11.3 Balanced vs. Unbalanced Transportation Models
A transportation model is classified as balanced when the total supply across all sources equals the total demand across all destinations:
∑ Supply = ∑ Demand
In such cases, the model can be solved directly using standard transportation algorithms. For example, if both the total supply and total demand equal 180 units, the model is considered balanced.
However, when this equality does not hold, the model is termed unbalanced. There are two primary types of unbalanced models:
- Supply exceeds demand:
∑ Supply > ∑ Demand
This indicates surplus capacity at one or more supply points. - Demand exceeds supply:
∑ Supply < ∑ Demand
This reflects a shortfall in available supply relative to market needs.
For instance, if the total supply is 180 units and the total demand is only 170 units, the model is unbalanced due to excess supply.
| M1 | M2 | M3 | Supply | |
| DC1 | 2 | 4 | 3 | 50 |
| DC2 | 3 | 1 | 5 | 70 |
| DC3 | 4 | 2 | 6 | 60 |
| Demand | 60 | 80 | 30 |
Converting Unbalanced Models to Balanced Form
To facilitate the use of standard solution methods, unbalanced models are typically converted into balanced models by introducing dummy supply or demand nodes:
- If supply exceeds demand, a dummy demand point is added with a demand equal to the surplus. The transportation cost to this dummy point is usually set to zero.
- If demand exceeds supply, a dummy supply point is introduced with a supply equal to the shortfall, again with zero transportation cost.
These adjustments ensure that the model becomes mathematically balanced, allowing for the application of classical transportation algorithms.
In the sections that follow, we will first explore the solution of balanced transportation models, followed by techniques for handling and converting unbalanced models.
