Given the following information set up the problem in a transportation table and
ID: 452026 • Letter: G
Question
Given the following information set up the problem in a transportation table and solve for the minimum-cost plan:
PERIOD
Suppose that an increase in warehousing costs and other costs brings inventory carrying costs to $2 per unit per month. All other costs and quantities remain the same. Determine a revised solution to this transportation problem. (Omit the "$" sign in your response.)
Given the following information set up the problem in a transportation table and solve for the minimum-cost plan:
Explanation / Answer
Find Solution of Transportation Problem Using Least Cost Method
TOTAL no. of supply constraints : 3
TOTAL no. of demand constraints : 3
Problem Table is
Here Demand And Supply are not equals. So Add supply or demand constraint.
Now, TOTAL no. of supply constraints : 4
Now, TOTAL no. of demand constraints : 3
Now, Problem Table is
The smallest transportation cost is 0 in cell (S4, D1)
The maximum which can be allocated to this cell 550.
This satisfies the entire demand of D1 and leaves 1330 - 550 = 780 units with S4
Table-1
The smallest transportation cost is 0 in cell (S4, D2)
The maximum which can be allocated to this cell 700.
This satisfies the entire demand of D2 and leaves 780 - 700 = 80 units with S4
Table-2
The smallest transportation cost is 0 in cell (S4, D3)
The maximum which can be allocated to this cell 80.
This exhausts the capacity of S4 and leaves 750 - 80 = 670 units with D3
Table-3
The smallest transportation cost is 62 in cell (S1, D3)
The maximum which can be allocated to this cell 500.
This exhausts the capacity of S1 and leaves 670 - 500 = 170 units with D3
Table-4
The smallest transportation cost is 82 in cell (S2, D3)
The maximum which can be allocated to this cell 50.
This exhausts the capacity of S2 and leaves 170 - 50 = 120 units with D3
Table-5
The smallest transportation cost is 92 in cell (S3, D3)
The maximum which can be allocated to this cell 120.
Table-6
Final Allocation Table is
Here, the number of allocation is equal to m + n - 1 = 4 + 3 - 1 = 6
The solution is feasible.
Total Transportation cost = 62 × 500 + 82 × 50 + 92 × 120 + 0 × 550 + 0 × 700 + 0 × 80 = 46140
The minimized total transportation cost = 46140
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