Question

If the total availahility is nqual to the total mquirements, the trensportation problem is called ___ .

Short answer

Balanced.

Step-by-step solution

Understanding the Terminology

In a transportation problem, supply refers to the total availability of resources at the origins, while demand refers to the total requirements at the destinations. These must be compared to determine the type of problem.

Identifying the Type of Problem

A transportation problem is called 'balanced' if the total availability (supply) equals the total requirements (demand). Therefore, when these two quantities are equal, the problem is precisely defined as 'balanced'.

Key concepts

Understanding the Transportation Problem

The transportation problem is a specific type of optimization problem. It deals with finding the most cost-efficient way to distribute a product from a number of suppliers to a number of consumers. Imagine factories producing goods and aiming to deliver them to various stores. This can be quite complex!
The goal is to minimize the shipping cost while satisfying the requirements of the destinations. The problem is usually represented in a matrix with rows representing the suppliers and columns representing the destinations.

• Cost Matrix: Indicates the cost of shipping goods from each supplier to each destination.
• Supply: Total amount each supplier can provide.
• Demand: Total amount each destination wants.

Balancing supply and demand efficiently is key here.

Connecting Supply and Demand

Supply and demand are crucial factors in the transportation problem. Supply refers to the available resources at the origins such as factories or farms. Demand, on the other hand, indicates the needs at the destinations like stores or restaurants.
Both aspects must be considered and compared to determine the approach to take.
In a balanced transportation problem, supply equals demand. This means that every unit available can be perfectly allocated to meet the need. If these do not match, the problem is either unbalanced with excess supply or excess demand, requiring adjustments.

Efficient Resource Allocation

Resource allocation in transportation problems is about distributing the available resources to meet the demand with minimal cost. This requires understanding both the supply and demand sides.
To allocate resources efficiently, you must consider both:

• The capacity of each supplier, specifying how much they can produce or send.
• The requirements of each destination, indicating how much they need to receive.

Balancing these elements helps ensure that resources are used wisely. The objective is to reach a state where costs are minimized and resources are neither wasted nor lacking.

Using Optimization Techniques

Optimization techniques are the tools used to solve transportation problems effectively. These methods help in finding the Optimal Solution by minimizing costs.
One popular technique is the "Simplex Method." It iterates through potential solutions to find the most cost-effective one. Another technique is the "Modified Distribution Method (MODI)," which improves initial feasible solutions to get closer to optimal solutions.
Both methods involve:

• Formulating the transportation problem in a quantitative manner.
• Iteratively moving towards cost minimization.

By using these methods, you can ensure resources are distributed most effectively, aligning with overall supply and demand.