₂₁ = 6.
The maximum allocation in this cell is 60.
It satisfy supply of S₂ and adjust the demand of D₁ from 110 to 50 (110 - 60 = 50).
Table-4

The maximum penalty, 10, occurs in column D₃.
Allocate At [3][3] = 100
The minimum Cij in this column is C₃₃ = 10.
The maximum allocation in this cell is 100.
It satisfy demand of D₃ and adjust the supply of S₃ from 150 to 50 (150 - 100 = 50).
Table-5

The maximum penalty, 9, occurs in row S₃.
Allocate At [3][1] = 50
The minimum Cij in this row is C₃₁ = 9.
The maximum allocation in this cell is 50.
It satisfy supply of S₃ and adjust the demand of D₁ from 50 to 0 (50 - 50 = 0).
Final Allocation Table is

Here, the number of allocation is equal to m + n - 1 = 3 + 3 - 1 = 5
The solution is feasible.
Total Transportation cost = 14 × 120 + 6 × 60 + 17 × 20 + 9 × 50 + 10 × 100 = 3830

The minimized total transportation cost = 3830