Unbalanced Problem

Posted in Operations and Supply Chain Terms, Total Reads: 3710
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Definition: Unbalanced Problem

Unbalanced problems are typically encountered in transportation problems in operations research where the total supply does not equal the total demand. The main objective of a transportation problem is to determine the transportation schedule that minimizes the overall transportation cost, while meeting the supply and demand requirements. But in reality, the problems that we encounter involve unbalanced conditions where the supply and demand are not equal.


Let us consider a problem where a company has three warehouses – warehouse 1, warehouse 2, and warehouse 3. The company provides supplies to retailers Retailer A and Retailer B. The supply and demand for the warehouses and retailers is shown below. The table shows the supply from each warehouse, the demand of individual retailer and the distance between the individual warehouses and the retailers. The cost of transportation can be taken proportionate to the distance between the warehouse and retailer.

 

Warehouse 1

Warehouse 2

Warehouse 3

Supply

Retailer A

10

25

10

3000

Retailer B

15

8

6

2500

Demand

2000

2000

1000

 

 

The problem can be simplified by introducing dummy dealers or dummy suppliers, who will either supply or consume the excess. So the above problem boils down to

 

Warehouse 1

Warehouse 2

Warehouse 3

Supply

Retailer A

10

25

10

3000

Retailer B

15

8

6

2500

Dummy Retailer

0

0

0

1500

Demand

2000

3000

2000

7000


The cost of transportation from the individual warehouses to the retailers is taken as zero, because the dummy supplier or dealer does not exist in reality. Now, algorithms or linear programming equations can be used to find out find out a solution.

 

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